A numerical study on the flow of water-based ternary hybrid nanomaterials on a stretchable curved sheet

Nanomaterials are quite promising in electronic cooling systems, heat exchangers, engine lubricants, brake liquids, shock absorbers, radiators, etc. Therefore, the study of heat transfer characteristics on the flow of trihybrid nanofluids on an exponentially stretched curved surface is developed. Purpose: In this study, trihybrid nanofluid is taken into consideration, which is composed of Fe3O4, Ag and Cu as nanoparticles and water as the basefluid. Heat generation and magnetic field impacts are addressed. Based on these assumptions, the governing partial differential equations were reduced to a favorable set of ordinary differential equations using adequate transformations. Formulation: The highly nonlinear coupled system of equations was numerically solved using the shooting method with the Runge-Kutta-Fehlberg technique. Findings: Trihybrid nanofluids improve the thermal performance of fluid when compared with other fluids such as hybrid nanofluids, nanofluids, and basefluids. The trihybrid nanofluid is efficient in heat transfer phenomenon and has a significant impact on the overall performance of a system, including cooling systems, heat exchangers, electronics, and many industrial processes. Graphical representation for the physical variables of the fluid velocity and temperature is discussed. The local Nusselt number and skin friction coefficient are computed and analyzed. A magnetic field decreases the velocity but escalates the temperature. The Nusselt number decreases for larger solid volume fractions. Novelty: The Tiwari and Das model for hybrid nanofluid extended for trihybrid nanoparticles has not been investigated previously. Heat transfer examination on the flow of trihybrid nanomaterials on exponentially curved stretching sheets considering magnetism force and heat generation consequence has not yet been studied.

KHA model comprising MoS4 and CoFe2O3 in engine oil invoking non-similar Darcy-Forchheimer flow with entropy and Cattaneo-Christov heat flux

Objective: Nanoliquid flows are widely utilized in industrial, petroleum, engineering, and pharmaceutical applications including electric cooling, drug delivery, nuclear reactor cooling, solar collectors, heat exchangers, magnetohydrodynamic power generators, aerospace, porous media, thermal storage systems, and many others. Darcy-Forchheimer magnetized hybrid nanoliquid subjected to a stretchable cylinder was addressed, and the Cattaneo-Christov heat flux analysis was considered. Herein, disulfido (dithioxo) molybdenum (MoS4) and cobalt ferrite (CoFe2O4) were considered as nanoparticles, and engine oil as a conventional liquid. The thermal relationship of heat generation and radiation was discussed, and the influence of the entropy rate was addressed. Methodology: Governing expressions were transformed into dimensionless forms. Simulation by the ND-solve technique was implemented. Conclusions: Features for the entropy rate, liquid flow, and temperature against emerging variables for nanoliquid (MoS4/engine oil) and hybrid nanoliquid (MoS4 + CoFe2O4/engine oil) were explored. The numerical results of the coefficient of skin friction and thermal transport rate for nanoliquid (MoS4/engine oil) and hybrid nanoliquid (MoS4 + CoFe2O4/engine oil) were examined. Reduction in velocity clearly occurred through a magnetic field, whereas the reverse impact held for the entropy rate. The thermal field and entropy rate against the curvature parameter were enhanced. A decrease in liquid flow occurred for higher porosity variables. An enhancement in the entropy rate was witnessed for radiation and porosity parameters. Higher radiation and thermal relaxation time variables resulted in enhancement of the thermal transport rate.

Entropy generation in bioconvection hydromagnetic flow with gyrotactic motile microorganisms

Here, the magnetohydrodynamic bioconvective flow of a non-Newtonian nanomaterial over a stretched sheet is scrutinized. The characteristics of convective conditions are analyzed. Irreversibility analysis in the presence of gyrotactic micro-organisms is discussed. Energy expression is assisted with thermal radiation, heat generation and ohmic heating. Buongiorno's model is employed to discuss the characteristics of the nanoliquid through thermophoresis and random diffusions. Nonlinear expressions of the given model are transformed through adequate transformations. The obtained expressions have been computed by the Newton built in-shooting technique. Results of influential variables for velocity, concentration, microorganism field, temperature and entropy rate are graphically studied. Clearly, velocity reduction is witnessed for the bioconvection Rayleigh number and magnetic variable. A higher heat generation variable leads to augmentation of temperature. An increase in the magnetic variable results in entropy and temperature enhancement. A higher Peclet number results in microorganism field reduction. Temperature distribution rises for radiation and the thermal Biot number. A higher solutal Biot number intensifies the concentration. The entropy rate for radiation and diffusion variables is enhanced.

