Entropy generation minimization (EGM) in nonlinear mixed convective flow of nanomaterial with Joule heating and slip condition

Entropy generation minimization of higher-order endothermic/exothermic chemical reaction with activation energy on MHD mixed convective flow over a stretching surface

The present investigation aims to analyze higher-order endothermic/exothermic chemical reactions with activation energy by considering thermophoresis and Brownian motion effects on MHD mixed convective flow across a vertical stretching surface. The influence of velocity slip, thermal slip, and concentration slip along with an inclined external magnetic field is also considered. The governing coupled non-linear partial differential equations are transformed into ordinary differential equations using similarity transformation. The resulting system of non-linear ODEs is solved by the Newton Raphson shooting technique using the RK-4 algorithm. The impact of various physical parameters discovered in the problem viz. endothermic/exothermic reaction variable, thermophoresis parameter, activation energy parameter, Brownian motion parameter, chemical reaction parameter have been analyzed on velocity profile, temperature profile, and concentration profile. The effects of these parameters on skin-friction coefficient, Nusselt number, and Sherwood number are displayed in tabular form as well as surface plots. The impact of various physical parameters that appeared in the entropy generation is shown using surface and contour plots. The numerical findings are in good agreement with the previously published results. It is observed that an increment in thermophoresis and Brownian motion parameters results in a declination of entropy profiles, whereas an increment in Bejan number profiles is observed. A small region near the surface exhibits an inclination in concentration profiles with an increase in the order of the chemical reaction. In contrast, the opposite effect is analyzed near the boundary layer. Also, the contour and surface plots are displayed to portray real-world applications in industrial and technical processes and the physical depiction of flow characteristics that arise in the current study.

Influence of Liquid Hydrogen Diffusion on Nonlinear Mixed Convective Circulation around a Yawed Cylinder

A yawed cylinder is a cylinder inclined in the plane of a flowing liquid. The liquid flow past the yawed cylinder is important for practice, namely, for bubble suppression and control of the boundary layer transition in undersea applications. It should be noted that an inclined cylinder characterizes an asymmetrical behavior of fluid flow and heat transfer. Energy and mass transference characteristics of a steady nonlinear convective flow over the yawed cylinder by accounting for chemically reactive species and viscous dissipation are analyzed in this investigation. The differential equations defining the boundary layer parameters are then transformed into a dimensionless view, taking into account the non-similar transformation. It should be noted that the governing equations have been written using the conservation laws of mass, momentum, energy, and concentration. These considered equations allow the simulation of the analyzed phenomenon using numerical techniques. Further, quasilinearization and implicit finite difference approximation are used to work out the non-dimensional governing equations. A parametric investigation of all the pertinent characteristics accompanies this. A descriptive system of computation outcomes for the velocity, temperature, and concentration patterns, the drag coefficients, Nu and Sh, is demonstrated by graphs. Enhancing the magnitudes of the Eckert number raises the temperature pattern while energy transport strength is reduced. As the species concentration profile diminishes, the mass transfer characteristics are enhanced for raising magnitudes of the nonlinear chemical reaction parameter. Further, a velocity profile along the chordwise direction rises with enhancing magnitudes of nonlinear convection characteristics and yaw angle. Furthermore, the velocity pattern along the spanwise direction enhances with the growing magnitudes of yaw angle. For assisting buoyancy flow, the friction parameter at the border in the spanwise direction enhances with rising values of yaw angle.

