Non‐Darcian Unsteady Flow of a Micropolar Fluid over a Porous Stretching Sheet with Thermal Radiation and Chemical Reaction

An analysis is presented to investigate the effects of a chemical reaction on an unsteady flow of a micropolar fluid over a stretching sheet embedded in a non‐Darcian porous medium. The governing partial differential equations are transformed into a system of ordinary differential equations by using similarity transformation. The resulting nonlinear coupled differential equations are solved numerically by using a fourth‐order Runge–Kutta scheme together with shooting method. The influence of pertinent parameters on velocity, angular velocity (microrotation), temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number has been studied and numerical results are presented graphically and in tabular form. Comparisons with previously published work are performed and the results are found to be in excellent agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21090     

Thermophoretic Deposition Effect on Transient Free Convection Hydromagnetic Flow Along an Accelerated Inclined Permeable Surface with Time‐Dependent Temperature and Concentration

This work investigates the thermophoretic deposition effect on a transient free convection hydromagnetic flow along an accelerated infinite inclined permeable surface in the presence of heat generation, suction (or injection), thermal diffusion, and diffusion‐thermo taking into account that the surface temperature and concentration are time dependent. The governing partial differential equations are transformed into a set of nonlinear coupled ordinary differential equations, which are then solved numerically by applying the shooting method with a sixth‐order Runge–Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, concentration distributions as well as wall thermophoretic velocity are reported and examined for the pertinent parameters showing the interesting aspects of the obtained solutions. The local skin‐friction coefficient, the local Nusselt number, and the local Sherwood number are also computed. The results show that higher flow rates can be obtained when the temperature and concentration are time independent. Smaller buoyancy is observed for higher temperature indexes. Wall thermophoretic velocity is decreased with the increasing values of the Prandtl number, the thermophoretic parameter, as well as heat generation parameter. The results further show that the presence of thermal diffusion and diffusion‐thermo intensify the shear stress but reduce the rate of heat as well as mass transfer. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 352–367, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21081     

Analysis of heat and chemical reaction on an asymmetric laminar flow between slowly expanding or contracting walls

The present study investigates the effects of heat and mass transfer on asymmetric laminar flow in a porous channel with expanding or contracting walls in the presence of a chemical reaction. Both walls are assumed to have different permeabilities and expand or contract uniformly at a time‐dependent rate. The governing equations are reduced to ordinary differential equations by using similarity transformation. A perturbation technique in the permeation Reynolds number and wall dilation ratio is employed to obtain the analytical solutions. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21036 PACS: 47.15, 47.63.mf, 44.25+f, 47.70. Fw     

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     

Analysis of Gaseous Flow Between Parallel Plates by Second‐ Order Velocity Slip and Temperature Jump Boundary Conditions

In this study the momentum and energy equations are solved to analyze the flow between two parallel plates by employing second‐order velocity slip and temperature jump conditions. The flow is considered to be laminar, incompressible, hydrodynamically/thermally fully developed, and steady state. In addition to the isoflux condition, viscous dissipation is included in the analysis. Closed form expressions for the temperature field and Nusselt number are obtained as a function of the Knudsen number and Brinkman number. The Nusselt number obtained by employing the second‐order model is found to be lower compared to the continuum value and agrees well with the other theoretical models. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21116     

Unsteady MHD Mixed Convective Boundary‐Layer Slip Flow and Heat Transfer with Thermal Radiation and Viscous Dissipation

A numerical analysis has been carried out to investigate the problem of MHD boundary‐layer flow and heat transfer of a viscous incompressible fluid over a moving vertical permeable stretching sheet with velocity and temperature slip boundary condition. A problem formulation is developed in the presence of radiation, viscous dissipation, and buoyancy force. A similarity transformation is used to reduce the governing boundary‐layer equations to coupled higher‐order nonlinear ordinary differential equations. These equations are solved numerically using the fourth‐order Runge–Kutta method along with shooting technique. The effects of the governing parameters such as Prandtl number, buoyancy parameter, slip parameter, magnetic parameter, Eckert Number, suction, and radiation parameter on the velocity and temperature profiles are discussed and shown by plotting graphs. It is found that the temperature is a decreasing function of the slip parameter S_T. The results also indicate that the cooling rate of the sheet can be improved by increasing the buoyancy parameter. In addition the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. The numerical results are compared and found to be in good agreement with previously published results on special cases of the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 412–426, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21086     