Unsteady nanofluid flow over a cone featuring mixed convection and variable viscosity

This article addresses unsteady nanofluid flow over a cone with MHD and mixed convection effects. Effects of variable viscosity and viscous dissipation are also considered. The resulting system of equations is tackled through the Homotopy Analysis Method (HAM). The impact of different influential variables on skin friction coefficient, heat and mass flux are discovered through numerical tables and graphs. It is noted that the surface drag force in x and y directions increases against the buoyancy force parameter. Also, it is observed that the tangential and azimuthal velocity decrease against the variable viscosity parameter. Furthermore, the temperature of fluid is observed to decay against the unsteady parameter but it increases against the Eckert number.

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.

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.

Cattaneo-Christov heat flux (CC model) in mixed convective stagnation point flow towards a Riga plate

This research article proposes an improved Fourier law of heat conduction (Cattaneo-Christov) in presence of heat source/sink. The heat transport characteristics are modeled for mixed convective stagnation point flow by a Riga plate. Flow is generated due to linear stretching velocity. The partial differential system is changed to ordinary differential system through implementing appropriate transformations. Series solutions are developed through semi-analytical method called as homotopy analysis method. Present research article is related to the improved Fourier law of heat conduction (Cattaneo-Christov) over a linear stretchable surface of Riga plate when fluid saturates porous space. The main outcomes of present communication are summarized as: (i) velocity of material particles decreases subject to larger inverse Darcy-number while it enhances via velocity ratio and magnetic parameters (ii) temperature distribution as well as layer thickness enhance for higher estimations of Eckert number and heat source parameter while it decays against Prandtl number (iii) skin friction coefficient decreases through higher values of inverse Darcy number and mixed convection parameter.

Analytical evaluation of Oldroyd-B nanoliquid under thermo-solutal Robin conditions and stratifications

Chilling systems are important in the improved technological thermal mechanisms which are considered continuously in passive along with active heat-transference improvement procedures. Engineers recommended several approaches to upsurge heat transference of thermal structures. The pulsating flow, corrugated tube, magnetic field aspect and nanoliquids are the heat-transference improvement procedures delved continuously. In present research work, we addressed the heat-transference characteristics of non-Newtonian (Oldroyd-B) liquid towards heated stratified surface. Thermally radiative laminar flow is modeled. In addition, we accounted Buongiorno's nanoliquid model which includes Brownian along with thermophoretic diffusions. Modeling is further based on heat source, magnetohydrodynamics, dual stratification, thermal radiation and convective conditions. Mathematical system is simplified through boundary-layer idea. Similarity variables are reported with the aim to simplify complex mathematical system. Homotopy algorithm yields convergent results of non-dimensional expressions. Our study unveils diminution of thermal along with solutal fields when stratification factors are increased.

Corrigendum to "Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects" [Computer methods and programs in biomedicine 184 (2020) 105,086]

In this published paper, a mathematical modeling has been conducted for the peristaltic transport in flow of hybrid nanofluid between rotating channel in the presence of nonlinear thermal radiation, slip effects and entropy generation. This corrigendum correct the flow geometry, figures captions and plots "Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects" [Computer Methods and Programs in Biomedicine 184 (2020) 105,086] where these mistake are occurred during production process and therefore, some captions are shuffled. The difference in the captions and plots however does not affect the authenticity and mathematical validity of the problem in purpose of this published research article is to investigate the peristaltic transport in flow of hybrid nanofluid between rotating channel subject to nonlinear thermal radiation, slip effects and entropy generation. However, the flow geometry and the captions and plots should be arranged.

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.

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.

