MHD free convection with Joule heating and entropy generation inside an H-shaped hollow structure

In this research, a free convective flow of water inside an H-shaped hollow structure which is subjected to the existence of an exterior magnetic field and Joule heating is computationally investigated. The structure's right and left upright surfaces are maintained at invariant ambient thermal condition, while the top and bottom-most surfaces of the structure are in adiabatic condition. The rest of the inner walls are heated isothermally. Computational analysis is carried out for different configurations of the chamber by solving Navier-Stokes and heat energy equations via the finite element approach. Parametric computations are conducted by varying Hartmann numbers (0 ≤ Ha ≤ 20), Rayleigh numbers (103 ≤ Ra ≤ 106), width of the vertical sections (0.2 ≤ d/L ≤ 0.4, where L denotes the structure's reference dimension), and thickness of the horizontal middle section (0.2 ≤ t/L ≤ 0.4). To find out the impact of the governing parameters on thermal performance for different configurations, the mean Nusselt number along the hot walls, mean temperature of fluid, overall entropy generation, and thermal performance criterion are assessed. In addition, the variations in fluid motion and thermal patterns are reported in terms of streamlines, isotherms, and heatlines. With a larger mean Nusselt number and smaller thermal performance criterion, better heat transmission performance is found for thicker horizontal middle section and wider vertical sections. The maximum reduction in thermal performance criterion is found to be 87.8 % for increasing the width of the vertical sections. However, in the cases of Ha and d/L, there is an interesting transition in Nusselt number noticed for different Rayleigh numbers.

Assessment of thermohydraulic performance and entropy generation in an evacuated tube solar collector employing pure water and nanofluids as working fluids

This study conducts a numerical comparison of the thermal performance of three distinct working fluids (pure water, TiO2, and SiO2 water-based nanofluids) within an evacuated tube solar collector using Computational Fluid Dynamics. The study evaluates thermohydraulic performance alongside global and local entropy generation rates, while considering variations in solar radiation values and inlet mass flow rates. Results indicate that nanofluids demonstrate superior performance under low solar radiation, exhibiting higher outlet temperatures, velocities, thermal efficiency, and exergy efficiency compared to pure water. However, at the higher solar radiation level, the efficiency of SiO2 water-based nanofluid diminishes due to its impact on specific heat. Furthermore, the entropy generation analysis reveals significant reductions with TiO2 water-based nanofluid in all the phenomena considered (up to 79 %). The SiO2 nanofluid performance aligns closely with pure water under high radiation value. This investigation offers valuable insights into the utilization of nanofluids in solar collectors across diverse operating conditions, emphasizing their pivotal role in enhancing overall performance.

Numerical entropy analysis of MHD electro-osmotic flow of peristaltic movement in a nanofluid

The present study investigates the MHD electro-osmotic flow of entropy generation analysis for peristaltic movement in a nanofluid with temperature-dependent viscosity. Long wavelengths, i.e., The magnitude of a wave's energy corresponds directly to its frequency while being inversely related to its wavelength in terms of velocity, temperature, and concentration, govern and confine the flow stream in the laminar region. Ohmic heating and hall effects are also included. Graphs are used to obtain and examine numerical solutions for axial velocity, temperature, concentration, Bejan number, and entropy generation. The effects of this research can help to improve pumping and gastrointestinal movements in different engineering devices. Debye-Huckel and lubrication approximations are studied to access the Boltzmann distribution of electric potential across an electric double layer. The investigations of an existing model are important in illuminating the microfluidics machinery used at the micro level for various transport phenomena in which fluids as well as particles are transported together. The current study has many applications and can be further extended to a three-dimensional profile with appropriate modifications and assumptions. When studying entropy generation, it is essential to examine the irreversible factors, while also taking into account the velocity and thermal slip conditions at channel boundaries. Moreover, the concept of entropy generation holds significant importance in comprehending various biological phenomena. Hence, the current research holds promising implications for both industrial and medical fields. The entropy generation is minimum at left wall of the channel for negative values of Helmholtz-Smoluchowski velocity.

Numerical investigation of effect of geometric parameters on performance of rotational hydrodynamic cavitation reactor

The objective of this paper is to discuss the influence of geometric parameters on the performance of the rotational hydrodynamic cavitation reactor (RHCR) using numerical method. The novel RHCR is implemented by modifying a centrifugal impeller into a new one using the annular slit constriction (ASC) with circumferentially distributed blind holes. The cavitation intensity and cavitation generation rate are selected to evaluate the cavitation performance, the head is used to assess conveying performance, and the entropy generation theory is used to evaluate the energy loss in the impeller. The effect of the axial width, radial length and radial position of the ASC on the cavitating flow of the RHCR is investigated by CFD method. The results indicate that three patterns of cavitation are induced in the RHCR, including separation cavitation, vortex cavitation and shear cavitation. The axial width, radial length and radial position of the ASC are the important geometric parameter that affect the performance of the RHCR. A small width is superior to a large width in terms of cavitation performance, although the conveying performance suffers as a result. The energy loss in the impeller initially increases and then decreases as the width decreases. Both a reduction in radial length and radial position leads to higher cavitation and conveying capacity, accompanying slight increase in energy loss. Compared to the original model, the RHCR with an axial width of 3 mm, a radial length of 17 mm, and a radial position of 0.541 achieves the highest performance.

Thermodynamic analysis of mono and hybrid nanofluid effect on the photovoltaic-thermal system performance: A comparative study

The energy and exergy efficiency of a photovoltaic thermal (PV/T) system at various volume fractions is investigated with mono TiO2 nanofluid and new hybrid TiO2-Fe2O3 nanofluid. Serpentine tubes soldered on an absorbing plate attached to the rear of the PV module have been proposed to evaluate the effect of nanofluids on the PV/T temperature reduction, energy produced, and exergy losses. The study compared energy and exergy with previous studies and delivered an economic analysis to confirm the feasibility of applying nanofluids. The results indicated that using TiO2-Fe2O3 nanofluid reduced the PV cell's temperature by 42.19% compared to water, TiO2 nanofluid, which increased the electrical power by 74.5% and 46.22% when cooling by mono and hybrid nanofluid at 0.3 vol%. The PV/T system's maximum thermal and electrical efficiency recorded with mono and hybrid nanofluids was 34.6%, 8.44%, 47.2%, and 12.62%, respectively. Dispersion of hybrid nanocomposite in DI water has enhanced the Nu number and HTC by 42.72% and 23% higher than mono nanofluid, which improved the exergy efficiency of the PV/T system by 14.89%. A better payback period was achieved with a hybrid nanofluid by 54 days with reduced exergy losses by 45.5% and entropy generation by 86.29%.

Biomedical aspects of entropy generation on MHD flow of TiO2-Ag/blood hybrid nanofluid in a porous cylinder

This study aims to analyze the heat transfer behavior of the magnetohydrodynamic blood-based Casson hybrid nanofluid in the occurrence of a non-Fourier heat flux model and linear thermal radiation over a horizontal porous stretching cylinder with potential applications in biomedical engineering. The present investigation utilised titanium dioxide and silver nanoparticles, which exhibit considerable potential in the realm of cancer therapy. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. Suitable self-similarity variables are employed to transform the nonlinear mathematical equations such as velocity, temperature, skin friction coefficient, and heat transfer rate, which are computed via homotopy perturbation method (HPM). HPM computations have been executed to solve the influences of various parameters such as porosity parameter ( K = 0.0 , 1.0 , 2.0 ) , Curvature parameter ( α = 0.0 , 1.0 , 3.0 , 5.0 ) , Casson parameter ( β = 0.0 , 0.5 , 1.5 ) , inertia coefficient ( F r = 0.5 , 1.5 , 2.5 ) , thermal relaxation parameter ( δ ∗ = 0.0 , 0.5 , 1.0 ) , radiation ( R d = 0.0 , 0.5 , 1.0 ) , Eckert number ( E c = 0.0 , 0.1 , 0.2 ) , Brinkman number ( B r = 0.5 , 1.0 , 1.5 ) and temperature difference parameter ( α 1 = 0.0 , 0.5 , 1.0 ) . The comparison using the homotopy perturbation technique produces a more accurate and reliable consequence than the numerical method (Runge-Kutta method). The higher values of the Casson and Curvature parameters decrease the velocity profile. The temperature profile of M = 1 and M = 0 increases with improving values of the thermal relaxation parameter. Entropy generation rises to enhance Brinkman number values, whereas Bejan number exhibits the reverse influence. Improving the value of the heat source parameter declines the Nusselt number.