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     

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     

MHD flow over an inclined radiating plate with the temperature‐dependent thermal conductivity,variable reactive index,and heat generation

We study the effects of higher‐order chemical reaction and heat generation on coupled heat and mass transfer by MHD mixed convection from a permeable radiating inclined plate with the thermal convective boundary condition. The governing boundary layer equations are formulated and transformed into a set of similarity equations using dimensionless similarity variables developed by Lie group analysis. The resulting equations are then solved numerically using Maple 13 which uses a fourth–fifth order Runge–Kutta–Fehlberg algorithm for solving nonlinear boundary value problems. A representative set of numerical results are displayed graphically and discussed to show some interesting aspects of the parameters: convective heat transfer (γ), the angle of inclination (α), generation order of chemical reaction (n), reaction rate (λ), the Prandtl number (Pr), and the Schmidt number (Sc) on the dimensionless axial velocity, the temperature, and the concentration profiles. Also effects of pertinent parameters on the skin friction factor, the rate of heat, and the rate of mass transfer are obtained and displayed in tabular form. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20409     

Casson fluid flow and heat transfer past a symmetric wedge

Boundary‐layer forced convection flow of a Casson fluid past a symmetric wedge is investigated. Similarity transformations are used to convert the governing partial differential equations to ordinary ones and the reduced equations are then solved numerically with the help of the shooting method. Comparisons with various previously published works on special cases are performed and the results are found to be in excellent agreement. A representative set of graphical results is obtained and illustrated graphically. The velocity is found to increase with an increasing Falkner–Skan exponent whereas the temperature decreases. With the rise of the Casson fluid parameter, the fluid velocity increases but the temperature is found to decrease in this case. The skin friction decreases with increasing values of the Casson fluid parameter. It is found that the temperature decreases as the Prandtl number increases and thermal boundary layer thickness decreases with increasing values of the Prandtl number. A significant finding of this investigation is that flow separation can be controlled by increasing the value of the Casson fluid parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 665–675, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21065     

Numerical Investigation of Nanofluid Mixed‐Convection Flow in the Entrance Region of a Vertical Channel Partially Filled with Porous Medium

In this article, transient two‐dimensional mixed convection of nanofluids in the entrance region of a vertical channel has been studied carefully. The geometry under consideration consisted of a parallel‐plate channel partly filled with a porous medium with a constant wall temperature. In the free flow region, the two‐dimensional flow field has been governed by the Navier–Stokes equations. The general formulation of the momentum equations accounting for the inertial and the viscous effects in the presence of a porous medium has been used. Viscous dissipation effects have also been incorporated in the thermal energy equation. Effects of Brownian diffusion and thermophoresis have also been included for nanoparticles in the nanofluid. The governing equations have been given in terms of the stream function‐vorticity formulation and have been non‐dimensionalized and then solved numerically subject to appropriate boundary conditions. The characteristics of the flow and temperature fields have been presented in the terms of mixed‐convection parameter (GR), Brinkman number (Br), Darcy number (Da), Lewis number (Le), and other important parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 607–627, 2014; Published online 21 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21099     

Flow and Heat Transfer of Maxwell Fluid Over an Exponentially Stretching Sheet: A Non‐similar Solution

In this investigation, the boundary layer flow and heat transfer analysis in a Maxwell fluid over an exponentially continuous moving sheet are studied. The transformed boundary layer equations are solved numerically for a non‐similar solution using a shooting method with the Runge–Kutta algorithm. The purpose of this article is to look into the influence of the Deborah number on the velocity, temperature, and Nusselt number. The obtained results show that an increase in the Deborah number decreases the fluid velocity and boundary layer thickness. On the other hand, it increases the temperature and thermal boundary layer thickness. It is also found that the numerical results are in excellent agreement with the previous existing results for the case of a Newtonian fluid (λ = 0). © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 233–242, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21074     

Double Diffusive Flows over a Stretching Sheet of Variable Thickness with or without Surface Mass Transfer

