Mixed Convection From a Convectively Heated Vertical Plate to a Fluid With Internal Heat Generation

Abstract

A numerical approach has been adopted to study steady mixed convection from the right face of a vertical plate of finite thickness. Cold fluid flowing over the right face of the plate contains a heat generation that decays exponentially with a dimensionless distance from the wall. The left face of the plate is in contact with a hot flowing fluid. The heating process on that side is characterized by a convective boundary condition that takes into account the conduction resistance of the plate as well as a possible contact resistance between the hot fluid and the left face of the plate. Using a pseudo similarity approach, the continuity, momentum, and energy equations for mixed convective flow over the right face of the plate are transformed into a set of coupled ordinary differential equations. It is found that for a true similarity solution, the convective heat transfer coefficient associated with the hot fluid must be proportional to x−1/2 , and both the thermal expansion coefficient and the internal heat generation rate for the cold fluid must be proportional to x−1 , where x is the upward distance along the plate. The equations give local similarity solutions. The effects of local Grashof number (defined to represent a mixed convection parameter), Prandtl number, Biot number, and the internal heat generation parameter on the velocity and temperature profiles are illustrated and interpreted in physical terms. The present results agree closely with the existing results for the special cases of the problem. This close agreement lends support to the validity of the present analysis and the accuracy of the numerical computations. The paper also contains a table in which the data for the local skin friction and local Nusselt number are provided for various combination values of the parameters that govern the momentum and energy transport in the mixed boundary layer.