Soret and Dufour effects on transient free convention heat and mass transfer flow in a vertical channel with ramped wall temperature and specie concentration: an analytical approach

Abstract

This work investigates unsteady free convection heat and mass transfer flow in a vertical channel in the presence of Soret and Dufour effects. The bounding walls and the specie are considered to have ramped temperature and ramped concentration respectively. Perturbation method is first used to decouple the governing equations that arise from the model due to the presence of combined Soret and Dufour effects. Laplace transform technique is then used to obtain an analytical solutions for the temperature, concentration and velocity. In order to cross check the accuracy of the proposed analytical method, numerical solutions are obtained using PDEPE in MATLAB. The influences of the two effects as well as the ramped boundary conditions on the fluid flow are graphically presented and discussed. The results show that these two effects and the imposed boundary conditions affect the fluid temperature, concentration, velocity, rate of heat transfer, rate of mass transfer and wall Skin friction. Moreover, it is found that the solutions obtained by the authors Jha and Gambo correspond to the results of the present work when Soret effect is absent.