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     

Numerical Study of Heat and Mass Transfer MHD Viscous Flow Over a Moving Wedge in the Presence of Viscous Dissipation and Heat Source/Sink with Convective Boundary Condition

In this article, the effects of viscous dissipation and internal heat generation/absorption on combined heat and mass transfer MHD viscous fluid flow over a moving wedge in the presence of mass suction/injection with the convective boundary condition are carried out numerically for the various values of dimensionless parameters. With the help of similarity transformation, the momentum, energy, and concentration equations are reduced to a set of dimensionless non‐linear ordinary differential equations. The significance of the dimensionless velocity, temperature, mass profiles, and their gradients are presented in graphical form. Three types of flows—particularly the flat plate, vertical wedge, and stagnation point flows—in favorable and unfavorable regimes are analyzed. The obtained results confirm that the flow field is substantially influenced by the magnetic, stretching/shrinking, pressure, Prandtl number, heat generation/dissipation, and mass suction/injection parameters. Current results indicate that stretching a wall boundary causes an increase in velocity, temperature, shear stress, temperature, and mass gradients while shrinking causes a decreasing trend with these profiles. The special modified form of the current problem is found to be in good agreement with the other published data. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 17–38, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21063     

MHD Mixed Convection and Mass Transfer Due to Unsteady Stretching Sheet

Heat and mass transfer in the flow of a viscous incompressible fluid along a vertical isothermal unsteady stretching sheet in the presence of heat generation and a transverse magnetic field is investigated. The governing equations of continuity, momentum, energy, and species concentration are transformed into a system of nonlinear ordinary differential equations and solved numerically by using the Runge–Kutta fourth‐order method with shooting technique. The velocity, temperature, and concentration distributions are discussed numerically and shown through graphs. The expressions of skin‐friction coefficient, Nusselt number, and Sherwood number at the sheet are discussed numerically and their variations are presented through tables. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 447–458, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21088     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114     

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     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

Analytical solution for slip flow and heat transfer due to a stretching sheet

An analysis has been carried out to investigate the analytical solution to the flow and heat transfer characteristics of a viscous flow over a stretching sheet in the presence of second‐order slip in flow. The governing partial differential equations of flow and heat transfer are converted into non‐linear ordinary differential equations by using suitable similarity transformations. The exact solution of momentum equation is assumed in exponential form and analytical solutions of heat transfer for both PST and PHF cases are obtained by the power series method in terms of Kummer's hypergeometric function. The temperature profiles are drawn for different governing parameters. The numerical values of wall temperature gradient and wall temperature are compared with earlier numerical results which have a good agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21044     

Coupled heat and mass transfer by MHD free convection flow along a vertical plate with streamwise temperature and species concentration variations

The problem of steady, laminar, coupled heat and mass transfer by MHD free convective boundary‐layer flow along a vertical flat plate with the combined effects of streamwise sinusoidal variations of both the surface temperature and the species concentration in the presence of Soret and Dufour effects is considered. A suitable set of dimensionless variables is used to transform the governing equations of the problem into a non‐similar form. The resulting non‐similar equations have the property that they reduce to various special cases previously considered in the literature. An adequate and efficient implicit, tri‐diagonal finite difference scheme is employed for the numerical solution of the obtained equations. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the velocity, temperature, and concentration profiles as well as the surface shear stress, rate of heat transfer, and the rate of mass transfer is presented graphically for various parametric conditions and is discussed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21033     

Effects of slip conditions on stretching flow with ohmic dissipation and thermal radiation

The present work addresses the magnetohydrodynamic (MHD) flow and heat transfer over a permeable stretching sheet. Analysis has been carried out in the presence of thermal radiation and ohmic dissipation. The velocity and thermal slip effects are given main attention. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non‐linear partial differential equations are reduced to a set of non‐linear ordinary differential equations which are solved analytically by the homotopy analysis method (HAM). The effects of emerging physical parameters on the velocity and temperature profiles are interpreted. Numerical data for skin friction coefficient and Nusselt number have been tabulated for various values of the parameters. The results have been compared with the known exact solution from the literature in a limiting sense. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20367     

Effect of double stratification on mixed convection heat and mass transfer from a vertical surface in a fluid‐saturated porous medium

This paper presents the mixed convection heat and mass transfer near a vertical surface in a stratified porous medium using an integral method. The conservation equations that govern the problem are reduced to a system of coupled non‐linear ordinary differential equations, which is then reduced into a single algebraic equation using exponential profiles for the temperature and concentration. The results for heat and mass transfer rates in terms of Nusselt and Sherwood number are presented for a wide range of governing parameters like the buoyancy ratio (N), Lewis number (Le), flow driving parameter (Ra/Pe), in addition to both thermal and solutal parameters (S and R). The results indicate that the stratification effects have considerable influence on both the heat and mass transfer rates. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20300     

Heat and mass transfer effects on peristaltic flow of an Oldroyd‐B fluid in a channel with compliant walls

This investigation describes the peristaltic motion of a magnetohydrodynamic (MHD) Oldroyd‐B fluid with heat and mass transfer. An incompressible Oldroyd‐B fluid is considered in a channel with flexible walls. The relevant equations are developed by employing equations of continuity, momentum, energy, and concentration. Expressions of stream function, temperature, concentration field, and heat transfer coefficient are presented when the wave number is small. The obtained solutions are graphically discussed for the several interesting parameters entering into the problem. It is found that relaxation and retardation times have opposite effects on the size of the trapped bolus. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20380     