Entropy optimized flow of Sutterby nanomaterial subject to porous medium: Buongiorno nanofluid model

Owing to enhanced thermal impact of nanomaterials, different applications are suggested in engineering and industrial systems like heat transfer devices, energy generation, extrusion processes, engine cooling, thermal systems, heat exchanger, chemical processes, manufacturing systems, hybrid-powered plants etc. The current communication concerns the optimized flow of Sutterby nanofluid due to stretched surface in view of different thermal sources. The investigation is supported with the applications of external heat source, magnetic force and radiative phenomenon. The irreversibility investigation is deliberated with implementation of thermodynamics second law. The thermophoresis and random movement characteristics are also studied. Additionally, first order binary reaction is also examined. The nonlinear system of the governing problem is obtained which are numerically computed by s method. The physical aspects of prominent flow parameters are attributed graphically. Further, the analysis for entropy generation and Bejan number is focused. It is observed that the velocity profile increases due to Reynolds number and Deborah number. Larger Schmidt number reduces the concentration distribution. Further, the entropy generation is improved against Reynolds number and Brinkman parameter.

Enhancement in the efficiency of heat recovery in a Williamson hybrid nanofluid over a vertically thin needle with entropy generation

The purpose of the present research is to conduct an examination of entropy generation in a 2D magneto Williamson hybrid nanofluid flow that contains cobalt ferrite and titanium oxide nanoparticles and undergoes surface-catalyzed reactions through a thin vertical needle. The consequences of joule heating and viscous dissipation are considered to elaborate the features of heat transport. Further, the influence of thermal stratification, thermal radiation, and homogeneous-heterogeneous reaction is also taken into account. Through the application of appropriate similarity variables, the dimensionless system of coupled ordinary differential equations is achieved. The coupled system of equations is numerically solved by the usage of the bvp4c technique in the MATLAB algorithm. The current investigation also compared the existing outcomes with the available literature, which shows great harmony between the two. The consequences of the physical parameters are discussed graphically and with numerical data. It is worth noting that larger values of homogeneous reaction strength and the surface-catalyzed parameter diminish the concentration field. Further, the velocity distribution and their related momentum boundary layer thickness, diminishes with the enlargement of the Weissenberg parameter.

How does exercise affect energy metabolism? An in silico approach for cardiac muscle

We explored an in silico model of muscle energy metabolism and demonstrated its theoretical plausibility. Results indicate that energy metabolism triggered by activation can capture the muscle condition, rest, or exercise, and can respond accordingly adjusting the rates of their respiration and energy utilization for efficient use of the nutrients. Our study demonstrated during exercise higher respiratory activity causes a substantial increase in exergy release with an increase in exergy destruction, and entropy generation rate. The thermodynamic analysis showed that at the resting state when the exergy destruction rate was 0.66 W/kg and the respiratory metabolism energetic efficiency was 36% and exergetic efficiency was 32%; whereas, when the exergy destroyed was 1.24 W/kg, the energetic efficiency was 58% and exergetic efficiency was 50% during exercise. The efficiency results suggest the ability of the system to regulate itself in response to higher work demand and become more efficient in terms of converting energy coming from nutrients to useable energy when the circulating medium has sufficient energy precursor.

Mixed convection and activation energy impacts on MHD bioconvective flow of nanofluid with irreversibility assessment

In this communication irreversibility minimization in bio convective Walter's-B nanofluid flow by stretching sheet is studied. Suspended nanoparticles in Walter's-B fluid are stabilized by utilizing microorganisms. Total irreversibility is obtained via thermodynamics second law. The influences of applied magnetic field, radiation, Joule heating and activation energy are accounted in momentum, temperature and concentration equations. Furthermore thermophoresis and Brownian movement impacts are also accounted in concentration and temperature expressions. The flow governing dimensional equations are altered into dimensionless ones adopting transformation procedure. Homotopy Analysis Method (HAM) code in Mathematica is implemented to get the convergent series solution. The influences of important flow variables on temperature, velocity, motile density, irreversibility, mass concentration, Bejan number and physical quantities are analyzed graphically. The obtained results revel that the velocity profile decreases for escalating magnetic parameter and Forchheimer number. Entropy generation is increased for higher Brinkman variable while Bejan number declines versus Brinkman variable. The important observations are given at the end.

Thermodynamic irreversibility effects with Marangoni convection for third grade nanofluid flow

In this study, an analysis was performed to investigate the thermal and mass transport of radiative flow of a third-grade nanofluid with magnetohydrodynamic. The analysis concerns two-dimensional flow around an infinite disk. Heat transport is studied via heat generation/absorption, thermal radiation and Joule heating. Chemical reaction with activation energy is also considered. The nanofluid characteristics, including Brownian motion and thermophoretic diffusion, are explored via the Buongiorno model. Entropy analysis is also conducted. Moreover, the surface tension is assumed to be a linear function of concentration and temperature. Through adequate dimensionless variables, governed PDEs are non-dimensionlized and then tackled by ND-solve (a numerical method in Mathematica) for solutions purposes. Entropy generation, concentration, velocity, Bejan number and temperature are plotted as functions of the involved physical parameters. It is noticed that higher Marangoni number intensify velocity however it causes a decrease in the temperature. Entropy rate and Bejan number boost for large value of diffusion parameter.

Analyses of entropy generation in micropolar liquid using overlapping multi-domain spectral quasilinearization method

In this article, entropy generation on Micropolar fluid through a perpendicular hot sheet is studied. The governing equations of the mathematical model of this article will transfer to non-dimensional system of ordinary differential equations by similarity transformations. This system of non-dimensional ODEs will be solved by a newly developed spectral collocation method. The dimensionless mathematical calculations are handled through utilizing the spectral quasilinearization method (SQLM) along with the concept of overlapping grids. Condition numbers, residual error and solution error norms estimations are provided to appraise accuracy, convergence and the stability of this numerical method. Using the overlapping multi-domain (M-D) approach has been found to produce most accurate, stable and convergent solutions when contrasted to the single-domain (S-D) technique. The outcomes are displayed and depicted graphically and through tabular forms. The effects of different non-dimensional parameters on flow, temperatures, concentration and entropy generation are studied. The accuracy of the numerical method has been checked through comparison with previously published articles and error analyses test.

Impacts of entropy generation in radiative peristaltic flow of variable viscosity nanomaterial

Current analysis highlights the aspects of different nanoparticles in peristalsis with entropy generation. Mathematical equations of considered problem are modelled via conservation laws for mass, momentum and energy. Such equations contain variable viscosity, nonlinear thermal radiation, viscous dissipation, heat generation/absorption and mixed convection aspects. Boundary conditions comprise the second order velocity and first order thermal slip effects. Entropy expression is obtained by utilization thermodynamics. Simplified and dimensionless forms of the considered conservative laws are obtained through lubrication technique. Resulting system of equations subject to the considered boundary conditions is solved numerically via built-in shooting procedure in Mathematica. Such numerical procedure is very suitable to obtain numerical results directly and fastly in the form of graphs. Further all the considered flow quantities are discussed graphically for the significant parameters of interest in detail. Both velocity and temperature are decreasing against large volume fraction parameter. Increasing temperature dependent viscosity effects decrease the entropy and enhance the Bejan number.

Irreversibility analysis of an unsteady micropolar CNT-blood nanofluid flow through a squeezing channel with activation energy-Application in drug delivery

BACKGROUND AND OBJECTIVE

Due to the low toxicity, unique physiochemical properties, and appropriate surface modifications, Carbon Nanotubes (CNTs) are used as target carriers in drug delivery systems. In the present problem, we have considered both single-walled and multi-walled CNTs to study the impact of irreversibility on the micropolar nanofluid flow through a squeezing channel with the base fluid blood. The blood is considered a micropolar fluid in the presence of different blood cells and their rotational nature. Further, blood is influenced by the external magnetic field parallel to the microrotation along with viscous and Joule dissipations.