Modeling and numerical simulation of micropolar fluid over a curved surface: Keller box method

BACKGROUND

This paper examines the flow behavior of micropolar liquid over a curved surface. MHD fluid is considered. The surface inducing the fluid motion has a prescribed temperature different from the ambient fluid moreover the heat transfer mechanism is investigated. Curvilinear coordinates are used for the mathematical formulation of the flow equation. Similarity variables are derived and are utilized to alter the governing expressions for the flow of momentum and heat transfer characteristic.

METHOD

The resulting non-linear ODEs are resolved systematically by two numerically approaches namely; the Keller box method and the shooting method.

RESULTS

The numerical results for the temperature and velocity fields has been presented through tables and graphs against the independent parameters and non-dimensional numbers i.e., material parameter, power law index, radius of curvature, magnetic parameter, Prandtl and Eckert numbers, skin friction (drag force) and Nusselt number. Physical explanation of the graph presented is given to understand the performance of fluid flow and heat transport phenomena in different emerging situation.

CONCLUSION

The main outcomes in the presence of various flow variables on the skin friction velocity, Nusselt number, temperature are highlighted via graphical sketch and Tables. Velocity field displays a decreasing trend with magnetic parameter, power law index and radius of curvature of the stretching velocity whereas, opposite behavior observed for the material parameter. Near the surface curvature and magnetic parameter shows an enhancement in microrotation profile whereas, it shows reverse behavior when it is far away. Material parameter increases for large values of microrotation profile on the other hand power-law index decreases for large values. For higher values magnetic parameter, radius of curvature and Eckert number temperature profile increases. But temperature reduces subject to material parameter and Prandtl number.

Entropy generation minimization (EGM) in magneto peristalsis with variable properties

OBJECTIVE AND BACKGROUND

This article featuring the peristaltic transport of viscous material with variable properties (i.e. temperature dependent viscosity and thermal conductivity) through curved configuration. Fluid saturating through porous channel walls of uniform space. Entropy generation consideration here is to analyze irreversibility aspects. Channel boundaries retain the velocity and thermal slip conditions.

METHOD

Wave frame of reference is attained with the utilization of long wavelength and small Reynolds number approach. Solution of the simplified coupled system of dimensionless constraints is obtained numerically. Detailed analysis of important quantities of interest has been presented in discussion portion.

RESULTS

Entropy generation variation near center is very small whereas in the vicinity of the channel wall is larger. Bejan number has reverse variation as observed for entropy generation.

CONCLUSION

Variable characteristics of viscosity has opposite impact on velocity and temperature is observed. It is also noticed small irreversibility effects are obtained for higher varying viscosity and thermal conductivity near the vicinity of the channel walls.

Cattaneo-Christov (CC) heat flux model for nanomaterial stagnation point flow of Oldroyd-B fluid

Background Magnetohydrodynamic (MHD) stagnation point flow of Oldroyd-B nanoliquid is discussed in presence of Cattaneo-Christov mass and heat fluxes. Impacts of Brownian motion and thermophoresis are discussed. Convergent solution for nonlinear analysis are organized for velocity, temperature and concentration. Method Average residual error is calculated with the help of optimal homotopy analysis method (OHAM). Results Prominent features of interesting parameters on concentration, velocity and temperature are scrutinized. Velocity field has reverse trend for Deborah number against retardation and relaxation times. Temperature and concentration have similar results versus thermophoresis parameter. Conclusions: 1: Velocity has opposite impact for Deborah number for relaxation and retardation time. 2: Velocity boosts up for higher ratio parameter. 3: Velocity against magnetic parameter is decreased. 4: Thermal upsurges versus thermal relaxation time parameter. 5: Outcomes of thermophoretic parameter and Brownian motion parameter on temperature are quantitatively similar. 6: Concentration boosts up via Brownian parameter. 7: Concentration have similar characteristics for both Prandtl number and thermophoretic parameter.

