The present paper deals with possible similarity solution of unsteady boundary layer flow over a vertical plate in the presence of internal heat generation, thermal radiation and buoyancy force. Under suitable similarity transformations, the non-linear partial differential equations are transformed into a set of ordinary differential equations. The transformed ordinary differential equations with boundary conditions are then solved numerically by using sixth order Runge-Kutta integration scheme. The effects of the governing parameters on the flow and thermal fields are investigated and shown graphically for various parameters in the velocity and the temperature distributions. The most essential case is discussed in this paper.

Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction coefficient , Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.

Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed. The plate surface is reactive with the fluid and generates inert specie which diffuses inside the boundary. The flux of the specie at the plate is proportional to specie concentration at the plate. The governing equations of continuity, momentum, energy and specie diffusion are transformed into ordinary differential equation by using the similarity transformation and solved numerically by using free parameter method along with shooting technique. The dimensionless velocity, temperature and concentration profiles are obtained and presented through figures for different parameters entering into the problem. The local Skin-friction coefficient , Nusselt number and Sherwood number at the plate for physical interest are also discussed through tables.

This paper is focused on the analysis of thermophoresis on an unsteady two dimensional free convective boundary layer flow along a permeable inclined flat plate in the presence of magnetic field and thermophoresis. Governing time dependent partial differential equations are non-dimensionalzed and transformed into a system of nonlinear ordinary differential equations by applying similarity transformations. These are solved numerically by using the shooting method along with Runge-Kutta sixth order integration scheme. Numerical results for the dimensionless velocity, temperature and concentration profiles have been obtained and displayed graphically. The skinfriction coefficient, wall heat transfer coefficient and wall deposition flux rate have also been obtained and are presented in tabular form. The obtained numerical results also show that increased unsteadiness parameter significantly controls the thermophoretic particle.

Abstract:In this paper we analyze the effects of free convection for internal heat generation and thermal radiation of an unsteady boundary layer flow over a vertical plate. We have applied free parameter method to obtain possible similarity cases. One of these cases have been investigated analytically and numerically. In this case, the governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge-Kutta method with shooting technique for better accuracy. The effects of the governing parameters on the flow and thermal fields are investigated numerically and displayed graphically. The skin-friction coefficient, heat transfer coefficient have also been obtained and presented in tabular form.