Heat and mass transfer in a MHD non‐Darcian micropolar fluid over an unsteady stretching sheet with non‐uniform heat source/sink and thermophoresis

The effect of heat and mass transfer in a MHD non‐Darcian flow of a micropolar fluid over an unsteady stretching sheet with thermophoresis and non‐uniform heat source/sink is discussed. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The arising nonlinear problem is solved by the Keller box method. The effects of various physical parameters on skin friction, local Nusselt number, and Sherwood number are presented graphically and in tabular form. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21018     

A semianalytical technique for MHD peristalsis of pseudoplastic nanofluid with temperature‐dependent viscosity: Application in drug delivery system

An analysis has been implemented to study the influences of nonconstant viscosity and magnetohydrodynamics on pseudoplastic nanofluid through a porous medium. Ohmic dissipation, chemical reaction, and heat generation are taken into consideration. The current problem is debated under the molds of tiny or zero and approximation. Two models of nonconstant viscosity are deliberated. Model (I)—all parameters are nondimensional and have been measured as constants inside the flow. Model (II)—all these stated nondimensional parameters have been considered to differ with the temperature. Comparison among the solutions achieved by utilizing numerical results and multi‐step differential transform method (Ms‐DTM) is displayed in excellent agreement. Attention is dedicated to , ‐, and parameters. The governing equations for each case have been explained by an easy and highly perfect series established seminumerical Ms‐DTM utilizing Mathematica 11, which uses mathematical software package. Nanofluids are active for drug carrying and drug delivery systems because of the control with the velocity of fluid.     

Entropy and radiation on a pipe MHD flow with variable viscosity

The present work, the entropy generation due to radiation and variable viscosity magnetohydrodynamic effects with a porous medium in a circular pipe, has been obtained and studied numerically. The governing continuity, momentum, and energy equations in cylindrical coordination are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically by a Runge-Kutta method and shooting technique. Numerical results are presented for velocity, temperature profiles, pressure profile, entropy generation rates, and Bejan number for different physical parameters of the problem. Also, the effects of the pertinent parameters on the skin friction and the rate of heat transfer are obtained and discussed numerically and illustrated graphically.     

Heat and mass transfer for Soret and Dufour's consequences on unsteady MHD free convection flow over a porous media with heat absorption

The significance of this article lies in explaining the influence of Soret and Dufour numbers on an unsteady MHD free convection of flow of heat and mass transfer through porous media. The substances and radiation along the viscous, incompressible, and conductive compounds respond to the unstable convection of the liquid. Using physical quantities, the dimensional governing equations are converted to non-dimensional equations. Finite element Galerkin method is applied to numerically solve the resulting partial differential equations. Flow parameters on velocity, temperature, and concentration are studied and explained graphically to reflect their effects. Similarly, the skin friction number and Nusselt number are also observed and recorded in tables.     

Soret and Dufour effects on MHD flow of viscoelastic fluid past an infinite vertical stretching sheet

Heat and mass transmission taking place in a magnetohydrodynamics fluid of substantial viscosity via a permeable object has been currently a subject of study inviting research. This transmission takes place along an infinite expanding vertical surface showing Soret and Dufour effects. Differential forms of nonlinear nature such as energy, momentum, and equations defining concentration are ascertained by means of similarity transformation with the existing buoyancy force, and by making use of the homotopy analysis method, the equations have been analytically resolved. The impacts arising out of applied factors on temperature, velocity, and concentration forms have been appropriately designed and established.     

A model for entropy generation in stagnation‐point flow of non‐Newtonian Jeffrey,Maxwell, and Oldroyd‐B nanofluids

We present a generalized model to describe the flow of three non‐Newtonian nanofluids, namely, Jeffrey, Maxwell, and Oldroyd‐B nanofluids. Using this model, we study entropy generation and heat transfer in laminar nanofluid boundary‐layer stagnation‐point flow. The flow is subject to an external magnetic field. The conventional energy equation is modified by the incorporation of nanoparticle Brownian motion and thermophoresis effects. A hydrodynamic slip velocity is used in the initial condition as a component of the stretching velocity. The system of nonlinear equations is solved numerically using three different methods, a spectral relaxation method, spectral quasilinearization method, and the spectral local linearization method, first to determine the most accurate of these methods, and second as a measure to validate the numerical simulations. The residual errors for each method are presented. The numerical results show that the spectral relaxation method is the most accurate of the three methods, and this method is used subsequently to solve the transport equations and thus to determine the empirical impact of the physical parameters on the fluid properties and entropy generation.     

Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

The current theoretical study describes the Marangoni thermal convective flow of magnetohydrodynamic dusty nanofluids along a wavy vertical surface. The two‐phase mathematical model is developed under the influence of thermal radiation and exponentially varying space‐dependent heat source. Pure and hybrid nanoparticles together with dust particle suspension in the base fluid are taken into consideration to characterize the behavior of the flow. Brownian motion and thermophoresis mechanisms are considered, since it enhances the convection features of dusty nanofluid. Appropriate transformations are adopted to modify the flow governing equations and boundary conditions to dimensionless form. The forward finite difference scheme is implemented to illustrate the resultant coupled partial differential equations. The Newton quasi‐linearization technique is utilized to reduce the nonlinear system into a linear form, which is solved thereafter by Thomas algorithm. The responses of velocity, temperature, concentration, friction factor, and heat and mass transfer rate profiles with various governing parameters are discussed and portrayed graphically. The study evidences that the radiation and space‐dependent heat generating parameters strengthen the temperature distribution. Also, the heat transfer rate appreciably rises with the increment in Marangoni convection. The solution methodology and accuracy of the model is validated by generating the earlier outcomes for nonradiating nanofluid flow without heat source/sink.     

Soret and Dufour Effects on Non‐Darcy Free Convection in a Power‐Law Fluid in the Presence of a Magnetic Field and Stratification

In this article, effects of Soret and Dufour on free convection heat and mass transfer along a vertical plate embedded in a doubly stratified power‐law fluid‐ saturated non‐Darcy porous medium in the presence of a magnetic field is considered. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations, with the location along the plate as a parameter and then solved numerically. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 592–606, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21098     

Effect of Joule heating on MHD non‐Newtonian fluid flow past an exponentially stretching curved surface

The current endeavor examines the convective heat transfer characteristics on magnetohydrodynamic stagnation point flow of micropolar fluid past an exponential curved surface. The flow is supposed to be laminar and time‐independent. The influence of radiation, irregular heat source/sink, Joule heating, and variable thermal conductivity are supposed. Suitable similarity renovations are considered to transform the original partial differential equations as ordinary ones and then resolved by shooting and fourth‐order Runge–Kutta methods. Graphs are drawn to inspect the impacts of sundry nondimensional parameters on the distributions of velocity, microrotation, and temperature. We detect that there is an escalation in temperature with Eckert number and variable heat source/sink parameters. Also, it is motivating to comment that Biot number is an increasing function of local Nusselt number.     

Conjugate heat transfer from a circular cylinder to a power‐law non‐Newtonian fluid

In this paper, conjugate heat transfer from a circular cylinder with a heat source to a non‐Newtonian power‐law fluid is studied. Numerical calculations are carried out in an unconfined computational domain for Reynolds numbers (), power‐law indices (), and Prandtl numbers () with different heat source values. The pressure coefficient, value, and position of maximum temperature inside the cylinder and the local and average Nusselt number are calculated. Also, the effects of Re, Pr, n, and heat source value on the thermal characteristics in the solid cylinder and the fluid around it are studied and discussed.     

Fractional order simulation for unsteady MHD nanofluid flow in porous medium with Soret and heat generation effects

In this paper, unsteady magnetohydrodynamics nanofluid flow with thermo-diffusion and heat generation effects is studied. The fluid flow at the plate is considered exponentially accelerated through a porous medium. The governing system of equations is made dimensionless with the help of similarity transformation. A Caputo–Fabrizio fractional-order derivative is employed to generalize the momentum, energy, and concentration equations, and the exact expression is obtained using Laplace transformation techniques. To realize the physics of the problem, numerical results of velocity, temperature, and concentration profiles are obtained and presented through graphs. Also, the numerical values of the Nusselt number and Sherwood number are obtained and compared which strongly agree with the previous studies. From the results, it is concluded that velocity distribution decline by improving the value of the chemical reaction and magnetic field while the reverse trend is observed for volume fraction and micropolar parameter. It is also seen that the heat transfer process improves with heat generation and thermal radiation whereas, mass transfer declines with the chemical reaction parameter.     