Diabetic peripheral neuropathy in people with type 2 diabetes: too little too late

Diabetic peripheral neuropathy in people with type 2 diabetes is poorly managed because of its insidious onset, delayed diagnosis and more complex aetiology resulting from the contribution of not only hyperglycaemia, but also ageing, hyperlipidaemia, hypertension and obesity. Because there is no US Food and Drug Adminstration-approved disease-modifying therapy for diabetic peripheral neuropathy, the key to ameliorating it in type 2 diabetes has to be through earlier diagnosis and timely multi-factorial risk factor reduction. The management of painful diabetic peripheral neuropathy also requires a detailed appraisal of the choice of therapy, taking into account efficacy, patient wishes, comorbidities, side effect profile and potential for abuse.

Theoretical and numerical investigation of Carreau-Yasuda fluid flow subject to Soret and Dufour effects

BACKGROUND

Newtonian fluids can be categorized by a single coefficient of viscosity for specific temperature. This viscosity will change with temperature; it doesn't change with strain rate. Just a small group of liquids show such steady consistency. A fluid whose viscosity changes subject to relative flow velocity is called non-Newtonian liquids. Here we have summarized a result for the flow of Carreau-Yasuda fluid over a porous stretchable surface. Mixed convection is considered. Modeling of energy expression is performed subject to Soret and Dufour effects.

METHOD

The nonlinear PDE's are changed to ODE's through suitable transformations and then solved for numerical solutions via Built-in shooting method (bvp4c).

RESULTS

Variation of important variables is studied on the concentration, temperature and velocity fields. Tabular representation for study of skin friction and heat transfer rate is presented for important variables. Our results show that velocity decreases versus higher estimations of Weissenberg number, porosity parameter, buoyancy ratio and mixed convection parameter. Temperature decays via Weissenberg number and porosity parameter. Increase in concentration is noticed through higher Soret number and porosity parameter. Skin friction and heat transfer rate (Nusselt number) boosts versus larger porosity parameter and Prandtl number respectively while it decays against Weissenberg number and Dufour and Eckert number.

On the numerical simulation of stagnation point flow of non-Newtonian fluid (Carreau fluid) with Cattaneo-Christov heat flux

BACKGROUND

This research article is devoted to evaluating the impact of Cattaneo-Christov heat in MHD stagnation point flow over a stretched and shrinking surface of the cylinder. MHD liquid of Carreau fluid is considered. Flow is generated due to stretching and shrinking aspects. The energy equation is developed in the presence of Cattaneo-Christov heat flux, where thermal relaxation time plays an important role in the heat transport.

METHOD

The appropriate transformations are employed to solve a differential system via shooting method (bvp4c).

RESULTS

The velocity, skin friction coefficient, temperature and Nusselt number are discussed versus different pertinent flow variable graphically. Over results indicate that the velocity distribution decreases against larger magnetic power law index and Weissenberg number. Temperature field diminishes via Prandtl number and thermal relaxation variable. Engineering quantities are discussed graphically. Magnitude of skin friction or velocity gradient upsurges versus magnetic parameter. Moreover, temperature gradient or Nusselt number shows the increasing impact via Prandtl number. Main observations of the considered flow problem are listed as concluding remarks.

Development of thixotropic nanomaterial in fluid flow with gyrotactic microorganisms, activation energy, mixed convection

BACKGROUND

In this article, impact of gyrotactic microorganisms on nonlinear mixed convective MHD flow of thixotropic nanoliquids is addressed. Effects of Brownian motion and thermophoresis diffusion are considered. Characteristics of heat and mass transfer are analyzed with activation energy, Joule heating and binary chemical reaction. Nonlinear PDE's are reduced to ordinary equation by using suitable transformations.

METHOD

For convergent series solution the given system is solved by the implementation of the homotopic analysis technique (HAM).

RESULTS

Influences of different flow controlling variables on the velocity, microorganisms, concentration and temperature are examined through graphs. Surface drag force, density number, Sherwood number and gradient of temperature are examined versus different flow parameters through graphs. For larger thixotropic fluid parameters the velocity field boosts up. For rising values of Hartmann number the velocity and temperature have opposite behaviors.

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.

