Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink

The boundary layer flow and heat transfer of a fluid through a porous medium towards a stretching sheet in presence of heat generation or absorption is considered in this analysis. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. These transformations are used to convert the partial differential equations corresponding to the momentum and the energy equations into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity decreases with increasing temperature-dependent fluid viscosity parameter up to the crossing-over point but increases after that point and the temperature decreases in this case. With the increase of permeability parameter of the porous medium the fluid velocity decreases but the temperature increases at a particular point of the sheet. Effects of Prandtl number on the velocity boundary layer and on the thermal boundary layer are studied and plotted.     

Impact of thermal radiation on MHD slip flow over a flat plate with variable fluid properties

The influence of partial slip, thermal radiation and temperature dependent fluid properties on the hydro-magnetic fluid flow and heat transfer over a flat plate with convective surface heat flux at the boundary and non-uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature respectively. Using the similarity transformation, the governing system of non-linear partial differential equations are transformed into similarity non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0. The numerical values obtained within the boundary layer for the dimensionless velocity, temperature, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed from the physical point of view.     

Slip effects on heat and mass transfer in MHD micropolar fluid flow over an inclined plate with thermal radiation and chemical reaction

The influence of partial slip, thermal radiation, chemical reaction and temperature‐dependent fluid properties on heat and mass transfer in hydro‐magnetic micropolar fluid flow over an inclined permeable plate with constant heat flux and non‐uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. With the use of the similarity transformation, the governing system of non‐linear partial differential equations are transformed into non‐linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0 (Wolfram Research, Champaign, IL). The numerical values obtained for the velocity, microrotation, temperature, species concentration, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed.Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.The study considers the effects of frictional heating(viscous dissipation) and internal heat generation or absorption.The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations.The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method.An analysis is carried out for two different cases of heating processes,namely,variable wall temperature(VWT) and variable heat flux(VHF).The effects of various physical parameters such as the magnetic parameter,the fluid-particle interaction parameter,the unsteady parameter,the Prandtl number,the Eckert number,the number density of dust particles,and the heat source/sink parameter on velocity and temperature profiles are shown in several plots.The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.     

Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material

The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel(formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium.The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates.The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles.Then,the skin friction and the rate of heat transfer are consequently derived.It is noticed that,at different sections within the vertical channel,the fluid flow and the temperature profiles increase with time,which are both higher near the moving plate.In particular,increasing the gap between the plates increases the velocity and the temperature of the fluid,however,reduces the skin friction and the rate of heat transfer.     

Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier's partial slip

In this paper, the effects of viscous and Ohmic heating and heat generation/absorption on magnetohydrodynamic flow of an electrically conducting Casson thin film fluid over an unsteady horizontal stretching sheet in a non-Darcy porous medium are investigated. The fluid is assumed to slip along the boundary of the sheet. Similarity transformation is used to translate the governing partial differential equations into ordinary differential equations. A shooting technique in conjunction with the 4 th order Runge-Kutta method is used to solve the transformed equations. Computations are carried out for velocity and temperature of the fluid thin film along with local skin friction coefficient and local Nusselt number for a range of values of pertinent flow parameters. It is observed that the Casson parameter has the ability to enhance free surface velocity and film thickness, whereas the Forchheimer parameter, which is responsible for the inertial drag has an adverse effect on the fluid velocity inside the film. The velocity slip along the boundary tends to decrease the fluid velocity. This investigation has various applications in engineering and in practical problems such as very large scale integration(VLSI) of electronic chips and film coating.     

Radiation Effect on MHD Free Convection Flow of a Gas Past a Semi-infinite Vertical Plate with Variable Viscosity

The radiation effect in the presence of a uniform transverse magnetic field on steady free convection flow with variable viscosity is investigated. The fluid viscosity is assumed to vary as the reciprocal of a linear function of temperature. Boundary layer equations are derived. The resulting approximate non-linear ordinary differential equations are solved linearly and nonlinearly by shooting methods. The velocity and temperature profiles are shown, and the skin friction on the plate and heat transfer coefficient are presented and discussed. The results of the present study show that in the presence of magnetic field, as the radiation parameter increases the temperature increases, but the velocity decreases.     

Effect of local thermal non-equilibrium on unsteady heat transfer by natural convection of a nanofluid over a vertical wavy surface

This paper uses thermal non-equilibrium model to study transient heat transfer by natural convection of a nanofluid over a vertical wavy surface. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Three-temperature model is applied to represent the local thermal non-equilibrium among the particle, fluid, and solid-matrix phases. Finite difference method is used to solve the dimensionless governing equations of the problem. The obtained results are displayed in 2D graphs to illustrate the influences of the different physical parameters on local skin-friction coefficient, local Nusselt numbers for fluid, particle and solid phases and local Sherwood number. The results for velocity component, nanoparticle volume fraction, fluid temperature, particle temperature and solid-matrix temperature are presented in 3D graphs as a function of the axial and transverse coordinates. All the obtained results are discussed.     

