Heat Transfer in Boundary Layer Viscolastic Fluid Flow Over Anexponentially Stretching Sheet

The paper presents the study of momentum and heat transfer characteristics in a visco-elastic boundary layer fluid flow over an exponentially stretching continuous sheet with non-uniform heat source. The flow is generated solely by the application of two equal and opposite forces along the x-axis such that stretching of the boundary surface is of exponential order in x and influenced by uniform magnetic field applied vertically. The non-linear boundary layer equation for momentum is converted into ordinary differential equation by means of similarity transformation. Approximate analytical similarity solutions is obtained for the dimensionless stream function and velocity distribution function after transforming the boundary layer equation into Riccati type and solving it sequentially. Heat transfer equation is then solved using Runge-Kutta fourth order method. The accuracy of the analytical solutions is also verified by comparing the solutions obtained to those in literature when Hartmann number is zero. The effects of various physical parameters on velocity, skin friction, temperature and Nusselt number profiles are presented graphically

UNSTEADY MIXED CONVECTION WITH SORET AND DUFOUR EFFECTS PAST A POROUS PLATE MOVING THROUGH A BINARY MIXTURE OF CHEMICALLY REACTING FLUID

This study investigates the unsteady mixed convection flow past a vertical porous flat plate moving through a binary mixture in the presence of radiative heat transfer and nth-order Arrhenius type of irreversible chemical reaction by taking into account the diffusion-thermal (Dufour) and thermo-diffusion (Soret) effects. Assuming an optically thin radiating fluid and using a local similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth-order Runge-Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, and concentration distributions are shown for various values of the thermophysical parameters controlling the flow regime. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented in tabular form

Effects of chemical reaction, thermal radiation, internal heat generation, Soret and Dufour on chemically reacting MHD boundary layer flow of heat and mass transfer past a moving vertical plate with suction/injection

In the present analysis, we study the two-dimensional, steady, incompressible electrically conducting, laminar free convection boundary layer flow of a continuously moving vertical porous plate in a chemically reactive medium in the presence of transverse magnetic field, thermal radiation, chemical reaction, internal heat generation and Dufour and Soret effect with suction/injection. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The problem is solved numerically using shooting techniques with the sixth order Runge-Kutta integration scheme. Comparison between the existing literature and the present study were carried out and found to be in excellent agreement. The influence of the various interesting parameters on the flow and heat transfer is analyzed and discussed through graphs in detail. The values of the local Nusselt number, Skin-friction and the Sherwood number for different physical parameters are also tabulated. Comparison of the present results with known numerical results is shown and a good agreement is observed

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

This article presents a numerical solution for the steady two-dimensional mixed convection MHD flow of an electrically conducting viscous fluid over a vertical stretching sheet, in its own plane. The stretching velocity and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function of the temperature and a linear function of the temperature. A generalized similarity transformation is introduced to study the influence of temperature dependent fluid properties. The transformed boundary layer equations are solved numerically, using a finite difference scheme known as Keller Box method, for several sets of values of the physical parameters, namely, the stretching parameter, the temperature dependent viscosity parameter, the magnetic parameter, the mixed convection parameter, the temperature dependent thermal conductivity parameter and the Prandtl number. The numerical results thus obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of the physical parameters on the flow and heat transfer characteristics. Here it may be noted that, in the case of the classical Navier-Stokes fluid flowing past a horizontal stretching sheet, McLeod and Rajagopal (1987) 42 showed that there exist an unique solution to the problem. This may not be true in the present case. Hence we would like to explore the non-uniqueness of the solution and present the findings in the subsequent paper. © 2009 Elsevier Ltd. All rights reserved

Further Results on the Effects of Variable Viscosity and Magnetic Field on Flow and Heat Transfer to a Continuous Flat Plate in the Presence of Heat Generation and Radiation with a Convective Boundary Condition