METHOD

Highly coupled and nonlinear partial differential equations are solved with Homotopy Analysis Method (HAM) after simplified equations using similarity transformation. Further, we have concluded the minimum squared residual errors to show the method's accuracy. A comparison made with the existing literature and shows a good agreement.

RESULTS

The angular velocity of the fluid particles is enhanced by increasing the squeezing number. In the case of the squeezing, volume fraction has improved the viscous drag and is found high for MWCNT embedded nanofluid. The heat transfer rate is higher for the MWCNT embedded nanofluid than the SWCNT embedded nanofluid. A descent found in entropy generation boosts up with the Brinkman parameter while opposite phenomena appear for radiation and Hartman number and vortex viscosity. Both Bejan number and entropy generation profiles are restricted with an increase in vortex viscosity.

CONCLUSION

SWCNTs are showed to be more effective and efficient than the MWCNTs in elevating velocity, temperature and irreversibility of the system. Outcomes of this problem will help to understand the implementation of the drug carrier and irreversibility phenomena during drug delivery.

Effect of Joule heating and entropy generation on multi-slip condition of peristaltic flow of Casson nanofluid in an asymmetric channel

In the present investigation, the effect of multi-slip condition on peristaltic flow through asymmetric channel with Joule heating effect is considered. We also considered the incompressible non-Newtonian Casson nanofluid model for blood, which is electrically conducting. Second law of thermodynamics is used to examine the entropy generation. Multi-slip condition is used at the boundary of the wall and the analysis is also restricted under the low Reynolds number and long wavelength assumption. The governing equations were transformed into a non-dimensional form by using suitable terms. The reduced non-dimensional highly nonlinear partial differential equations are solved by using the Homotopy Perturbation Sumudu transformation method (HPSTM). The influence of different physical parameters on dimensionless velocity, pressure gradient, temperature, concentration and nanoparticle is graphically presented. From the results, one can understand that the Joule heating effect controls the heat transfer in the system and as the magnetic parameter is increased, there will be decay in the velocity of fluid. The outcomes of the present investigation can be applicable in examining the chyme motion in the gastrointestinal tract and controlling the blood flow during surgery. Present study shows an excellent agreement with the previously available studies in the limiting case.

Irreversibility process analysis for SiO2-MoS2/water-based flow over a rotating and stretching cylinder

Entropy is the measure of the amount of energy in any physical system that is not accessible for the useful work, which causes a decrease in a system's thermodynamic efficiency. The idea of entropy generation analysis plays a vital role in characterizing the evolution of thermal processes and minimizing the impending loss of available mechanical power in thermo-fluid systems from an analytical perspective. It has a wide range of applications in biological, information, and engineering systems, such as transportation, telecommunication, and rate processes. The analysis of the entropy generation of axisymmetric magnetohydrodynamic hybrid nanofluid (SiO2-MoS2)/water flow induced by rotating and stretching cylinder in the presence of heat radiation, ohmic heating, and the magnetic field is focus of this study. Thermal energy transport of hybrid nanofluids is performed by applying the Maxwell model. Heat transport is carried out by using convective boundary condition. The dimensionless ordinary differential equations are acquired by similarity transformations. The numerical solution for these differential equations is obtained by the bvp4c program in MATLAB. A comparison between nanofluid and hybrid nanofluid is made for flow field, temperature, and entropy generation. Comparison of nanofluid flow with hybrid nanofluid flow exhibits a higher rate of heat transmission, while entropy generation exhibits the opposite behavior. It is observed that the flow and heat distribution increase as the solid volume fraction's value grows. An increase in entropy is indicated by augmentation in the Brinkman number and temperature ratio parameter, but the Bejan number shows a declining trend. Furthermore, outcomes of the Nusselt number for hybrid nanofluid and nanofluid are calculated for various parameters. It is noticed that the Nusselt number is reduced for enlarging the magnetic field and Eckert number. The axial and azimuthal wall stress parameters are declined by augmenting the Reynolds number.

Entropy generation in nanofluid flow due to double diffusive MHD mixed convection

This work is concerned with the numerical study of laminar, steady MHD mixed convection flow, and entropy generation analysis of Al2O3-water nanofluid flowing in a lid-driven trapezoidal enclosure. The aspect ratio of the cavity is taken very small. The cavity is differentially heated to study the fluid flow, heat, and mass transfer rate. The adiabatic upper wall of the enclosure is allowed to move with a constant velocity along the positive x-direction. The second-order finite difference approximation is employed to discretize the governing partial differential equations, and a stream-function velocity formulation is used to solve the coupled non-linear partial differential equations numerically. The simulated results are plotted graphically through streamlines, isotherms, entropy generation, Nusselt number, and Sherwood number. The computations indicate that the average Nusselt number and average Sherwood number are decreasing functions of Hartmann number, aspect ratio, and nanoparticle volume fraction. Significant changes in streamlines, temperature and concentration contours for high Richardson number are observed.

Modeling and interpretation of peristaltic transport in single wall carbon nanotube flow with entropy optimization and Newtonian heating

Due to some special characteristics like the effective thermal conductivities, appropriate mechanical features, and superior electrical properties, carbon nanostructures have been known as the proper materials to reach the desired characteristics of fluids. In the recent past fluid flows through peristaltic mechanism subject to carbon nanotubes are utilized to handle the overcome of industrial and physiological materials thermal properties. Due to rich thermal characteristics nanotubes are used into basic industrial materials to improve the required ability of thermal properties of these industrial materials. Thus various kinds of nanoparticles e.g. aluminum, copper, zinc oxides and carbon nanotubes are significantly utilized to increase the thermal abilities of base liquids. Because of the several significant special qualities such as improved thermal conductivities, applicable mechanical structures, and rich electrical properties, CNTs have been acknowledged as the accurate tools to reach the wanted features of fluids, due to such abilities CNTs are high demanding research topic in all domains. Keeping such efficiencies of CNTs in notice, this analysis is prepared for peristalsis of carbon nanotubes through non-uniform asymmetric channel. Flow mechanism is modeled in view of conservation principles under desired assumptions likely porous medium, non-linear mixed convection, heat generation absorption and Newtonian heating. Rate of total entropy is evaluated by using thermodynamics second law. Lubrication approach utilized here to attain the simplified form of the complex flow expressions. The pressure gradient, velocity along axial direction, temperature, effective heat transfer rate and entropy expressions subject to boundary conditions are evaluated numerically via built-in-Shooting procedure. Furthermore these numerical results are used to sketch the variations of all the above mentioned quantities against the pertinent parameters of interest. According to physical discussion temperature reduces for heat absorption case and enhances for heat generation case. Impact of Prandtl number on entropy indicates that entropy is minimum due to less fluid friction (i.e. Prandtl number less than 1).

Fully developed entropy optimized second order velocity slip MHD nanofluid flow with activation energy

Hydromagnetic second order velocity slip flow of viscous material with nonlinear mixed convection towards a stretched rotating disk is numerically examined here. Important slip mechanism of Buongiorno's nanofluid model i.e., Brownian motion and thermophoretic diffusion is incorporated in the mathematical modeling. Heat transport aspects are examined via Joule heating, thermal radiation and dissipation. Convective conditions at the stretchable surface of disk is implemented for the heat transport analysis. Chemical reaction subject to activation energy is also considered. Through appropriate transformations and shooting method the outcomes are computed and demonstrated graphically. The flow field, temperature, surface drag force, concentration and Nusselt number are deliberated subject to pertinent parameters. Total entropy rate is obtained. The outcomes show that magnetic field significantly affects the flow field as well as entropy rate.

On the evaluation of stratification based entropy optimized hydromagnetic flow featuring dissipation aspect and Robin conditions

BACKGROUND AND OBJECTIVE

The scrutiny of nonlinear convected flow aspect has continuously appealed researchers attention because of its ample demands in processes like heat exchangers, building insulation, crystal growth, insulation of nuclear reactor, food processing, solar energy and electronic element chilling etc. Taking into consideration the aforesaid utilizations, we modeled differential type (second-grade) nanoliquid considering non-linear mixed convection. The considered differential type nonlinear model elaborates viscoelasticity (elastic and viscous) characteristics. Furthermore the thermal systems emphases on transportation of heat and irreversibility reduction. Especially, evaluating the systems via thermodynamic second relation is essential with the purpose of finding a standard communication between power input prerequisite and heat transference augmentation.

