Numerical approach to non-Darcy mixed convective flow of non-Newtonian fluid on a vertical surface with varying surface temperature and heat source

摘要

An analysis is performed on non-Darcy mixed convective flow of non-Newtonian fluid past a vertical surface in the presence of volumetric heat source originated by some electromechanical or other devices. Further, the vertical bounding surface is subjected to power law variation of wall temperature, but the numerical solution is obtained for isothermal case. In the present non-Darcy flow model, effects of high flow rate give rise to inertia force. The inertia force in conjunction with volumetric heat source/sink is considered in the present analysis. The Runge-Kutta method of fourth order with shooting technique has been applied to obtain the numerical solution. To avoid mathematical impasse for applying R-K method we have considered isothermal wall condition. The results of major interest include velocity as well as temperature profiles and the local Nusselt number for some representative values of power-law indices. Most importantly, introduction of the co-ordinate and parametric transformation applied to governing equations, rarely reported in the existing literature, add to the knowledge front. Some important findings of the study are: Ergun number reduces the pseudoplastic fluid velocity boundary layer, a desirable outcome, but enhances the thermal boundary layer whereas, in case of Newtonian and dilatant fluid, the effect is not so significant. An increase in all the flow and heat transfer parameters leads to decelerate the surface cooling from pseudoplasticity to dilatancy through Newtonian; thus the present model slows down the surface cooling and decreases the skin friction in the presence of heat source for dilatant fluid.