The steady, laminar boundary layer flow with a convective boundary condition, to a continuously moving flat plate is studied taking into account the variation of viscosity with temperature in the presence of a magnetic field, heat gen-eration and thermal radiation. The fluid viscosity is assumed to vary as a linear function of temperature. The resulting, gov-erning equations are non-dimensionalized and transformed using a similarity transformation and then solved numerically by sixth order Runge-Kutta method alongside with shooting method. Comparison with previously published work is performed and there was a perfect agreement at large value of the Biot number. A parametric study of all the embedded flow parameters involved is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the skin-friction parameter and the Nusselt number is illustrated graphically to show typical trend of the solutions. It is worth pointing out that, when the variation of viscosity with temperature is strong in the presence of the effect of a magnetic field, radiation, heat generation, the results of the present work are completely different from those that studied the same problem in the absence of magnetic field, thermal radiation and the heat generation. It is interesting to note that higher the values of Prandtl number lesser the effects of Biot number and the magnetic field intensit

Effect of Variable Viscosity, Dissipation and Hall Currents on Convective Heat and Mass Transfer Flow Past a Stretching Sheet

We consider the influence dissipation, variable viscosity, Hall current of a magneto-hydrodynamic free-convective flow and heat and mass transfer flow past a stretching sheet in the presence of heat generation/absorption. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The boundary-layer equations governing the fluid flow, heat and mass transfer under consideration have been reduced to a system of non-linear ordinary differential equations by employing a similarity transformation. Using the finite difference scheme, numerical solutions to the transform ordinary differential equations have been obtained and the results are presented graphically. The rare of heat anf mass transfer sre discussed numerically for different variations. Keywords: Radiation absorption, Variable viscosity, Soret effect, MHD, Hall current, Heat and mass transfer

Heat transfer over a nonlinearly stretching sheet with non-uniform heat source and variable wall temperature

In this paper we study the flow and heat transfer characteristics of a viscous fluid over a nonlinearly stretching sheet in the presence of non-uniform heat source and variable wall temperature. A similarity transformation is used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme is used to obtain the solution of the boundary value problem. The effects of various parameters (such as the power law index n, the Prandtl number Pr, the wall temperature parameter λ, the space dependent heat source parameter A* and the temperature dependent heat source parameter B*) on the heat transfer characteristics are analyzed. The numerical results for the heat transfer coefficient (the Nusselt number) are presented for several sets of values of the parameters and are discussed. The results reveal many interesting behaviors that warrant further study on the effects of non-uniform heat source and the variable wall temperature on the heat transfer phenomena at the nonlinear stretching sheet. © 2011 Elsevier Ltd. All rights reserved.postprin

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. © 2009 Elsevier B.V. All rights reserved

Free Convection Boundary Layer Flow and Heat Transfer of a Nano Fluid over a Moving Plate with Internal Heat Generation

This paper presents considers the extended Blasius Flow problem and Heat transfer characteristics in Nano fluid with internal heat generation by considering free stream parallel to a moving plat plate which has much practical significance. The total transport model employed here includes the effect of Blasius motion and internal heat generation in energy transfer. It is also assumed that the plate moves in same or opposite direction to the free stream. Using the Similarity transformations, the transport equations followed by their Numerical computations. The governing system of highly non-linear ordinary differential equations are solved for three kinds of nanoparticals namely Cooper(Cu), Alumina() and Titania() in the water base fluid with the value of Prandtl Number Pr=6.2 numerically. Initially by the similarity analysis the governing partial differential equations are converted into system of non linear ordinary differential equations. The governing p.d.e’s are converted into system of first order o.d.e’s and are solved numerically using MATLAB ode45 solver. The effect of various Physical parameters encountered in the problem such as solid volume fraction of three types of nano particles on velocity transfer and Energy transfer are analysed and studied by representing through graphs. The results are compared with earlier published results and are well in agreement. Keywords: Nano fluid, moving plate, heat transfer, ode solver, solid volume fractio