METHOD

Formulated non-dimensional problem is non-linear subject to the assumptions (i.e., Non-linear mixed convection, magnetic field, viscous dissipation, double stratification, Joule heating and convective conditions). Analytic simulations for modeled non-linear systems is not possible. Hence we considered bvp4c scheme for non-linear analysis.

CONCLUSIONS

Velocity [Formula: see text] of second grade (non-Newtonian) fluid intensifies for larger estimations of R* and λ* whereas it dwindles for M. Temperature of nanoliquid deteriorates with S₁ while (θ(η)) rises against Ec. Entropy generation (EG) and (BN) (Bejan number) significantly affected by physical parameters M, α₂ and Br.

Entropy generation effect of a buoyancy force on hydromagnetic heat generating couple stress fluid through a porous medium with isothermal boundaries

This investigation addresses the influence of a buoyancy force on the flow of a couple stress hydromagnetic heat generating fluid across a porous channel with isothermal boundaries. The analytical formulations for the momentum and energy equations are derived to seek the solutions for the rate of fluid momentum, heat transfer and the rate of entropy generation with the use of a well known and efficient series solution of Adomian decomposition method (ADM). The findings are compared with earlier acquired findings for validation and hereby showed the speedy convergence of the series solution. The results showed the substantial influence of inward warmth inside the stream and buoyancy force on the motion and thermal energy of the flow system. Also, the activities of entropy generation generally occur maximally at the centreline of the flow stream with significant reduction with respect to buoyancy force and magnetic field strength.

Magnetohydrodynamics (MHD) radiated nanomaterial viscous material flow by a curved surface with second order slip and entropy generation

BACKGROUND

Magnetohydrodynamics or hydro-magnetics (MHD) is the study of dynamics in the presence of magnetic characteristics and impact of electrically conducting liquids which has a significant applications in engineering and biomedical sciences. Liquid metals, plasma, electrolytes and salt water are the examples of such magneto-fluids. MHD liquid flow in various geometries significant to engineering sciences is an interesting and noteworthy scientific area because of applications. The above applications of magnetohydrodynamics insist the engineers and analyst to develop new mathematical modeling in the field of fluid mechanics. Therefore, we considered electrical conducting viscous fluid flow over a curved surface with second order slip. The Buongiorno model is utilized in the modeling of flow problem with thermophoretic and Brownian diffusions. The effects of viscous dissipation, thermal radiation and Joule heating (Ohmic heating) is used in the modeling of energy equation. Homogeneous-heterogeneous reactions are further considered. The energy equation is modeled.

METHOD

The nonlinear ODE's are obtained through utilization of appropriate transformations and numerical results are computed via NDSolve MATHEMATICA.

RESULTS

Velocity field is decreasing function of first order slip parameter. Both Bejan number and entropy generation is upsurged versus heterogeneous reaction parameter.

Entropy optimized MHD nanomaterial flow subject to variable thicked surface

Here we investigate the irreversibility aspects in magnetohydrodynamics flow of viscous nanofluid by a variable thicked surface. Viscous dissipation, Joule heating and heat generation/absorption in energy expression is considered. Behavior of Brownian diffusion and thermophoresis are also discussed. The nanoliquid is considered electrical conducting under the behavior of magnetic field exerted transverse to the sheet. Using similarity variables the nonlinear PDEs are altered to ordinary one. The obtained system are computed through Newton built in shooting method. Significant behavior of various involving parameters on entropy generation rate, velocity, concentration, Bejan number and temperature are examined. Gradient of velocity and heat transfer rate are numerically computed through tabulated form. Velocity field is augmented versus power index (n). Temperature and velocity profiles have opposite characteristics for larger approximation of Hartmann number. Concentration profile has similar impact against Brownian diffusion variable and Lewis number. Entropy optimization is boost up via rising values of Brinkman and Hartmann numbers. Bejan number is declined for increasing value of Hartmann number.

Entropy generation analysis of different solar thermal systems

The entropy generation analysis is an approach to optimize the performance of different thermal systems by investigating the related irreversibilities of the system. This paper provides a concise review of the entropy generation analysis performed for different solar thermal energy systems including solar collectors, solar heaters, solar heat exchangers, and solar stills. The mathematical formulation and the equations for calculating the entropy generation are briefly presented. Moreover, main passive techniques including the usage of nanofluids, porous materials, and inserts which are used to improve the efficiency of different solar systems are discussed. It is shown that using entropy generation minimization method is an efficient tool to find the optimal design of solar systems. The current review aims to motivate researchers in the field of solar energy for using entropy generation analysis to reduce the lost work and consequently improving the system performance.

Fully developed Darcy-Forchheimer mixed convective flow over a curved surface with activation energy and entropy generation

BACKGROUND

Mixed convection (forced+natural convection) is frequently observed in exceptionally high output devices where the forced convection isn't sufficient to dissipate all of the heat essential. At this point, consolidating natural convection with forced convection will frequently convey the ideal outcomes. Nuclear reactor technology and a few features of electronic cooling are the examples of these processes. Mixed convection problems are categorized by Richardson number (Ri), which is the ratio of Grashof number (for natural convection) and Reynolds number (for forced convection). For buoyancy or mixed convection the relative effect can be addressed by Richardson number. Typically, the natural convection is negligible when Richardson number is less than 0.1 (Ri < 0.1), forced convection is negligible when Richardson number is greater than 10 (Ri > 10) and neither is negligible when (0.1 < Ri < 10). It might be noticed that generally the forced convection is large comparative with natural convection except in case of remarkably low forced flow velocities. The current work gives significant insights regarding dissipative mixed convective Darcy-Forchheimer flow with entropy generation over a stretched curved surface. The energy equation is developed with respect to nonlinear radiation, dissipation and Ohmic heating (Joule heating). Binary reaction via activation energy is accounted.

METHOD

Curvilinear transformations are utilized to change the nonlinear PDE's into ordinary ones. Computational outcomes are obtained via NDSolve MATHEMATICA. The results are computed and discussed graphically.

RESULTS

Velocity decays for Forchheimer number. Entropy generation enhances for diffusion parameter and chemical reaction parameter. Concentration profile reduces chemical reaction parameter and enhances for activation parameter.

Numerical solution of MHD flow of power law fluid subject to convective boundary conditions and entropy generation

BACKGROUND

The application of entropy optimization has consistently incorporated in traditional and industrial fields. The system is permanently sustainable, usually a final ideal structure may not exist in general, as common evolution shows trends in a long time. The measurement of the entropy generation related to heat transport can be proportional to temperature difference. The minimization of entropy generation through various parameters is our main purpose in this research article. Therefore, here we have discussed 2D flow of non-Newtonian liquid over a stretched surface with entropy optimization. Convective boundary conditions of temperature are implemented in the current flow phenomenon. Furthermore, viscous dissipation has been taken into account.

METHOD

The involved nonlinear differential system has been tackled through ND solve numerical technique (Shooting method).

RESULTS

The key observations are summarized as follows: (i) Velocity grows for larger estimations of power law index of fluid. (ii) Temperature θ˜(ξ) increases for Ec. (iii) Surface drag enhances for higher values of Ha. (iv) The temperature gradient Nu_xRe^-1n+1 is inversely proportional to Ec and Ha. (v) Entropy N_G(ξ) is larger for higher Ec and Ha while the opposite impact is examined for M. (vi) Bejan number Be decreases with Prand M, while it upsurges with Ha and Ec.

Entropy optimized stretching flow based on non-Newtonian radiative nanoliquid under binary chemical reaction

BACKGROUND AND OBJECTIVE

Developed electronic mechanisms frequently deal with defies about thermal management from developed phase of heat diminution or generation of available surface area regarding heat exclusion. Such promising defy can be subjugated either by introducing an optimal geometry for chilling equipments or intensifying heat transportation attributes. Nanoliquid in this perspective executes an extraordinary function to address all such matters. Having such usefulness of entropy in view, we formulated the hydromagnetic non-Newtonian nanoliquid in frames of mixed convection. Nanoliquid model comprises Brownian movement and thermophoretic mechanisms. In addition, the novel mass transportation approach featuring binary chemically reacting species is introduced. Energy expression formulation is developed through dissipation phenomenon. Besides, new conditions for Buongiorno model along with radiating flux are considered.

