Combined effect of variable viscosity and thermal conductivity on free convection flow of a viscous fluid in a vertical channel using DTM

Abstract

An analysis is performed for fully developed free convection flow of a viscous fluid in a vertical channel including the effect of viscous dissipation for the cases of separated effect of variable viscosity, variable thermal conductivity and combined effect of variable viscosity and variable thermal conductivity. The viscosity of the fluid is assumed to depend on the temperature and the thermal conductivity is assumed to vary linearly with temperature. Flow governing motion and energy balance equations are solved using semi-analytical–numerical method called differential transform method (DTM). The principle of differential transformation is briefly introduced, and then applied for the aforementioned problem. Effect of variable viscosity and variable thermal conductivity as well as the effect of buoyancy ratio and wall temperature ratio on the velocity and temperature fields are presented. Effects of the above parameters on volumetric flow rate, skin friction and Nusselt number are also calculated. The current results are then compared with those derived from the Runge–Kutta shooting method (RKSM) in order to verify the accuracy of the proposed method. The findings reveal that DTM and RKSM agree to the order of 10−6.