Natural Convection Flow along an Isothermal Vertical Flat Plate with Temperature Dependent Viscosity and Heat Generation

The purpose of this study is to investigate the natural convection laminar flow along an isothermal vertical flat plate immersed in a fluid with viscosity which is the exponential function of fluid temperature in presence of internal heat generation. The governing boundary layer equations are transformed into a nondimensional form and the resulting nonlinear system of partial differential equations is reduced to a convenient form which are solved numerically using an efficient marching order implicit finite difference method with double sweep technique. Numerical results are presented in terms of the velocity and temperature distribution of the fluid as well as the heat transfer characteristics, namely, the wall shear stress and the local and average rate of heat transfer in terms of the local skin-friction coefficient, the local and average Nusselt number for a wide range of the viscosity-variation parameter, heat generation parameter, and the Rayleigh number. Increasing viscosity variation parameter and Rayleigh number lead to increasing the local and average Nusselt number and decreasing the wall shear stress. Wall shear stress and the rate of heat transfer decreased due to the increase of heat generation. 1. Introduction A large number of physical phenomena involve natural convection driven by heat generation. The study of heat generation in moving fluids is important in view of several physical problems such as those dealing with chemical reactions and those concerned with dissociating fluids. Possible heat generation effects may alter the temperature distribution and, therefore, the particle deposition rate. This may occur in such applications related to nuclear reactor cores, fire and combustion modeling, electronic chips, and semiconductor wafers. In fact, the literature is replete with examples dealing with the heat transfer in laminar flow of viscous fluids. Vajravelu and Hadjinicolaou [1] studied the heat transfer characteristics in the laminar boundary layer of a viscous fluid over a linearly stretching continuous surface with viscous dissipation or frictional heating and internal heat generation. In this study, Vajravelu and Hadjinicolaou [1] considered that the volumetric rate of heat generation, [W/m3], should be where is the heat generation constant. The above relation, explained by Vajravelu and Hadjinicolaou [1], is valid as an approximation of the state of some exothermic process and having as the onset temperature. Following Vajravelu and Hadjinicolaou [1], Molla et al. [2–5] investigated the natural convection with heat generation