Dufour Effect with Ramped Wall Temperature and Specie Concentration on Natural Convection Flow Through A Channel

Abstract

In this paper, we have obtained an analytical solution to the problem of unsteady free convection and mass transfer flow of an incompressible fluid through a vertical channel in the presence of Dufour effect (or diffusion thermo). The bounding plates are assumed to have ramped wall temperature as well as specie concentration. The mathematical model responsible for the physical situation is presented in dimensionless form and solved analytically using the powerful Laplace Transform Technique (LTT) under relevant initial and boundary conditions. In order to cross check the accuracy of the analytical results, numerical solutions are obtained using PDEPE solver in MATLAB. The expressions for temperature, concentration, and velocity are obtained. The effects of Dufour parameter, Prandtl number (Pr), Schmidt number (Sc), and dimensionless time are described during the course of these discussions. The temperature, concentration, and velocity profiles are graphically presented for some realistic values of Pr=0.025, 0.71, 7.0, 11.62, 100.0 and Sc=0.22, 0.60, 1.00, 2.62, while the values of all other parameters are arbitrarily taken.