Free Convection Flow on a Nonisothermal Flat Plate under Nonuniform Gravity

In this paper, we present results obtained by using a numerical procedure for the free convection flow along a rotating nonisothermal plate subject to a nonuniform gravity field. Several specific forms for the temperature distributions of the plate are considered. For these instances the skin-friction and heat transfer rate on the wall at selected values ofthe distance from the leading edge and for some values of Prandtl numbers are presented. The method employed is shown to be very accurate in comparison with previous solutions. NOMENCLATURE Subscripts a,,a,, a2,. . . , constants; r, W, a, local skin-friction coefficient ; reduced stream function; wall skin-friction parameter; nonuniform gravity field in the direction opposite of the x-axis, rfr w’(x,, f x) ; uniform gravity field, + ozxo ; dimensionless temperature function; wall heat transfer parameter ; local Grashof number, g&T, T,)x”/? ; local heat transfer coefficient ; thermal conductivity; local Nusselt number, h,x/k; wall temperature function ; Prandtl number, v/c( ; local surface heat transfer rate per unit area ; Reynolds number, u,x,/v; dimensionless wall temperature; temperature ; velocity component in x direction ; velocity component in y direction ; axial coordinate; distance of leading edge of the plate from the center of rotation; coordinate measured normal to the plate. Greek symbols a, thermal diffusivity ; B> bulk coefficient of thermal expansion; ‘I> transformed coordinate in y direction ; 8, dimeniionless temperature ; P> dynamic viscosity; V, kinematic viscosity; 4, transformed coordinate in x direction; P? density of fluid ; TW, wall skin-friction; Y’, stream function ; w, angular velocity of rotating plate. reference condition ; wall condition ; ambient condition. Superscripts I differentiation with respect to q; dimensionless condition.