The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet

An analysis has been carried out to study the momentum and heat transfer characteristics in an incompressible electrically conducting non-Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly non-linear coupled ordinary differential equations by similarity transformations. The effect of variable fluid viscosity, Magnetic parameter, Prandtl number, variable thermal conductivity, heat source/sink parameter and thermal radiation parameter are analyzed for velocity, temperature fields, and wall temperature gradient. The resultant coupled highly non-linear ordinary differential equations are solved numerically by employing a shooting technique with fourth order Runge–Kutta integration scheme. The fluid viscosity and thermal conductivity, respectively, assumed to vary as an inverse and linear function of temperature. The analysis reveals that the wall temperature profile decreases significantly due to increase in magnetic field parameter. Further, it is noticed that the skin friction of the sheet decreases due to increase in the Magnetic parameter of the flow characteristics.     

Unsteady flow and heat transfer of a second grade fluid over a stretching sheet

The problem of unsteady boundary layer flow of a second grade over a stretching sheet is investigated in this paper. The governing equations of motion are reduced into a partial differential equation with two independent variables by using similarity transformations. The heat transfer analysis has been also carried out for two heating processes namely the prescribed surface temperature (PST case) and prescribed surface heat flux (PHF case). The series solutions of the problem are developed by employing homotopy analysis method (HAM). Convergence of the obtained series solutions are analyzed. It is noted that the present solutions of a second grade are valid for all dimensionless times. Finally, the results are obtained and discussed through graphs for various parameters of interest.     

Second-order fluid flow past a stretching sheet with heat transfer

Summary The heat transfer in the flow of a second-order fluid, obeying Coleman and Noll's constitutive equation based on the postulate of gradually fading memory, over a stretching sheet has been studied. The boundary layer characteristics of this flow have been obtained. The velocity boundary layer thickness decreases for increasing values of the parameterKC/v. The thermal boundary layer thickness decreases and the Nusselt numberNu _x increases for increasing Prandtl numberP _r orC.     

Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity,non-uniform heat source and radiation

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.     

Stagnation slip flow and heat transfer over a nonlinear stretching sheet

Stagnation slip flow and heat transfer characteristics of a viscous fluid over a nonlinear stretching surface has been investigated. The governing partial differential equations are transformed to nonlinear ordinary differential equations using similarity transformations. The analytical solution of the nonlinear system is obtained in series form using the very efficient homotopy analysis method (HAM). Convergence of the series solution is shown explicitly. Important features of flow and heat transfer characteristics are plotted and discussed. Comparison is made with existing numerical results when the stagnation‐point and slip effects are excluded. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

MHD flow of a Newtonian fluid over a stretching sheet: an approximate solution

An approximate solution to the problem of steady laminar flow of a viscous incompressible electrically conducting fluid over a stretching sheet is presented. The approach is based on the idea of stretching the variables of the flow problem and then using least squares method to minimize the residual of a differential equation. The effects of the magnetic field on the flow characteristics are demonstrated through numerical computations with different values of the Hartman number.     

Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with non-uniform heat source/sink

This paper presents the study of momentum and heat transfer characteristics in a hydromagnetic flow of viscoelastic liquid over a stretching sheet with non-uniform heat source, where the flow is generated due to a linear stretching of the sheet and influenced by uniform magnetic field applied vertically. Here an analysis has been carried out to study the effect of magnetic field on the visco-elastic liquid flow and heat transfer over a stretching sheet with non-uniform heat source. The non-linear boundary layer equation for momentum is converted into ordinary differential equation by means of similarity transformation and is solved exactly. Heat transfer differential equation is also solved analytically. The effect of magnetic field on velocity, skin friction and temperature profiles are presented graphically and discussed.     