Heat and mass transfer effects on MHD flow of a couple‐stress fluid in a horizontal wavy channel with viscous dissipation and porous medium

This paper looks at heat and mass transfer effects on an unsteady MHD flow of a couple‐stress fluid in a horizontal wavy porous space with travelling thermal waves in the presence of a heat source and viscous dissipation. Initially the temperatures of the walls are maintained at different constant temperatures. The analytical expressions for velocity, temperature, and concentration field are obtained by the regular perturbation technique. The results are presented graphically for various values of emerging dimensionless parameters of the problem and are discussed to show interesting aspects of the solution. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21040 PACS: 44.15.+a, 44.30.+f, 44.27.nd, 47.50.Cd     

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

In this paper, an attempt has been made to analyze the effects of various parameters, such as Soret and Dufour effects, chemical reaction, magnetic field, porosity on the fluid flow, and heat and mass transfer of an unsteady Casson fluid flow past a flat plate. Convective boundary conditions in heat and mass transfer and slip constant on velocity have been taken into account for analysis. The governing equations of the model have been solved numerically using the MATLAB program bvp4c. The impact of various parameters of the model on the velocity, temperature, and concentration profiles has been analyzed through different graphs. To get an insight into the physical quantities of engineering interest, viz, skin friction, Sherwood number, and Nusselt number, their numerical values have been computed for various parameters. The range of the parameters used in numerical computations are , , , , , , and . It has been noticed from the tabulated values that the skin friction gets enhanced with the increase in the thermal and solutal Grashof number, whereas its reverse effects have been observed with an increase in the Biot number. In limiting case, the present study is also compared with the available results in the literature.     

Hall and ion slip effects on MHD laminar flow of an elastico‐viscous (Walter's‐B) fluid

We investigated the magnetohydrodynamic (MHD) laminar flow of an elastico‐viscous electrically conducting (Walter's‐B) fluid through a circular cylinder or pipe, loosely packed with a porous material subjected to Hall and ion‐slip effects. The innovation of the study is to consider the entire flow domain without boundary layer approximation in the governing equations. Fully developed solutions of the velocity and pressure drop are obtained making use of perturbation approximation and computationally discussed with reference to flow governing parameters. It is quite exciting that the elastic parameter almost reduces the speed of the liquid in the center of the channel and then continuously expands into the cylinder. For engineering interest, we found the analytical solution and then computationally discussed for skin friction. The occurrence of a magnetic field and a porous matrix gives a fairly uneven flow between the pipes. Elasticity and suction are resistant to experience greater skin friction and are therefore useful for controlling flow separation. A porch has been made to include studies of non‐Newtonian fluids with Hall and ion‐slip effects due to the vast number of possible engineering applications, like power generators, MHD accelerators, refrigeration coils, electric transformers, and heating elements.     

Salient features of Dufour and Soret effect in radiative MHD flow of viscous fluid by a rotating cone with entropy generation

BackgroundHere physical characteristics of convective magnetohydrodynamic flow of viscous liquid subject to a rotating cone are discussed. Dissipation, Joule heating, thermal flux and heat generation/absorption are scrutinized in energy expression. Physical aspects of diffusion-thermo and thermo diffusion effect are deliberated. Thermo-diffusion is the mechanisms of transportation in which particles are transferred in a multi-factor mixture determined by temperature gradient. Furthermore irreversibility analysis is considered.MethodNonlinear partial differential system are reduced to ordinary one with the help of similarity variables. Here we implemented ND solve technique to get numerical results for given nonlinear system.ResultsCharacteristics of influential variables for entropy optimization, velocity, concentration, Bejan number and temperature are scrutinized. Numerical outcomes of gradient of velocity and Nusselt and Sherwood numbers are examined through tabulated form. Velocity components are declined against higher velocity slip parameters. For larger estimation of heat generation and radiation parameters the temperature is upsurges. Entropy generation and Bejan number are boost up via rising values of diffusion and radiation parameters. For larger estimation of Brinkman number both Bejan number and entropy rate have opposite effect. Comparative studies of the current and previous results are discussed in tabularized form and have a good agreement.     