Unsteady MHD mixed convection flow of a micropolar fluid along an inclined stretching plate

In this research, the unsteady magnetohydrodynamic mixed convection flow of a micropolar fluid over an inclined plate has been investigated. The problem is reduced to a system of non‐dimensional partial differential equations, which are solved numerically using the implicit finite‐difference scheme. Velocity profiles, temperature profiles, concentration profiles, the skin friction coefficient, the rate of heat transfer, and the rate of mass transfer are computed numerically for various values of different physical parameters. In this study, we consider both assisting and opposing flow. It is found that in the assisting flow case, a solution could be obtained for all positive values of the buoyancy parameter λ, while in the opposing flow case the solution terminated at $\lambda = {\lambda _c}(\lambda < 0)$ . © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21034     

Mixed convective heat and mass transfer on a peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel

In the present analysis we discuss the effects of mixed convective heat and mass transfer on the peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel. The flow is investigated in a wave frame of reference moving with the velocity c away from the fixed frame. The governing equations for the present flow problem are first modeled and then discussed. The analytical solution of the present flow problem is discussed using regular perturbation technique. The graphical results are discussed to see the effects of various physical parameters of interest. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21020     

Influence of heat transfer on the nonorthogonal stagnation point flow of a third‐order fluid towards a stretching surface

The present article looks at the theoretical analysis of a steady stagnation‐point flow with heat transfer of a third‐order fluid towards a stretching surface. The formulation of the problem has been carried out for a third order fluid and constructed partial differential equations are rehabilitated into ordinary differential equations. The consequential ordinary differential equations are solved analytically using the homotopy analysis method (HAM). Graphical illustrations are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients and heat flux are computed and presented through tables. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21042     

Mixed convection heat and mass transfer over a vertical plate in a power‐law fluid‐saturated porous medium with radiation and chemical reaction effects

Mixed convection heat and mass transfer from a vertical plate embedded in a power‐law fluid‐saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using the shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21058     

Solutal Dispersion and Viscous Dissipation Effects on Non‐Darcy Free Convection Over a Cone in Power‐Law Fluids

The effects of viscous dissipation and solutal dispersion on free convection about an isothermal vertical cone with a fixed apex half angle, pointing downwards in a power‐law fluid‐saturated non‐Darcy porous medium are analyzed. The governing partial differential equations are transformed into partial differential equations using non‐similarity transformation. The resulting equations are solved numerically using an accurate local non‐similarity method. The accuracy of the numerical results is validated by a quantitative comparison of the heat and mass transfer rates with previously published results for a special case and the results are found to be in good agreement. The effects of viscous dissipation, solutal dispersion, and/or buoyancy ratio on the velocity, temperature, and concentration field as well as on the heat and mass transfer rates are illustrated, by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 476–488, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21095     

Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

The present study considers two‐dimensional mathematical modeling of non‐Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second‐grade differential viscoelastic constitutive model is adopted for blood to mimic non‐Newtonian characteristics, and blood is considered to contain a homogenous suspension of nanoparticles. The Vogel model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier‐Stokes equations with linear Boussinesq's approximation and Buongiorno's nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate nondimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery, and, furthermore, that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nanoparticle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid‐independence study is included. Blood flow, heat, and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity, and magnetic parameters, that is, stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (), Brownian motion parameter (), and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature, and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration, and skin‐friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nanoparticle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multiphysical nanoscale, and thermomagnetic behavior, and also the simultaneous presence of biorheological behavior (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat, and mass transfer characteristics. The simulations are relevant to the diffusion of nano‐drugs in magnet‐targeted treatment of stenosed arterial disease.     

Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate

This paper discusses the unsteady flow and heat transfer of a Casson fluid over a moving flat plate with a parallel free stream. The analytic solutions of the system of nonlinear partial differential equations valid for all times in the whole spatial domain are constructed in the series form by a homotopic approach. The influences of the governing parameters on the velocity, temperature, skin friction coefficient, and local Nusselt number are thoroughly investigated. It is revealed that an increase in the dimensionless time decreases the velocity and enhances the temperature. The surface shear stress and surface heat transfer are enhanced by increasing the Casson fluid parameter (β) and Eckert number (Ec), respectively. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20358     

Stagnation‐point flow of Maxwell fluid with magnetic field and radiation effects

The effect of heat transfer on the steady two‐dimensional stagnation point flow of a Maxwell fluid over a stretching sheet is discussed. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The radiation effect in the energy equation is taken into account. The arising nonlinear problem is solved by a homotopy analysis method (HAM). Convergence of the series solutions is checked. The values of skin friction coefficient and local Nusselt number have been computed and discussed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20385     

MHD Flow and Heat Transfer of a Dusty Fluid Over a Stretching Hollow Cylinder with a Convective Boundary Condition

In this study, we deal with the problem of a steady two‐dimensional magnetohydrodynamic (MHD) flow of a dusty fluid over a stretching hollow cylinder. Unlike the commonly employed thermal conditions of constant temperature or constant heat flux, the present study uses a convective heating boundary condition. The multi‐step differential transform method (multi‐step DTM), one of the most effective methods, is employed to find an approximate solution of the system of highly nonlinear differential equations governing the problem. Comparisons are made between the results of the proposed method and the numerical method in solving this problem and excellent agreement has been observed. The influence of important parameters on the flow field and heat transfer characteristics are presented and discussed in detail. The results show that both the thermal boundary layer thickness and the heat transfer rate at the wall increases with increasing Biot number Bi, while it has no effect on the skin friction coefficient. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 221–232, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21073