Biomagnetic viscoelastic fluid flow over a stretching sheet

Of concern in this paper is an investigation of biomagnetic flow of a non-Newtonian viscoelastic fluid over a stretching sheet under the influence of an applied magnetic field generated owing to the presence of a magnetic dipole. The viscoelasticity of the fluid is characterised by Walter’s B fluid model. The applied magnetic field has been considered to be sufficiently strong to saturate the ferrofluid. The magnetization of the fluid is considered to vary linearly with temperature as well as the magnetic field intensity. The theoretical treatment of the physical problem consists of reducing it to solving a system of non-linear coupled differential equations that involve six parameters, which are solved by developing a finite difference technique. The velocity profile, the skin-friction, the wall pressure and the rate of heat transfer at the sheet are computed for a specific situation. The study shows that the fluid velocity increases as the rate of heat transfer decreases, while the local skin-friction and the wall pressure increase as the magnetic field strength is increased. It is also revealed that fluid viscoelasticity has an enhancing effect on the local skin-friction. The study will have an important bearing on magnetic drug targeting and separation of red cells as well as on the control of blood flow during surgery.     

MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity

In this work, the effects of slip velocity on the flow and heat transfer for an electrically conducting micropolar fluid over a permeable stretching surface with variable heat flux in the presence of heat generation (absorption) and a transverse magnetic field are investigated. The governing partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformation, which is solved numerically using the Chebyshev spectral method. The effects of the slip parameter on the flow, micro-rotation and temperature profiles as well as on the local skin-friction coefficient, the wall couple stress and the local Nusselt number are presented graphically. The numerical results of the local skin-friction coefficient, the wall couple stress and the local Nusselt number are given in a tabular form and discussed.     

Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet

This paper deals with the unsteady axisymmetric flow and heat transfer of a viscous fluid over a radially stretching sheet. The heat is prescribed at the surface. The modelled non-linear partial differential equations are solved using an analytic approach namely the homotopy analysis method. Unlike perturbation technique, this approach gives accurate analytic approximation uniformly valid for all dimensionless time. The explicit expressions for velocity, temperature and skin friction coefficient are developed. The influence of time on the velocity, temperature and skin friction coefficient is discussed.     

Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink

An analysis has been carried out to study the flow and heat transfer characteristics for MHD viscoelastic boundary layer flow over an impermeable stretching sheet with space and temperature dependent internal heat generation/absorption (non-uniform heat source/sink), viscous dissipation, thermal radiation and magnetic field due to frictional heating. The flow is generated due to linear stretching of the sheet and influenced by uniform magnetic field, which is applied vertically in the flow region. The governing partial differential equations for the flow and heat transfer are transformed into ordinary differential equations by a suitable similarity transformation. The governing equations with the appropriate conditions are solved exactly. The effects of viscoelastic parameter and magnetic parameter on skin friction and the effects of viscous dissipation, non-uniform heat source/sink and the thermal radiation on heat transfer characteristics for two general cases namely, the prescribed surface temperature (PST) case and the prescribed wall heat flux (PHF) case are presented graphically and discussed. The numerical results for the wall temperature gradient (the Nusselt number) are presented in tables and are discussed.     

Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation

A mathematical analysis has been carried out to study magnetohydrodynamic boundary layer flow, heat and mass transfer characteristic on steady two-dimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field. Momentum boundary layer equation takes into account of transverse magnetic field whereas energy equation takes into account of Ohmic dissipation due to transverse magnetic field, thermal radiation and non-uniform source effects. An analysis has been performed for heating process namely the prescribed wall heat flux (PHF case). The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations which are then linearized by quasi-linearization method and solved very efficiently by finite-difference method. Favorable comparisons with previously published work on various special cases of the problem are obtained. The effects of various physical parameters on velocity, temperature, concentration distributions are presented graphically and in tabular form.     