A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

Numerical modelling of second‐grade fluid flow past a stretching sheet

The present numerical study reports the chemically reacting boundary layer flow of a magnetohydrodynamic second‐grade fluid past a stretching sheet under the influence of internal heat generation or absorption with work done due to deformation in the presence of a porous medium. To distinguish the non‐Newtonian behaviour of the second‐grade fluid with those of Newtonian fluids, a very popularly known second‐grade fluid flow model is used. The fourth order momentum equation with four appropriate boundary conditions along with temperature and concentration equations governing the second‐grade fluid flow are coupled and highly nonlinear in nature. Well‐established similarity transformations are efficiently used to reduce the dimensional flow equations into a set of nondimensional ordinary differential equations with the necessary conditions. The standard bvp4c MATLAB solver is effectively used to solve the fluid flow equations to get the numerical solutions in terms of velocity, temperature, and concentration fields. Numerical results are obtained for a different set of physical parameters and their behaviour is described through graphs and tables. The viscoelastic parameter enhances the velocity field whereas the magnetic and porous parameters suppress the velocity field in the flow region. The temperature field is magnified for increasing values of the heat source/sink parameter. However, from the present numerical study, it is noticed that the flow of heat occurs from sheet to the surrounding ambient fluid. Before concluding the considered problem, our results are validated with previous results and are found to be in good agreement.     

MHD Double‐diffusive thermosolutal Marangoni convection non‐Newtonian Casson fluid flow over a permeable stretchable sheet

In the present paper, we have discussed the thermosolutal Marangoni force acting on the electrically conducting Casson fluid flow over a permeable horizontal stretching surface. It is presumed that the condition at the interfaces is influenced by the surface tension, which is proportional to the temperature and concentration profiles. At the interface, both concentration and temperature are heated in such a way that they are quadratic functions in $x.$ Furthermore, we have introduced the magnetic field in the transverse direction of the fluid flow along with heat generation/absorption, thermal radiation, viscous dissipation, and first‐order chemical effect with heat and mass flux into the present system. Similarity transformations have been used to convert the system of the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The reduced ODEs are then solved using the MATLAB program bvp4c, which is based on the fourth‐order Runge‐Kutta and shooting method. The impact of various pertinent flow parameters on the flow field, temperature, and species concentration has been studied through graphs. To know the characteristics of shear stress, heat and mass rate near the boundary, numerical values of them are also calculated and given in the tabular form. The results show that the momentum boundary layer's thickness is getting thicker with an increase in solutal surface tension ratio, while its opposite trends have been observed in the thermal boundary layer region, this is due to the Marangoni effect. This Marangoni effect is very much important in the field of melting metals, crystal growth, welding, and electron beam.     

Entropy generation in an asymmetrically cooled slab with temperature‐dependent internal heat generation

The paper presents an entropy generation analysis for steady conduction in a slab with temperature‐dependent volumetric internal heat generation. The slab experiences asymmetric convective cooling on its two faces. The exact analytical solution for the temperature distribution is used to compute dimensionless local and total entropy generation rates in the slab. The total entropy generation rate depends on five dimensionless parameters: reference heat generation temperature Q, the heat generation–temperature variation parameter a, the temperature asymmetry parameter λ, and Biot numbers Bi₁ and Bi₂. Graphs illustrating the effect of these five parameters on the local and total entropy generation rates are presented and discussed. It is found that the total entropy generation in the slab can be minimized with a suitable choice of the cooling parameters. The paper corrects the flawed entropy results published recently. The present results for the special case of uniform internal heat generation confirm the results presented in a 2003 paper. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20404     

Numerical exploration of thermal radiation and Biot number effects on the flow of a non‐Newtonian MHD Williamson fluid over a vertical convective surface

A theoretical and computational study of the magnetohydrodynamic flow and free convection heat transfer in an electroconductive polymer on the external surface of a vertical plate under radial magnetic field is presented. The Biot number effects are considered at the vertical plate surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The nondimensional, transformed boundary layer equations for momentum and energy are solved with the second‐order accurate implicit Keller box finite difference method under appropriate boundary conditions. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Weissenberg number (ratio of the relaxation time of the fluid and time scale of the flow), magnetic body force parameter, stream‐wise variable, and Prandtl number on thermo fluid characteristics are studied graphically and via tables. A weak elevation in temperature accompanies increasing Weissenberg number, whereas a significant acceleration in the flow is computed near the vertical plate surface with increasing Weissenberg number. Nusselt number is reduced with increasing Weissenberg number. Skin friction and Nusselt number are both reduced with increasing magnetic field effect. The model is relevant to the simulation of magnetic polymer materials processing.