METHOD

We obtained highly nonlinear structure. The computations of such structure are not easy. Thus we employed bvp4c scheme to tackle the nonlinear structure.

RESULTS

Heat transportation rate boosts subject to higher chemical reaction parameter in comparison to thermophoretic factor and Eckert number. The considered rheological model yields viscous nanoliquid situation when material factors are assumed zero. Entropy owing to habituation of respiring air is more in comparison to its frictional factor and during hefty physical action. Entropy subject to respiring air friction under respiratory region is much higher in comparison to air habituation factor.

CONCLUSION

Velocity rises via higher material parameter for thickening situation while opposing trend is witnessed for thinning nature of liquid. Entropy is meaningfully higher owing to breathing air condition rather than frictional impact towards tract. No doubt, entropy have a feasible association with respiratory thermoplasty which assists to handle asthma.

Electro-magneto flow of nanomaterial with irreversibility

Here we discuss the analysis of irreversibility in electrical magnetohydrodynamic convective flow of nanomaterials over a stretchable surface. Energy equation deliberated through Joule heating, dissipation and heat source/sink. Furthermore features chemical reaction is also considered. Total entropy optimization is calculated. Salient features of thermophoresis effect and random motion of particles are studied. Nonlinear couple equations are converted to ordinary system by using the transformation. The obtained system are elucidated through ND solve technique. Salient features of pertinent variables on entropy optimization, velocity, Bejan number, concentration and temperature are discussed. Nusselt number, gradient of concentration and surface drag force are computationally calculated. Velocity and temperature show opposite behaviors via magnetic parameter. Electric and magnetic field parameters on entropy optimization have opposite results.

Predicting entropy generation in flow of non-Newtonian flow due to a stretching sheet with chemically reactive species

BACKGROUND

We have studied the steady Darcy Forchheimer MHD generalized non-Newtonian flow of an incompressible non-linear stretched surface in the presence chemical reactive species. Darcy Forchheimer effect and chemically reactive species are considered under entropy generation. Entropy generation analysis has been essentially applied in engineering procedure in order to improve the theoretical and mathematical evaluation problems.

METHOD

To approximate the entropy generation rate, the leading nonlinear equations are solved numerically by using Rung Kutta integration technique with shooting method.

RESULTS

Next using the reproduction date, the entropy generation results are discussed by using theoretical and mathematical approaches. The numerical results acquired for different physical mechanism are exposing through graphs and tables.

CONCLUSIONS

The physical effects of nanomaterials, skin friction coefficient, heat transfer, mass transfer and entropy generation have been illustrated for different values of involved parameters such as the Weissenberg number, magnetic field parameter, porous medium parameter, the Darcy parameter, the Lewis number, thermophoresis diffusion, the Brownian motion parameter, chemical reaction parameter and the Prandtl number. The numerical results acquired for different physical mechanism are exposing through graphs and tables.

Eyring-Powell nanofluid flow with nonlinear mixed convection: Entropy generation minimization

BACKGROUND

Entropy is the amount of energy which is lost during any irreversible process. Here our main focus is that how can we reduce this energy loss to enhance the capability of our system. Blood is an example of Eyring-Powell fluid. Many strategies are used to rise the capacity of heat transport. Heat transport can be enhanced by intensifying the materials thermal conductivity through nanoparticles. Thermal conductivity of the material can be enhanced by adding nanoparticles in base fluid. The objective of this work is to discuss entropy generation in MHD Eyring-Powell nanofluid flow. The flow is generated by a linear stretchable surface. Current analysis includes the effects of viscous dissipation, nonlinear mixed convection and Joule heating. Nanoparticles analyzed the consequences of Brownian motion and thermophoresis effects.

METHOD

The boundary layer flow equations are solved for series solutions by applying homotopic technique.

RESULTS AND CONCLUSION

Graphical results of involved quantities like entropy generation, velocity, concentration and thermal fields are presented. Skin friction, Sherwood and Nusselt number are numerically scrutinized.

Entropy optimized dissipative CNTs based flow with probable error and statistical declaration

BACKGROUND

CNTs are categorized subject to their structures i.e., SWCNTs (single wall nanotubes), DWCNTs (double wall nanotubes) and MWCNTs (multi-wall nanotubes). The various structures have distinct characteristics that make the nanotubes suitable for various physical applications. It is due their unique electrical, mechanical and thermal attributes CNTs present thrilling opportunities for mechanical engineering, industrial, scientific research and commercial applications. There is fruitful potential for carbon nanotubes in the composites business and industry. Today, CNTs find utilization in frequent various products, and analyst continue to explore new applications. Currently applications comprise wind turbines, bicycle components, scanning probe microscopes, flat panel displays, marine paints, sensing devices, electronics, batteries with longer lifetime and electrical circuitry etc. Such applications in mind, entropy optimized dissipative CNTs based flow of nanomaterial by a stretched surface. Flow is caused due to stretching phenomenon and studied in 3D coordinates. Both types of CNTs are studied i.e., SWCNTs and MWCNTs. CNTs are considered for nanoparticles and water for continuous phase fluid. Special consideration is given to the analysis of statistical declaration and probable error for skin friction and Nusselt number. Furthermore, entropy rate is calculated. Entropy rate is discussed in the presence of four main irreversibilities i.e., heat transfer, Joule heating, porosity and dissipation.

METHOD

Homotopy technique is utilized to develop the convergence series solutions.

RESULTS

Impacts of sundry variables subject to both SWCNTs (single) and MWCNTs (multi) are graphically discussed. Statistical analysis and probable error for surface drag force and Nusselt number are numerically calculated subject to various flow variables. Numerical results for such engineering quantities are displayed through tables. In addition, comparative analysis for SWCNTs and MWCNTs are presented for the velocity, concentration and thermal fields.

CONCLUSIONS

Results for entropy rate is calculated in the presence of various sundry variable through implementation of second law of thermodynamics. It is examined from the results that velocity decreases for both CNTs via higher magnetic, inertia coefficient and porosity parameters. Secondary velocity i.e., velocity in g-direction boosts up versus rotation parameter while it declines for larger slip parameter for both CNTs. thermal field intensifies for both CNTs via larger heat generation/absorption parameter. Concentration which shows the mass transfer of species increases subject to higher homogeneous parameter and Schmidt number in case of both CNTs. Entropy rate in more for larger magnetic, Reynolds number and slip parameter. Bejan number boosts up for higher Reynold number and slip parameter while it declines for magnetic parameter.

Evaluation of entropy generation in cubic autocatalytic unsteady squeezing flow of nanofluid between two parallel plates

BACKGROUND

Nanomaterials have advanced behaviors that make them possibly beneficial in various applications in mass and heat transports such as engine cooling, pharmaceutical processes, fuel cells, engine cooling and domestic refrigerator etc. Therefore here we deliberated the entropy generation in unsteady magnetohydrodynamic squeezing flow of viscous nanomaterials between two parallel plates. The upper plate is squeezing towards lower plate. The lower plate exhibits porous character. Energy attributes are discussed through heat flux, dissipation and Joule heating. Furthermore the irreversibility analysis with cubic autocatalysis chemical reaction is also accounted.

METHODS

Nonlinear differential systems are converted to ordinary differential system by transformations. For convergent series solution the given system are solved by homotopy analysis method (HAM).

RESULTS

Characteristics of various interesting variables on velocity, Bejan number, concentration, entropy optimization and temperature are deliberated through graphs. Gradient of velocity (C_fx) and Nusselt number (Nu_x) are numerically computed against various physical variables. Entropy generation and Bejan number both quantitatively enhance versus radiation parameter. For larger squeezing parameter the velocity and temperature field are increased.