Darcy-Forchheimer hybrid (MoS2, SiO2) nanofluid flow with entropy generation

BACKGROUND

The aim of this articles is to investigate the entropy optimization in Darcy-Forchheimer hybrid nanofluids flow towards a stretchable surface. The flow is caused due to stretching of surface. Energy equation is discussed through heat generation/absorption, viscous dissipation and heat flux. Here molybdenum disulfide and silicon dioxide are considered as a nanoparticles and water as continuous phase fluid. Furthermore we examined the comparative analysis of molybdenum disulfide (MoS₂) and silicon dioxide (SiO₂) suspended in water (H₂O). Entropy optimization rate is calculated through implementation of second law of thermodynamics.

METHOD

Nonlinear partial differential equations are reduced to ordinary system through adequate transformation. Here we have employed numerical built in ND solve method to develop numerical outcomes for obtained nonlinear flow expression.

RESULTS

Characteristics of various engineering parameters on entropy optimization, velocity, Bejan number and temperature are graphically examined for both molybdenum disulfide and silicon dioxide. Skin friction coefficient and Nusselt number are numerically computed for various interesting parameters for both nanoparticles (SiO₂ and MoS₂). From obtained results it is noted that entropy optimization enhances against larger estimation of radiation and porosity parameters. Temperature and velocity have opposite behaviors for porosity parameter. Comparative study of present and with previous published literature are examined in tabulated form and found good agreement.

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.

Modeling and computational analysis of 3D radiative stagnation point flow of Darcy-Forchheimer subject to suction/injection

BACKGROUND

This manuscript elaborates the three-dimensional radiated Darcy-Forchheimer viscous liquid flow subject to permeable stretched surface. The stretched surface is nonlinear and saturated via Darcy-Forchheimer medium. Energy expression is derived through implementation of first of thermodynamics and discussed subject to convective condition and nonlinear heat flux. Mixed convection is also considered.

METHOD

The governing systems of nonlinear equations are tackled numerically by Shooting method.

RESULTS

Graphical results are depicted and examined with different values of non-dimensional parameters for velocity and energy equations respectively. Drag force and Nusselt number are computationally computed and analyzed through Tables.

CONCLUSIONS

It is concluded from the derived outcomes that both component of velocity decay against higher values of local inertia coefficient and inverse Darcy number variables. For suction case both velocities increases while opposite trend is observed for injection case. Temperature profile has an increasing impact for higher values of Radiation, and Biot number while opposite result is seen for injection. Drag force or skin friction declines via larger injection variable. Nusselt number increases for radiation variable.

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.

Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects

BACKGROUND

In last few decades, a new class of working materials which comprises from two solid materials dispersed in a continuous phase liquid was established and deeply scrutinized. These materials are called hybrid nanomaterials. This research article aims to investigate entropy optimization in hybrid nanomaterial flow through a rotating peristaltic channel walls. Flow behavior is analyzed between the channels which is caused by propagation of sinusoidal waves. Viscosity of fluid is considered variable instead of constant characteristics. Fluid saturates through porous attributes of channel walls. Nonliear radiative flux and convective condition are considered. Slip conditions are imposed at the boundary of walls.

METHODS

Built-in-Shooting technique is employed to obtain the numerical outcomes for the considered flow problem.

RESULTS

Impacts of sundry variables on the entropy, temperature and velocity are scrutinized through different graphs. Numerical result presents that the axial velocity escalates with the inclusion of hybrid nanomaterial. The temperature of fluid enhances through higher estimations of hybrid nanoparticles.

CONCLUSIONS

Here the flow behavior is discussed between the channels which are caused by propagation of sinusoidal waves with speed c. Entropy generation rate is minimum for variable viscosity and maximum for hybrid nanoparticles. Hybrid nanoparticles increase the temperature of fluid. Bejan number presents the similar impact for variable viscosity and thermal slip parameters. Temperature field decays through higher values of Brinkman number.

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.