Radiative mixed convection flow of an Oldroyd-B fluid over an inclined stretching surface

A mixed convection flow of an Oldroyd-B fluid in the presence of thermal radiation is investigated. The flow is induced by an inclined stretching surface. The boundary layer equations of the Oldroyd-B fluid in the presence of heat transfer are used. Appropriate transformations reduce partial differential equations to ordinary differential equations. A computational analysis is performed for convergent series solutions. The values of the local Nusselt number are numerically analyzed. The effects of various parameters on velocity and temperature are discussed.     

Effects of thermal radiation on MHD viscous fluid flow and heat transfer over nonlinear shrinking porous sheet

This paper investigates the effects of thermal radiation on the magnetohy-drodynamic (MHD) flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent viscosity and the thermal conductivity are also assumed to vary as an inverse function and a linear function of the temperature, respectively. A generalized similarity transformarion is used to reduce the governing partial differential equations to their nonlinear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concern with the velocity and temperature profiles as well as the local skin-friction coefficient and the rate of the heat transfer at the porous sheet for different values of several physical parameters of interest.     

Stagnation-point flow of couple stress fluid with melting heat transfer

Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.     

Effect of thermal dispersion on free convection in a fluid saturated porous medium

The present article considers a numerical study of thermal dispersion effect on the non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. Forchheimer extension is considered in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The non-dimensional governing equations are solved by the finite element method (FEM) with a Newton–Raphson solver. Numerical results for the details of the stream function, velocity and temperature contours and profiles as well as heat transfer rates in terms of Nusselt number are obtained. The study shows that the increase in thermal dispersion coefficient of the porous medium results in more heat energy to disperse away in the normal direction to the wall. This induces more fluid to flow along the wall, enhancing the heat transfer coefficient particularly near the wall.     

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.     

Effects of thermal radiation and variable fluid viscosity on stagnation point flow past a porous stretching sheet

Similarity analysis is performed to investigate the structure of the boundary layer stagnation-point flow and heat transfer over a stretching sheet subject to suction. Fluid viscosity is assumed to vary as a linear function of temperature. Thermal radiation term is considered in the energy equation. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. With the help of them the partial differential equations corresponding to momentum and energy equations are transformed into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing values of the ratio of the free stream velocity to the stretching velocity. Velocity increases with the increasing temperature dependent fluid viscosity parameter when the free-stream velocity is less than the stretching velocity but opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. Temperature at a point of the surface is found to decrease with increasing thermal radiation.     

Magnetohydrodynamic and heat transfer effects on the stagnation-point flow of an electrically conducting nanofluid past a porous vertical shrinking/stretching sheet in the presence of variable stream conditions

A steady two-dimensional magnetohydrodynamic stagnation-point flow of an electrically conducting fluid and heat transfer with thermal radiation of a nanofluid past a shrinking and stretching sheet is investigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis. A similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher-order nonlinear ordinary differential equations. The result shows that the velocity, temperature, and concentration profiles are significantly influenced by the Brownian motion, heat radiation, and thermophoresis particle deposition.     

Free Convection Heat Transfer over a Vertical Cylinder in a Saturated Porous Medium Using a Local Thermal Non-equilibrium Model

In this article, free convection heat transfer over a vertical cylinder with variable surface temperature distributions in a porous medium is analyzed. It is assumed that the fluid and solid phases are not in local thermal equilibrium and, therefore, a two-temperature model of heat transfer is applied. The coupled momentum and energy equations are presented and then they are transformed into ordinary differential equations. The similarity equations are solved numerically. The resulting velocity, streamlines, temperature distributions for fluid and solid phases are shown for different values of parameters entering into the problem. The calculated values of the local Nusselt numbers for both solid and fluid phases are also shown.     

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.     

Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation

The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.     

Boundary layer flow of Oldroyd-B fluid by exponentially stretching sheet

The present paper investigates the steady flow of an Oldroyd-B fluid. The fluid flow is induced by an exponentially stretched surface. Suitable transformations reduce a system of nonlinear partial differential equations to a system of ordinary differential equations. Convergence of series solution is discussed explicitly by a homotopy analysis method (HAM). Velocity, temperature and heat transfer rates are examined for different involved parameters through graphs. It is revealed that for a larger retardation time constant, the velocity is enhanced and the temperature is lowered. It is noted that relaxation time constant and the Prandtl number enhance the heat transfer rate.