CONCLUSIONS

The obtained results show that for larger squeezing parameter the velocity field boosts up. Velocity have opposite impact For larger magnetic and porosity parameters. Temperature is decreased for higher values of radiation parameter and Prandtl number. Temperature and concentration have same outcome for thermophoresis parameter. Entropy generation and Bejan number both quantitatively enhance versus radiation parameter, while reverse is hold for Brinkman number.

Irreversibility characterization and investigation of mixed convective reactive flow over a rotating cone

BACKGROUND

Here we investigate the mixed convective unsteady magnetohydrodynamics chemically reactive flow of viscous liquid over a rotating cone. Energy attribution are deliberated in the presence of heat generation/absorption, viscous dissipation and Joule heating. Furthermore Irreversibility analysis with thermo-diffusion (Soret) effect and binary chemical reaction are also considered. Entropy optimization rate is computed with the help of thermodynamics second law.

METHOD

The partial differential expression are reduced to ordinary system by using the suitable transformation. Here we have employed Newton built in shooting technique to get computational results for proposed nonlinear system.

RESULTS

Influences of different interesting parameters on entropy optimization, velocity, Bejan number, concentration and temperature are discussed through graphs. The computational results of skin friction coefficient, gradient of temperature and Sherwood number are examined against different flow parameters through tables. From obtained outcome it is noticed that velocity and temperature have opposite behaviors for magnetic parameter and unsteadiness parameter. Concentration shows the opposite effect for Soret number and unsteadiness parameter. Bejan number and entropy generation rate hold opposite via larger Brinkman number, while have similar impact of temperature difference parameters. The assertion of recent work is established by comparison with previous published literature are discussed in tabulated form and found an excellent agreement.

Entropy optimization analysis in MHD nanomaterials (TiO2-GO) flow with homogeneous and heterogeneous reactions

BACKGROUND

Nanomaterials have higher inspiration in the growth of pioneering heat transportation fluids and good efforts were made in this field during the recent year. Nowadays numerous scientists and researchers have focused their struggle on nanomaterials study. Nanoliquids have advanced properties which make them efficient in various applications including engine cooling, hybrid-power engine, pharmaceutical processes, refrigerator and vehicle thermal management etc. Therefore such implication in mind the entropy optimization in magnetohydrodynamic nanomaterials (TiO₂ - GO) flow between two stretchable rotating disks is discussed here. Energy expression subject to Joule heating, thermal radiation and viscous dissipation is modeled. Entropy optimization rate is based upon thermodynamic second law. Here titanium dioxide (TiO₂) and graphene oxide (GO) and water (H₂O) are used as nanoliquids. Homogeneous and heterogeneous reactions have been accounted.

METHODS

Transformation process reduced nonlinear PDE's to ordinary differential systems. Formulated systems are solved due to implementation of Newton built in shooting method.

RESULTS

Salient behavior of influential variables on velocity, entropy optimization, temperature, Bejan number and concentration graphically illustrated for (TiO₂ and GO). Surface drag force and gradient of temperature ((C_f1, C_f2) and (Nu_x1, Nu_x2)) are numerically computed for various interesting parameters at lower and upper disks respectively. Axial and radial velocities components boost up for larger (Re) but opposite is hold for tangential velocity. Entropy optimization and temperature are increased for higher Brinkman number (Br).

CONCLUSIONS

A significant augmentation occurs in radial and axial velocities (f'(ξ) and f(ξ)) versus stretching parameter, while opposite is hold for tangential velocity (g(ξ)). For larger values of Reynold and Brinkman numbers the temperature increases. Temperature and entropy optimization have opposite effect for radiation parameter. Concentration has similar results for Reynold and Schmidt numbers. Entropy optimization and Bejan number for radiation parameter have similar outcome. Bejan number decays for Brinkman number.

Entropy optimization in CNTs based nanomaterial flow induced by rotating disks: A study on the accuracy of statistical declaration and probable error

BACKGROUND

CNTs (Carbon nanotubes) being allotropes of carbon, made of graphene and diameters of single and multi-walls carbon nanotubes are typically 0.8 to 2 nm and 5 to 20 mn, although diameter of MWCNTs can exceed 100 nm. Carbon nanotubes lengths range from less than 100 nm to 0.5 m. Their impressive structural, electronic and mechanical attributes subject to their small size and mass, their high electrical and thermal conductivities, and their strong mechanical potency. CNTs based materials are successfully applied in medicine and pharmacy subject to their huge surface area that is proficient of conjugating or adsorbing with a wide variety of genes, drugs, antibodies, vaccines and biosensors etc. Therefore, we have presented a theoretical study about mathematical modeling of CNTs based viscous material flow between two rotating disks. Both types of nanotubes i.e., SWCNTs and MWCNTs are considered. Xue model is used for the mathematical modeling. Fluid flow is due to rotating disks. Main focus here is given to probable error and statistical declaration. Entropy is calculated for both single and multi-walls nanotubes.

METHOD

Nonlinear PDEs are first converted into ODEs and then computed for homotopy convergent solutions.

RESULTS AND CONCLUSION

Statistical declaration and probable error for skin friction and Nusselt number are numerically computed and discussed through Tables. From obtained outcomes it is concluded that magnitude of skin friction increases at both disks surface for higher values of Reynolds number, lower stretching parameter and porosity parameter while it decays for both of disks versus larger rotation parameter. Nusselt number or heat transfer rate also enhances at both disks in the presence of radiation and Reynolds number while it decays against Eckert number.

Transportation of entropy optimization in radiated chemically dissipative flow of Prandtl-Eyring nanofluid with activation energy

BACKGROUND

There are frequent strategies to enhance the efficiency of heat transport. Some strategies are employed of extended surfaces, utilization of vibration to the heat transport surfaces, and use of small scale channels. Efficiency of heat transport can also be enhanced by intensifying the thermal conductivity of working material. Engine oil, water and ethylene glycol are frequently utilized for heat transport liquids having comparatively low thermal conductivities then solids. Thermal conductivity of solids can be employed to improve the thermal conductivity of fluid through addition of nano or micro type solid particles to that liquid. The viability of usage of such materials with sizes 2 µm or millimeters was recently scrutinized by numerous engineers and analyst. In this communication, we aim to analyze flow of non-Newtonian nanomaterial (Prandtl-Eyring nanofluid). Features of nanofluid discussed with Brownian and thermophoresis diffusion. Entropy generation, thermal radiation, dissipation, activation energy, Joule heating and radiative heat flux is discussed.

METHOD

Homotopic convergent solutions are developed by using OHAM. Governing nonlinear equations are developed.

RESULTS AND CONCLUSION

Fluid variable has opposite behavior on temperature and velocity. For larger thermophoresis parameter, temperature and concentration are increased. Concentration is reduced by improving Brownian motion parameter while temperature increases. Entropy generation improves with larger fluid parameter and Brinkman number, while Bejan number has opposite effect.

Investigation of physical aspects of cubic autocatalytic chemically reactive flow of second grade nanomaterial with entropy optimization

BACKGROUND

Nanofluids have innovative characteristics that make them potentially beneficial in numerous applications in heat and mass transports like fuel cells, hybrid-powered engines, microelectronics, pharmaceutical processes, domestic refrigerator, engine cooling, heat exchanger, chiller and in boiler flue gas temperature decay. Nanomaterial increased the coefficient of heat transport and thermal performance compared to continuous phase liquid. Having such significance in mind, the nanofluid flow of second grade material over a convectively heated surface is examined here. Nano-fluid is electrically conducting. Energy expression is studied through Joule heating, heat source/sink and dissipation. In addition, thermophoresis and Brownian diffusion are investigated. Physical aspects of entropy optimization in nanomaterials with cubic autocatalysis chemical reaction are accounted. Through second law of thermodynamics the total entropy generation rate is computed.

METHODS

The nonlinear governing PDE's are transformed to ordinary ones through transformations. Total residual error is calculated for momentum, energy and concentration equations using optimal homotopy analysis method (OHAM).

RESULTS

Behaviors of different variables on velocity, Bejan number, concentration, temperature and entropy optimization are examined via graphs. Local skin friction coefficient (C_fx) and gradient of temperature (Nu_x)are examined graphically. Comparison between the recent and previous result is given. Temperature and velocity are enhanced significantly versus (λ₁). Entropy generation rate boosts up for magnetic parameter and Brinkman number.

