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.     

MHD flow and heat transfer over a stretching surface with variable thermal conductivity and partial slip

In this paper we analyze the flow and heat transfer of an MHD fluid over an impermeable stretching surface with variable thermal conductivity and non-uniform heat source/sink in the presence of partial slip. The governing partial differential equations of the problem are reduced to nonlinear ordinary differential equations by using a similarity transformation. The temperature boundary conditions are assumed to be linear functions of the distance from the origin. Analytical solutions of the energy equations for Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF) cases are obtained in terms of a hypergeometric function, without applying the boundary-layer approximation. The effects of the governing parameters on the flow and heat transfer fields are presented through tables and graphs, and they are discussed. Furthermore, the obtained numerical results for the skin friction, wall-temperature gradient and wall temperature are analyzed and compared with the available results in the literature for special cases.     

Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet

We study the MHD flow and also heat transfer in a viscoelastic liquid over a stretching sheet in the presence of radiation. The stretching of the sheet is assumed to be proportional to the distance from the slit. Two different temperature conditions are studied, namely (i) the sheet with prescribed surface temperature (PST) and (ii) the sheet with prescribed wall heat flux (PHF). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The resulting non-linear momentum differential equation is solved exactly. The energy equation in the presence of viscous dissipation (or frictional heating), internal heat generation or absorption, and radiation is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation using a new variable and using the Rosseland approximation for the radiation. The governing differential equations are solved analytically and the effects of various parameters on velocity profiles, skin friction coefficient, temperature profile and wall heat transfer are presented graphically. The results have possible technological applications in liquid-based systems involving stretchable materials.     

MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface

Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable sur- face in the presence of magnetic field. To achieve this, one parameter linear group trans- formation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method （HAM） to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non- Newtonian fluid （Powell-Eyring model） parameters ε and δon the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ε whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.     

A similarity solution for the flow and heat transfer over a moving permeable flat plate in a parallel free stream

This paper presents both a numerical and analytical study in connection with the steady boundary layer flow and heat transfer induced by a moving permeable semi-infinite flat plate in a parallel free stream. Both the velocities of the flat plate and the free stream are proportional to x ^1/3. The surface temperature is assumed to be constant. The governing partial differential equations are converted into ordinary differential equations by a new similarity transformation. Numerical results for the flow and heat transfer characteristics are obtained for various values of the moving parameter, transpiration parameter and the Prandtl number. Approximate analytical solutions are also obtained when the suction or injection parameter is very large. It is found that dual solutions exist for the case when the fluid and the plate move in the opposite directions.     

Numerical studies for flow and heat transfer of the Powell-Eyring fluid thin film over an unsteady stretching sheet with internal heat generation using the chebyshev finite difference method

An analysis is carried out to study the unsteady two-dimensional Powell-Eyring flow and heat transfer to a laminar liquid film from a horizontal stretching surface in the presence of internal heat generation. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of a similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of nonlinear ordinary differential equations. A numerical solution of the resulting nonlinear differential equations is found by using an efficient Chebyshev finite difference method. A comparison of numerical results is made with the earlier published results for limiting cases. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.     

MHD forced convection boundary layer flow with a flat plate and porous substrate

The flow and heat transfer for an electrically conducting fluid with a porous substrate and a flat plate under the influence of magnetic field is considered. The magnetic field is assumed to be uniform and also along normal to the surface. The momentum and energy equations are transformed to ordinary differential equations by using suitable similarity transformation and are solved by standard techniques. But the energy equation is solved by considering two boundary layers, one in the porous substrate and the other above the porous substrate. Numerical results are presented through graphs with various values of magnetic parameter for both velocity and thermal boundary layers along with Nusselt number and for various values of Prandtl number and Eckert number in thermal boundary layer.     

MHD free convective flow and mass transfer over a stretching sheet with chemical reaction

The effect of chemical reaction on free convective flow and mass transfer of a viscous, incompressible and electrically conducting fluid over a stretching surface is investigated in the presence of a constant transverse magnetic field. The non-linear boundary layer equations with the boundary conditions are transferred by a similarity transformation into a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results of the skin friction coefficient, the local Nusselt number Nu, the local Sherwood number Sh, as will as the velocity, temperature and concentration profiles are presented for gases with a Prandtl number of 0.71 for various values of chemical reaction parameter, order of reaction, magnetic parameter and Schmidt number.     

Effect of melting on an MHD micropolar fluid flow toward a shrinking sheet with thermal radiation

The effect of melting on a steady boundary layer stagnation-point flow and heat transfer of an electrically conducting micropolar fluid toward a horizontal shrinking sheet in the presence of a uniform transverse magnetic field and thermal radiation is studied. A similarity transformation technique is adopted to obtain self-similar ordinary differential equations, which are solved numerically. The present results are found to be in good agreement with previously published data. Numerical results for the dimensionless velocity and temperature profiles, as well as for the skin friction and the rate of heat transfer are obtained.     

Heat transfer in a radiating, nonsteady, three-dimensional stagnation flow

A similar solution has been obtained to the problem of simultaneous radiation and convection for nonsteady stagnation point flow over a three-dimensional blunt body with both boundary layer suction and injection. The diffusion approximation is used to characterize the radiative heat flux. The three-dimensional, time-dependent equations of motion and the energy equation have been transformed into a set of ordinary differential equations by the similarity transformation and the resulting ordinary differential equations have been solved numerically. The effects of accelerating and decelerating flow, the three-dimensional geometry, injection and suction, hot and cold wall conditions, and the conduction-to-radiation parameter on the temperature distribution within the flow have been investigated.     

Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating

The combined effects of viscous dissipation and Newtonian heating on boundary layer flow over a moving flat plate are investigated for two types of water-based Newtonian nanofluids containing metallic or nonmetallic nanoparticles such as copper (Cu) and titania (TiO₂). The governing partial differential equations are transformed into ordinary differential equations through a similarity transformation and are solved numerically by a Runge-Kutta-Fehlberg method with a shooting technique. The conclusions are that the heat transfer rate at the moving plate surface increases with the increases in the nanoparticle volume fraction and the Newtonian heating, while it decreases with the increase in the Brinkmann number. Moreover, the heat transfer rate at the moving plate surface with Cu-water as the working nanofluid is higher than that with TiO₂-water.     

Effect of non-uniform heat source on MHD heat transfer in a liquid film over an unsteady stretching sheet

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a laminar liquid film over a flat impermeable stretching sheet in the presence of a non-uniform heat source/sink. The basic unsteady boundary layer equations governing the flow and heat transfer are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformation. Numerical solutions of the resulting boundary value problem are obtained by the efficient shooting technique. The effects of magnetic and the non-uniform heat source/sink parameters on the dynamics are discussed. Findings of the paper reveal that non-uniform heat sinks are better suited for effective cooling of the stretching sheet. Skin friction coefficient and the local Nusselt number are also explored for typical values of magnetic and non-uniform heat source/sink parameters. The results are in excellent agreement with the earlier published works, under some limiting cases.     

MHD free convective flow past semi-infinite vertical permeable wall

In this paper,the basic equations governing the flow and heat transfer of an incompressible viscous and electrically conducting fluid past a semi-infinite vertical permeable plate in the form of partial differential equations are reduced to a set of non-linear ordinary differential equations by applying a suitable similarity transformation.Approximate solutions of the transformed equations are obtained by employing the perturbation method for two cases,i.e.,small and large values of the suction parameter.From the numerical evaluations of the solution,it can be seen that the velocity field at any point decreases as the values of the magnetic and suction parameters increase.The effect of the magnetic parameter is to increase the thermal boundary layer.It is also found that the velocity and temperature fields decrease with the increase in the sink parameter.     

Viscous dissipation and thermal radiation effects on the magnetohydrodynamic (MHD) flow and heat transfer over a stretching slender cylinder

An axisymmetric magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a fluid over a slender cylinder are investigated numerically. The effects of viscous dissipation, thermal radiation, and surface transverse curvature are taken into account in the simulations. For this purpose, the governing partial differential equations are transformed to ordinary differential equations by using appropriate similarity transformations. The resultant ordinary differential equations along with appropriate boundary conditions are solved by the fourth-order Runge–Kutta method combined with the shooting technique. The effects of various parameters on the velocity and temperature profiles, local skin friction coefficient, and Nusselt number are analyzed.     

Effect of temperature dependent viscosity on revolving axi-symmetric ferrofluid flow with heat transfer

The prime objective of the present study is to examine the effect of temperature dependent viscosity μ(T) on the revolving axi-symmetric laminar boundary layer flow of an incompressible, electrically non-conducting ferrofluid in the presence of a stationary plate subjected to a magnetic field and maintained at a uniform temperature. To serve this purpose, the non-linear coupled partial differential equations are firstly converted into the ordinary differential equations using well-known similarity transformations. The popular finite difference method is employed to discretize the non-linear coupled differential equations. These discretized equations are then solved using the Newton method in MATLAB, for which an initial guess is made with the help of the Flex PDE Solver. Along with the velocity profiles, the effects of temperature dependent viscosity are also examined on the skin friction, the heat transfer, and the boundary layer displacement thickness. The obtained results are presented numerically as well as graphically.     

Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field

In this paper, flow and heat transfer of a nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge–Kutta integration scheme featuring a shooting technique. Different types of nanoparticles as copper (Cu), silver (Ag), alumina (Al₂O₃) and titanium oxide (TiO₂) with water as their base fluid has been considered. The influence of significant parameters such as nanoparticle volume fraction, nanofluids type, magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. It was found that the Nusselt number increases as each of Reynolds number or nanoparticles volume fraction increase, but it decreases as magnetic parameter increase. Also it can be found that choosing copper (for small of magnetic parameter) and alumina (for large values of magnetic parameter) leads to the highest cooling performance for this problem.     

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet with prescribed surface heat flux

The similarity solution for the problem of mixed convection boundary layer flow adjacent to a stretching vertical sheet in an incompressible electrically conducting fluid in the presence of a transverse magnetic field is presented. It is assumed that the sheet is stretched with a power-law velocity and is subjected to a variable surface heat flux. The governing partial differential equations are first transformed into a system of non-linear ordinary differential equations, before being solved numerically by the Keller-box method. The numerical results obtained are then compared with previously reported cases available in the literature as well as the series solution for certain values of parameters, to support their validity. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed.     

Effects of slip,viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.     

Axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis

The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method (OHAM). The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.     

Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk

In this paper we have studied the effects of temperature dependent fluid properties such as density, viscosity and thermal conductivity and variable Prandtl number on unsteady convective heat transfer flow over a porous rotating disk. Using similarity transformations we reduce the governing nonlinear partial differential equations for flow and heat transfer into a system of ordinary differential equations which are then solved numerically by applying Nachtsheim–Swigert shooting iteration technique along with sixth-order Runge–Kutta integration scheme. Comparison with previously published work for steady case of the problem were performed and found to be in very good agreement. The obtained numerical results show that the rate of heat transfer in a fluid of constant properties is higher than in a fluid of variable properties. The results further show that consideration of Prandtl number as constant within the boundary layer for variable fluid properties lead unrealistic results. Therefore, modeling thermal boundary layers with temperature dependent fluid properties Prandtl number must treated as variable inside the boundary layer.