Analytical solutions of the boundary layer flow of power-law fluid over a power-law stretching surface

This article discusses analytical solutions for a nonlinear problem arising in the boundary layer flow of power-law fluid over a power-law stretching surface. Using perturbation method analytical solution is presented for linear stretching surface. This solution covers large range of shear thinning and shear thickening fluids and matches excellently with the numerical solution. Furthermore, some new exact solutions are found for particular combination of m (power-law stretching index) and n (power-law fluid index). This leads to generalize the case of linear stretching to nonlinear stretching surface. The effects of fluid index n on the boundary layer thickness and the skin friction for nonlinear stretching surface is analyzed and discussed. It is observed that the boundary layer thickness and the skin friction coefficient increase as non-linear parameter n decreases. This study gives a new dimension to obtain analytical solutions asymptotically for highly nonlinear problems which to the best of our knowledge has not been examined so far.     

Analysis of fluid flow and heat transfer over an unsteady stretching surface

This article considers two situations involving unsteady laminar boundary layer flow due to a stretching surface in a quiescent viscous incompressible fluid. In one configuration, the surface is impermeable with prescribed heat flux, in the other, the surface is permeable with prescribed temperature. The boundary value problems governing a similarity reduction for each of these situations are investigated and the existence of a solution is proved for all relevant values of physical parameters. The uniqueness of the solution is also proved for some (but not all) values of the parameters. Finally, a priori bounds are obtained for the skin friction coefficient and local Nusselt number.     

Three-dimensional flow of a Jeffery fluid over a linearly stretching sheet

This investigation reports the three-dimensional flow of Jeffrey fluid over a linearly stretching surface. Transformation method has been utilized for the reduction of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are presented by a homotopy analysis method (HAM). The reported graphical results are analyzed. A comparative study with the previous results of viscous fluid in the literature is made.     

Exact solution of thermal radiation on MHD flow over a stretching porous sheet

The effect of radiation on MHD steady asymmetric flow of an electrically conducting fluid past a stretching porous sheet in the presence of radiation has been analyzed. Exact solutions for the velocity and temperature fields have been derived and the effects of radiation, magnetic, Prandtl number, wall temperature and suction (or injection) parameters have been studied with the help of graphs.     

Homotopy analysis method for solving the MHD flow over a non-linear stretching sheet

The problem of the boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is considered. Homotopy analysis method (HAM) is applied in order to obtain analytical solution of the governing nonlinear differential equations. The obtained results are finally compared through the illustrative graphs with the exact solution and an approximate method. The compression shows that the HAM is very capable, easy-to-use and applicable technique for solving differential equations with strong nonlinearity. Moreover, choosing a suitable value of none–zero auxiliary parameter as well as considering enough iteration would even lead us to the exact solution so HAM can be widely used in engineering too.     

Homotopy analysis method for MHD viscoelastic fluid flow and heat transfer in a channel with a stretching wall

In this paper, we analyze the flow and heat transfer characteristics of a magnetohydrodynamic (MHD) viscoelastic fluid in a parallel plate channel with a stretching wall. Homotopy analysis method (HAM) is used to obtain analytical solutions of the governing nonlinear differential equations. The analytical solutions are obtained in the form of infinite series and the convergence of the series solution is discussed explicitly. The obtained results are presented through graphs for several sets of values of the parameters, and the salient features of the solutions are analyzed. A comparison of our HAM results (for a special case of the study) with the available results in the literature (obtained by other methods) shows that our results are accurate for a wide range of parameters. Further, we point that our analysis finds application to the study of the haemodynamic flow of blood in the cardiovascular system subject to external magnetic field.     

MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface

The present analysis comprises the steady two-dimensional magnetohydrodynamic flow of an upper-convected Maxwell fluid near a stagnation-point over a stretching surface. The governing non-linear partial differential equation for the flow are reduced to an ordinary differential equation by using similarity transformations. The analytic solution of nonlinear system is constructed in the series form using Homotopy analysis method. Convergence of the obtained series is discussed explicitly. The effects of the sundry parameters on the velocity profile is shown through graphs. The values of skin-friction coefficient for different parameters is tabulated.