CONCLUSIONS

The obtained outcomes show that velocity is higher via mixed convective variable. Temperature boosts up in presence of higher magnetic parameter, thermophoretic paraemter, Brinkman number and second grade parameter while Biot number decays. Concentration has increasing behavior via larger Brownian and homogeneous and heterogeneous parameters. Entropy rate and Bejan number have similar impact through diffusion parameters with respect to both homogeneous and heterogeneous reactions variables.

Magneto rotating flow of hybrid nanofluid with entropy generation

BACKGROUND

Study of nanofluids has been enormously increased for the last couple of years. Regardless of some irregularity in the revealed outcomes and lacking consistency, yet the mechanisms of heat transport have been emerged as highly efficient. In the continuation of nanomaterials research, the investigators and analyst have also attempted to utilize hybrid nanomaterial recently, which is designed by suspending unique nanomaterials (nanoparticles) either in mixture or composite structure. The theory of hybrid nanofluids can be further modified for heat transport and pressure drop attributes by trade-off between disadvantages and advantages of individual suspension, ascribed to great aspect ratio, better thermal system and synergistic impact of nanomaterials. Therefore, we have conducted a theoretical attempt on MHD entropy optimized viscous hybrid nanomaterial flow between two parallel plates. The boundaries of plates are fixed with velocity and thermal slip aspects. Chemical reaction with novel aspect of activation energy is accounted. Furthermore, thermal radiation, heat generation and Joule heating are examined.

METHOD

The modeled system is numerically simulated through bvp4c technique.

RESULTS

Behaviors of pertinent variables on the velocity, skin friction, temperature, Nusselt number, entropy generation rate and concentration are presented and discussed through different graphs. Temperature field decays against higher values of Eckert number and thermal slip variable.

CONCLUSIONS

It is noticed that velocity of material particles increase against larger estimations of rotation parameter. Temperature declines versus larger Prandtl and Eckert numbers. Concentration decays when an enhancement is occurred in the Lewis number. Magnitude of surface drag force upsurges for rising values of Prandtl number and radiation parameter. Furthermore, magnitude of Nusselt number enhances through larger Eckert number, magnetic number and Prandtl number.

Theoretical and mathematical analysis of entropy generation in fluid flow subject to aluminum and ethylene glycol nanoparticles

BACKGROUND

Here we have conducted a magnetohydrodynamic (MHD) flow of viscous material with alumina water and ethylene glycol over a stretched surface. The flow is discussed with and without effective Prandtl number. MHD liquid is considered. Electric field is absent. Effect of uniform magnetic field is taken in the vertical direction to the surface. Influence of thermal radiation as well as Joule heating are taken into account for both aluminum oxide-water and aluminum oxide-Ethylene glycol nanofluids. Velocity slip and melting heat effects are considered.

METHODS

The nonlinear flow expressions are numerically solved via ND-solve technique (built-in-Shooting).

RESULTS

The physical impacts of flow variables like mixed convection parameter, magnetic parameter, Reynold number, Eckert number, melting parameter and heat source/sink parameter are graphically discussed. Moreover, entropy generation (irreversibility) and Bejan number are discussed graphically through various flow variables. Physical quantities like skin friction coefficient and Sherwood and Nusselt numbers are numerically calculated and discussed through Tables.

CONCLUSIONS

Impact of magnetic and slip parameters on the velocity field show decreasing behavior for both effective and without effective Prandtl number. Temperature field increases for both effective and without effective Prandtl number for higher values of magnetic and radiative parameters. Entropy number is an increasing function of Reynolds number while Bejan number shows opposite impact against Reynolds number. Moreover, heat transfer rate upsurges versus larger melting and radiative parameter.

Analysis of entropy generation in peristalsis of Williamson fluid in curved channel under radial magnetic field

The objective of present study is to analyze the peristaltic activity of Williamson fluid in curved configuration. Flow formulation is made by employing radial magnetic field and Soret and Dufour effects. Slip conditions for velocity, temperature and concentration are applied. Entropy analysis is also carried out. Modeling is given using lubrication approach. Stream function, velocity, temperature and concentration solutions have been derived. Effects of different parameters are analyzed on flow quantities of interest. Moreover streamlines are examined for different embedded parameters. Result reveals that Lorentz force tends to slow down the fluid velocity. The slip parameters for velocity and temperature lead to enhancement in corresponding profile whereas opposite behavior is noticed for concentration. Soret and Dufour effects lead to increase the temperature as well as entropy of the system. Complaint nature walls increase the fluid velocity for elastance parameters whereas damping nature reduces the fluid velocity.

Entropy generation in the human lung due to effect of psychrometric condition and friction in the respiratory tract

BACKGROUND AND OBJECTIVE

Entropy generation is associated with the irreversibility of any thermodynamic system. It provides an indication of lost energy and hence the efficiency of a system. In this paper, an attempt has been made to study the effects of specific humidity, relative humidity, ambient temperature change, breathing air friction with the respiratory tract on the entropy generation during the respiration process at different physiological conditions.

METHODS

To address the above issues, a human respiratory tract model with realistic length to diameter ratio at different branches has been considered. The analysis examines air flow rates of 6 lpm and 60 lpm during rest and exercise condition respectively; corresponding to breathing rates of 30 and 60 per minute, respectively. The body temperature has been considered at 36°C, and ambient condition of air has been taken at 25°C DBT and 50% RH. The respiratory tract geometry has been modelled on the basis of Weibel's experimental results.

RESULTS

It has been noticed that, at a particular Lewis number entropy generation per day decreases with the increase in specific humidity, again at a particular specific humidity entropy generation increases with the decrease in Lewis number. For a particular physical condition and Lewis number entropy generation decreases with the increase in relative humidity. In this work, it has been observed that negentropy increases with the increase in ambient temperature for a constant relative humidity, however the net entropy generation is always positive. This study reports that, maximum resistance of flow occurs where duct aspect ratio (i.e. tract diameter to length) is minimal. For a typical geometry of air passage, velocity of flow increases up to 3rd generation then it is decreases gradually till 23^rd generation. Amount of entropy generation goes on reducing as the duct goes on bifurcating except for the third generation where a local peak in entropy generation is observed. This is a consequence of typical geometry of human respiratory duct. This work reveals that, at rest entropy generation due to conditioning of breathing air is higher than its frictional component and during heavy physical activity, entropy generation due to breathing air friction with the respiratory tract is higher than its air conditioning component.

CONCLUSIONS

Entropy generation is significantly higher due to conditioning of breathing air than that of frictional effect with the tract. This is a preliminary attempt in quantifying this aspect and the authors believe that, these two components of entropy generation have a probable connection with the bronchial thermoplasty, which helps to treat the asthma.

Nanomaterial based flow of Prandtl-Eyring (non-Newtonian) fluid using Brownian and thermophoretic diffusion with entropy generation

BACKGROUND

The augmentation of cooling or heating in a mechanical and industrial process may create a saving in energy, decrease process time, protract the working existence of hardware and raise thermal rating. A few procedures are even influenced subjectively by the action of increased heat transport. The advancement of high performance thermal frameworks for heat transport augmentation has turned out to be well known these days. Various works has been conducted to gain an understanding of heat transport execution for their viable application to heat transport enhancement. Consequently the appearance of high heat flow procedures has made huge interest for new innovations to increase the heat transport. Therefore, entropy generation in dissipative nanomaterial flow of Prandtl-Eyring nanofluid subject to heated stretchable surface. The impact of zero shear rate viscosity is discussed through Prandtl-Eyring fluid model. Through implementation of thermodynamics second law's total entropy rate is calculated. Heat and mass transfer features are discussed using Brownian diffusion and thermophoresis. Homogeneous and heterogeneous chemical reactions are also accounted.

METHODS

Nonlinear partial differential systems are leads to ordinary systems through adequate similarity transformations. The obtained nonlinear ordinary systems are solved by Newton built in shooting technique.

RESULTS

Behaviors of different flow parameters on velocity, temperature, entropy generation rate, Bejan number and concentration are graphically discussed. Skin friction coefficient and heat transfer rate are discussed through tables. Entropy generation rate enhances for larger estimation of material parameter and Brinkman number. Bejan number is equal to one when Brinkman number is equal to zero and then progressively decreases for higher values of Brinkman number.