Variable characteristics of viscosity and thermal conductivity in peristalsis of magneto-Carreau nanoliquid with heat transfer irreversibilities

BACKGROUND

Peristaltic is a basic way of fluid transportation in physiology, engineering and nuclear industry. Importance of peristalsis is due to its contraction and compulsion property of symmetric and asymmetric type channel walls. Another beauty of this mechanism is that the channel walls propagates and push the material along the tube/conduit channel walls. This mechanism shows its presence in physiology while food particles are transferred through esophagus and stomach, urine through intestines, spermatoza transportation in reproductive tract. In industry it is found in roller and finger pumps, drug delivery and various nuclear materials e.g. toxic, corrosive, noxious etc. Magnetic field in peristalsis is found helpful in treatment of various treatments using magnets. Actually earth and human body as a whole comprises of magnetic and electric fields. The medical specialists found that unbalances of electromagnetic field in human body is the reason for emotional and physical disturbance. In addition it has significant and potential utilizations in modification of medical, industrial and chemical, procedures for example MRI, evaporation, convection, thermoregulation, MHD throttles, and in various types of tumor treatments. Entropy production work out irreversibility in complex systems which are frequently encountered in industrial mechanisms. In view of that, this methodology is effectually implemented in distinct technological applications covering porous media, propulsion ducts, electronic cooling, turbo-machinery and combustion.

METHOD

Modelled flow mechanism is nonlinear and coupled due to considered assumptions (i.e. nanofluid, nonlinear porous channel, mixed convection, variable viscosity and thermal conductivity, activation energy and chemical reaction). Such nonlinear and coupled system is difficult to tackle analytically. Thus to obtain the solution we employed RK algorithm for numerical simulations.

RESULTS

Stronger magnetic parameter shows resistive characteristics to the flow field. Nonlinear Darcy medium assists the fluid motion at channel center and resits at walls vicinity. Variable characteristics of thermal conductivity moderate the soak or disperse up heat ability which corresponds to temperature reduction. Thermal slip quantity increase the temperature whereas concentration slip deduct the concentration of Carreau nanomaterial. Entropy and Bejan number shows maximum response for higher dissipation estimations. Brownian and thermopherotic motions aspects has reverse impact on nanomaterial concentration.

CONCLUSION

Entropy and Bejan number deduces for higher variable thermal conductivity values. Carreau material variable enhance the entropy of the system as a whole.

Cattaneo-Christov Heat Flux Model for Second Grade Nanofluid Flow with Hall Effect through Entropy Generation over Stretchable Rotating Disk

The second grade nanofluid flow with Cattaneo-Christov heat flux model by a stretching disk is examined in this paper. The nanofluid flow is characterized with Hall current, Brownian motion and thermophoresis influences. Entropy optimization with nonlinear thermal radiation, Joule heating and heat absorption/generation is also presented. The convergence of an analytical approach (HAM) is shown. Variation in the nanofluid flow profiles (velocities, thermal, concentration, total entropy, Bejan number) via influential parameters and number are also presented. Radial velocity, axial velocity and total entropy are enhanced with the Weissenberg number. Axial velocity, tangential velocity and Bejan number are heightened with the Hall parameter. The total entropy profile is enhanced with the Brinkman number, diffusion parameter, magnetic parameter and temperature difference. The Bejan number profile is heightened with the diffusion parameter and temperature difference. Arithmetical values of physical quantities are illustrated in Tables.

Inspection of hybrid based nanofluid flow over a curved surface

BACKGROUND

In this paper, we discussed the Cu - Al₂O₃/H₂O (Hybrid nanofluid) flow over permeable exponentially stretching channel. The hybrid nanofluid involves two kinds of nanoparticles along with base fluid (pure water). Our research objective is to evaluate the heat transfer rate of hybrid nanofluid.

METHOD

The resulting system is numerically tackled via shooting method (bvp4c).

RESULTS

The hybrid nanofluid gains larger rate of heat transfer as compared to simple nanofluid. The impact of non-dimension parameter on temperature profile, boundary layer will be analyzed for enormous values of dimensionless parameter. Also, boundary layer thickness when γ < 0 (injection) and when γ > 0 (suction) will be compared. The present results with the existence literature will be compared for justification/validation.