This paper presents a numerical investigation of the steady two‐dimensional mixed convection flow along a vertical semi‐infinite stretching sheet of variable thickness. The effect of double diffusion on velocity, thermal and concentration fields in presence of power‐law temperature and concentration distributions at wall along with surface mass transfer is considered. The nonlinear coupled partial differential equations governing the flow, thermal and concentration fields are first transformed into a nondimensional set of coupled nonlinear partial differential equations and solved numerically using an implicit finite‐difference scheme in combination with the Newton's linearization technique to obtain nonsimilar solutions at each stream‐wise location. Numerical results are presented to discuss the effects of various physical parameters on the velocity, temperature, and concentration fields. Furthermore, the numerical results for the local skin friction coefficient, local Nusselt number, and local Sherwood number are also reported. For a fixed buoyancy force, the skin friction coefficient and Nusselt number increase with Prandtl number. The increase in the Prandtl number causes about a 30% reduction in the thickness of the thermal boundary layer. The wall thickness parameter enhances the thickness of the momentum boundary layer and the velocity overshoot is observed up to 20% for wall thickness parameter . In contrast, the increase of power‐law index parameter m from to reduces approximately 10% to 25% the momentum and thermal boundary layer thicknesses depending on the values of other parameters     

A Mathematical Study for Laminar Boundary‐Layer Flow,Heat, and Mass Transfer of a Jeffrey Non‐Newtonian Fluid Past a Vertical Porous Plate

In this article, we investigate the nonlinear steady‐state boundary‐layer flow, heat and mass transfer of an incompressible Jeffrey non‐Newtonian fluid past a vertical porous plate. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite‐difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non‐dimensional parameters, namely, Deborah number (De), Prandtl number (Pr), ratio of relaxation to retardation times (λ), Schmidt number (Sc), and dimensionless tangential coordinate (ξ) on velocity, temperature, and concentration evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate, mass transfer rate, and local skin friction are also investigated. It is found that the velocity is reduced with increasing Deborah number whereas temperature and concentration are enhanced. Increasing λ enhances the velocity but reduces the temperature and concentration. The heat transfer rate and mass transfer rates are found to be depressed with increasing Deborah number, De, and enhanced with increasing λ. Local skin friction is found to be decreased with a rise in Deborah number whereas it is elevated with increasing λ. And an increasing Schmidt number decreases the velocity and concentration but increases temperature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21111     

Effects of Thermal‐Diffusion,Diffusion‐Thermo,and Space Porosity on MHD Mixed Convective Flow of Micropolar Fluid in a Vertical Channel with Viscous Dissipation

This paper examines thermal‐diffusion and diffusion‐thermo effects on the fully developed MHD flow of a micropolar fluid through a porous space in a vertical channel with asymmetric wall temperatures and concentrations. The homotopy analysis method (HAM) is adopted to obtain the approximate analytical solution for the velocity, micro‐rotation, temperature, and concentration field. The convergence and the accuracy of the solutions are discussed. The role of pertinent parameters on the heat and mass transfer characteristics of the flow are presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 561–576, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21100     

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     

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     

Onset of Darcy‐Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer with Internal Heat Source

The onset of Darcy‐Brinkman convection in a binary viscoelastic fluid‐saturated sparsely packed porous layer with an internal heat source is studied using both linear and nonlinear stability analyses. The Oldroyd‐B model is employed to describe the rheological behavior of binary fluid. An extended form of the Darcy‐Oldroyd law incorporating Brinkman's correction and time derivative is used to describe the flow through a porous layer. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. There is a competition between the processes of thermal diffusion, solute diffusion, and viscoelasticity that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effect of internal Rayleigh number, relaxation and retardation parameters, solute Rayleigh number, Darcy number, Darcy‐Prandtl number, and Lewis number on the stability of a system is investigated and is shown graphically. The nonlinear theory based on the truncated representation of the Fourier series method is used to find heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained using numerical methods. Some known results are recovered for the particular cases of the present study. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 676–703, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21056     

Soret Effect on Darcy–Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer

A linear and weakly nonlinear stability analyses is performed to study the onset of Darcy–Brinkman double diffusive convection in a binary viscoelastic fluid‐saturated porous layer in the presence of the Soret effect. The modified Darcy–Brinkman–Oldroyd model including the time derivative term is employed for the momentum equation. The expressions for stationary, oscillatory, and finite amplitude Rayleigh number are obtained as a function of the governing parameters. There is a competition between the processes of the Soret coefficient, viscoelasticity, thermal diffusion, and solute diffusion that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effects of the Soret parameter, Darcy number, relaxation and retardation parameters, and Darcy–Prandtl number on the stationary, oscillatory, and finite amplitude convection is shown graphically. The weakly nonlinear theory is based on truncated representation of the Fourier series method and is used to find the Nusselt and Sherwood numbers. Further, the transient behavior of the Nusselt and Sherwood numbers is investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta method. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 297–320, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21076     

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