CONCLUSIONS

A significant increment has been observed in the velocity field versus material parameter, while opposite trends is noticed forβ.Temperature field enhances against higher values of thermophoresis and Brownian parameters while it decays through larger Prandtl number. Mass concentration upsurges versus higher thermophoresis parameter and declined via larger Brownian parameter and homogeneous and heterogeneous parameters. Furthermore, entropy rate and Bejan number show contrast impact versus material parameter and Brinkman number.

Modeling and computational analysis of hybrid class nanomaterials subject to entropy generation

BACKGROUND AND OBJECTIVE

Nanoliquids are dilute suspensions of nanoparticles with at least one of their principal dimensions smaller than 100 nm. Form literature, nanoliquids have been found to possess increased thermos-physical characteristics like thermal diffusivity, thermal conductivity, convective heat transport coefficients and viscosity associated to those of continuous phase liquids foe example oil, ethylene glycol and water. Nanoliquids have novel characteristics that make them possibly beneficial in numerous applications in heat transport like fuel cells, microelectronics, hybrid-powered engines, pharmaceutical processes, domestic refrigerator, engine cooling thermal management, chiller and heat exchanger. The above applications of nanofluids/hybrid nanofluids insist the researchers and engineers to develop new methodologies and technique in the field of heat transport. Therefore, we have considered mixed convective flow hybrid nanomaterial over a convectively heated surface of disk. Flow nature is discussed due to stretchable rotating surface of disk. Applied magnetic field is accounted. Ohmic heating and dissipation effects are utilized in the modeling of energy expression. Total entropy rate is calculated.

METHODS

Suitable transformation leads to ordinary differential equations. Shooting method is implemented for numerical outcomes. Comparative analysis is made for the present result with published ones.

RESULTS

The effects of key parameters like magnetic parameter, mixed convection variable and Eckert and Biot numbers on the dimensionless velocity, surface drag force, temperature, (heat transfer rate) Nusselt number and entropy rate are discussed in detail and presented graphically. Furthermore, the outcomes demonstrate that velocity of liquid particles decline against magnetic parameter. Temperature and associated layer upsurge versus magnetic parameter and Eckert number. Skin friction coefficient (drag force) improves through higher values of stretching and magnetic variables. Heat transfer rate is more for higher Eckert number and magnetic parameter. Entropy rate is also enhances against Eckert number and Brickman number.

CONCLUSIONS

Magnitude of surface drag force increases for higher values of stretching and magnetic variables. Magnitude of heat transfer rate is more when magnetic variable and Eckert number attain the maximum values. Brinkman number is used to decrease the entropy rate. Furthermore, velocity and temperature show contrast behavior versus magnetic parameter i.e., velocity of fluid particles decreases.

Numerical simulation of MHD double diffusive natural convection and entropy generation in a wavy enclosure filled with nanofluid with discrete heating

A numerical investigation of entropy generation, heat and mass transfer is performed on steady double diffusive natural convection of water-based Al₂O₃ nanofluid within a wavy-walled cavity with a center heater under the influence of an uniform vertical magnetic field. The top horizontal wavy wall, left and right vertical walls of the enclosure are kept at low temperature and concentration of T c and c c whereas central part of the bottom horizontal wall is maintained at high temperature and concentration of T h and c h and the remaining part is kept adiabatic where temperature and concentration gradient are taken as zero. The Bi-CGStab method and Tri-diagonal algorithm are used to solve the governing equations. The study has been performed for several relevant parameters such as Rayleigh number ( 10 3 ≤ R a ≤ 10 5 ), Hartmann number ( 0 ≤ H a ≤ 60 ), buoyancy ratio number ( - 2 ≤ N ≤ 2 ), volume fraction of nanoparticles ( 0.0 ≤ ϕ ≤ 0.2 ) and different undulation number of the upper wavy wall (n). The Prandtl number and Lewis number are kept fixed at Pr = 6.2 and Le = 2 . The effect of these parameters are revealed in terms of streamlines, isotherms, isoconcentrations, entropy generation, average Nusselt number and Sherwood number. Results indicate that heat and mass transfer rate augment as Rayleigh number and volume fraction of nanoparticles increase and are found to drop with the increase in Hartmann number and buoyancy ratio.

Theoretical investigation of Ree-Eyring nanofluid flow with entropy optimization and Arrhenius activation energy between two rotating disks

BACKGROUND AND OBJECTIVE

Improvement of high performance thermal systems for heat transport augmentation has become quite prevalent nowadays. Various works have been performed to pick up a comprehension of the heat transport execution for their practical utilization to heat transport augmentation. Therefore, the nanomaterial has been used in flow of Ree-Eyring fluid between two rotating disks for thermal conductivity enhancement of base fluid. Heat transfer characteristics are discussed through viscous dissipation and heat source/sink. Behaviors of Brownian motion and thermophoresis are also examinted. Physical behaviors of irreversibility in nanofluid with Arrhenius activation energy are also accounted.

METHODS

The nonlinear systems lead to ordinary differential problems through implementation of appropriate transformations. The relevant problems are tackled by (OHAM) Optimal homotopic method for series solutions.

RESULTS

Effects of various physical parameters on the velocity, entropy rate, Bejan number, concentration and temperature are discussed graphically. Skin friction coefficient and gradient of temperature are numerically examined and discussed with various parameters.

CONCLUSIONS

Entropy generation rate is control by minimizing the values of Brinkman number and stretching parameter. Entropy rate and Bejan number show the dual behaviors against Eckert number. Both decay near the lower disk while reverse holds near the upper disk. Entropy rate and Bejan number show similar behaviors for Weissenberg number.

Entropy generation and activation energy mechanism in nonlinear radiative flow of Sisko nanofluid: rotating disk

The theme of the present communication is to explore the novel analysis of entropy generation optimization, binary chemical reaction and activation energy for nonlinear convective flow of Sisko model on a radially stretchable rotating disk in the presence of a uniform vertical magnetic field. Nonlinear mixed convection, nonlinear thermal radiation, MHD, viscous dissipation, Joule heating and non-uniform heat generation/absorption are also considered. Nanofluid model includes significant slip mechanism of Brownian motion and thermophoresis. Apposite transformations are endorsed to get the nonlinear coupled ODEs system. The resultant system of ordinary differential equations is endeavoured for series solutions through homotopic technique. Total entropy generation is inspected through numerous emerging flow variables. Comparative study is made for temperature, velocity, heat transfer rate, Bejan number, entropy generation and mass transfer Nusselt number by considering shear thickening and thinning fluids. Finally, a comparison is specified with the previous existing results.

The analysis of a reactive hydromagnetic internal heat generating poiseuille fluid flow through a channel

In this paper, the analysis of a reactive hydromagnetic Poiseuille fluid flow under different chemical kinetics through a channel in the presence of a heat source is carried out. An exothermic reaction is assumed while the concentration of the material is neglected. The Adomian decomposition method together with Pade approximation technique are used to obtain the solutions of the governing nonlinear non-dimensional differential equations. Effects of various physical parameters on the velocity and temperature fields of the fluid flow are investigated. The entropy generation analysis, irreversibility distribution ratio, Bejan number and the conditions for thermal criticality for different chemical kinetics are also presented.

First steps towards a constructal Microbial Fuel Cell

In order to reach real operating conditions with consequent organic charge flow, a multi-channel reactor for Microbial Fuel Cells is designed. The feed-through double chamber reactor is a two-dimensional system with four parallel channels and Reticulated Vitreous Carbon as electrodes. Based on thermodynamical calculations, the constructal-inspired distributor is optimized with the aim to reduce entropy generation along the distributing path. In the case of negligible singular pressure drops, the Hess-Murray law links the lengths and the hydraulic diameters of the successive reducing ducts leading to one given working channel. The determination of generated entropy in the channels of our constructal MFC is based on the global hydraulic resistance caused by both regular and singular pressure drops. Polarization, power and Electrochemical Impedance Spectroscopy show the robustness and the efficiency of the cell, and therefore the potential of the constructal approach. Routes towards improvements are suggested in terms of design evolutions.