Heat transport and entropy optimization in flow of magneto-Williamson nanomaterial with Arrhenius activation energy

BACKGROUND

A newly developed approach in the field of nanotechnology for solving problems and collection of information is the use of nanoparticles. This idea has been further utilized in a better way in pharmaceutical industries. By using nanotechnology, the field of pharmaceutical science has been modernized and redeveloped. The use of nanotechnology in such industries has convinced the scientist to obtain more economical and easier applications. Therefore, with such effectiveness in mind, a theoretical study has been conducted to examine the effects of nonlinear radiative heat flux and magnetohydrodynamics for nanomaterial flow of Williamson fluid over a convectively heated stretchable surface. Brownian diffusion is utilized in mathematical modeling. Furthermore, heat source/sink, viscous dissipation and nonlinear radiative heat flux are examined. Convective boundary condition is implemented. Salient effects of chemical reaction and Arrhenius activation energy in mass transfer are considered. Total entropy rate is obtained through implementation of thermodynamics second law.

METHODS

The nonlinear PDEs are reduced into ordinary ones by appropriate similarity transformations. A semi-analytical technique i.e., homotopy method is implemented to obtain the convergent series solutions.

RESULTS

The obtained results indicate that the velocity of fluid particles increases versus higher fluid parameter. Schmidt number and activation energy variable have opposite effect on concentration. Entropy rate grows up with fluid parameter and Brinkman and Biot numbers while opposite trend is seen for Bejan number.

CONCLUSIONS

Velocity of the material particles declines through larger estimations of magnetic variable while it upsurges for higher fluid parameter. Thermal distribution shows similar impact for radiative and magnetic variables. Mass concentration decreases against chemical reaction parameter while it increases via activation energy variable. Entropy and Bejan numbers show opposite impacts versus Brinkman number. Skin friction coefficient increases through larger Weissenberg 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.

MHD peristaltic motion of Johnson-Segalman fluid in an inclined channel subject to radiative flux and convective boundary conditions

BACKGROUND

In abundant of a digestive tract like smooth muscle tissue, human gastrointestinal tract contracts in sequence to generate a peristaltic wave, which pushes a food along the tract. The peristaltic motion contains circular relaxation smooth muscles, then their shrinkage (contraction) behind the chewed material to keep it from moving backward, then longitudinal contraction to shove it ahead. Therefore, we have conducted a theoretical investigation on peristaltic transport in flow of Johnson-Segalman liquid subject to inclined magnetic field. The energy equation is developed with extra heat transport assumptions like thermal radiative flux and dissipation. The channel walls are heated convectively.

METHODS

Dimensionless problems subject to small Reynolds number and long wavelength are tackled. Perturbation technique is implemented for small Weissenberg number.

RESULTS

The physical importance of involved parameters that directly affect the heat transfer rate temperature and velocity. The pertinent variables are amplitude ratio, wave number, Reynolds number, Hartman number, Prandtl number, Weissenberg number, thermal radiative heat flux, Biot number, elasticity variables and Froude number are graphically discussed. The obtained outcome shows that the velocity field increases against higher values of elasticity variables but velocity the material decays through higher fluid parameter. Temperature field declines through higher Hartman number. Furthermore, it is also examined that the heat transfer rate decays against rising Hartman number.

CONCLUSIONS

The impact of complaint walls on radiative peristaltic transport of Johnson-Segalman liquid in symmetric channel subject to inclined angle. The influence of Johnson-Segalman variable on the velocity field shows decreasing behavior. Velocity also declines against larger Hartman number. Temperature and heat transfer rate boosts through rising values of E₁ E₂ while decays versus larger E₃. Furthermore, reduction in heat transfer coefficient is observed when the values of α and Br are increased.

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.

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.

Impact of Activation Energy in Nonlinear Mixed Convective Chemically Reactive Flow of Third Grade Nanomaterial by a Rotating Disk

Here impact of activation energy in binary chemically reactive flow of third grade fluid is addressed. Flow is discussed by a stretchable rotating disk. Novel characteristics regarding thermophoresis and Brownian movement have been analyzed. Nonlinear thermal radiation is considered. Convergent series solutions to nonlinear problems are computed. Impacts of various physical parameters like Brownian motion parameter, Prandtl number, mixed convection parameter, thermophoresis parameter, radiation parameter, activation energy, chemical reaction and Schmidt number on the velocity, concentration and thermal fields are discussed and analyzed. Velocity, temperature and concentration gradients are computed and discussed through various flow variables. Their obtained results present that velocity, temperature, concentration fields are strongly depends on the flow parameters. Main conclusions are presented.