Entropy optimized MHD 3D nanomaterial of non-Newtonian fluid: A combined approach to good absorber of solar energy and intensification of heat transport

BACKGROUND

The present work provides important insights regarding three dimensional unsteady magnetohydrodynamic flow and entropy generation of micropolar Casson Cross nanofluid subject to nonlinear thermal radiation and chemical reaction. The Buongiorno's nanofluid model featured with Brownian movement and thermophoresis is considered. Realistic aspects namely convective boundary condition, viscous dissipation and joule heating are introduced. The present problem is modeled by momentum, temperature, microrotation and nanoparticles concentration equations.

METHOD

The non-dimensional highly nonlinear differential equations are solved numerically via shooting iteration technique together with 4th order Runge-Kutta integration scheme.

RESULTS

The current study imparts a reasonable, pragmatic and realistic approach to a good absorber of solar energy. In addition, strong and visionary profiles of velocity, microrotation, temperature, nanoparticles concentration, entropy generation rate and Bejan number for concern nanofluids are presented. Besides, intensive physical interpretation of the involved thermophycal parameters has been well-addressed.

CONCLUSIONS

The present investigation shows that strengthening of Weissenberg number uplifts the axial as well transverse fluid velocities while that of Hartmann number turns out to be a reverse trend. Furthermore, heat and mass transfer rates exhibit ascending and descending trends for intensified Brownian motion and thermophoresis respectively. Improved thermal boundary layer due to the upgrading temperature ratio parameter is another outcome of the current analysis.

Transportation of magnetized micropolar hybrid nanomaterial fluid flow over a Riga curface surface

We deliberated the flow of magnetized micropolar hybrid nanoparticles fluid flow over the Riga curved surface. Exponentially stretching and slip effects are also considered in this analysis. Mathematical model has been established on the base of assumptions in the form of partial differential equations. Such equations are renewed into ordinary differential equations utilizing similarity transformations. Reduced model has been elucidated by means of bvp4c scheme. Impacts of physical parameters namely as stretching parameter R₀, curvature parameter K, solid nanoparticle volume fraction Φ₂, micropolar parameter K₁, microgyration parameter n, thermal slip parameter M, partial slip parameter γ, modified Harman number ∅ and dimensionless parameter ω. Magnetic parameter β and reciprocal magnetic Prandtl number λ are depicted by means of numerically and graphically. Our results help in the field of engineering and industrial. This model is presented in the first time through literatures. Our interest of study is to be analyzed about the heat transfer rate of magnetized micropolar hybrid nanomaterial fluid over a Riga curved surface. Comparison with the literature has been worked out and excellent agreement is found.

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.

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.

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.

On the Development of Mechanothermodynamics as a New Branch of Physics

This paper aims to substantiate and formulate the main principles of the physical discipline-mechanothermodynamics that unites Newtonian mechanics and thermodynamics. Its principles are based on using entropy as a bridge between mechanics and thermodynamics. Mechanothermodynamics combines two branches of physics, mechanics and thermodynamics, to take a fresh look at the evolution of complex systems. The analysis of more than 600 experimental results allowed for determining a unified mechanothermodynamical function of limiting states (critical according to damageability) of polymers and metals. They are also known as fatigue fracture entropy states.

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.

Stability Analysis of Darcy-Forchheimer Flow of Casson Type Nanofluid Over an Exponential Sheet: Investigation of Critical Points

In this paper, steady two-dimensional laminar incompressible magnetohydrodynamic flow over an exponentially shrinking sheet with the effects of slip conditions and viscous dissipation is examined. An extended Darcy Forchheimer model was considered to observe the porous medium embedded in a non-Newtonian-Casson-type nanofluid. The governing equations were converted into nonlinear ordinary differential equations using an exponential similarity transformation. The resultant equations for the boundary values problem (BVPs) were reduced to initial values problems (IVPs) and then shooting and Fourth Order Runge-Kutta method (RK-4th method) were applied to obtain numerical solutions. The results reveal that multiple solutions occur only for the high suction case. The results of the stability analysis showed that the first (second) solution is physically reliable (unreliable) and stable (unstable).