Unsteady free convection and mass transfer flow past an impulsively started vertical plate with Soret and Dufour effects: an analytical approach

Abstract

This research presents an analytical solution of unsteady free convection and mass transfer flow past a vertical plate with Soret and Dufour effects. The dimensionless system of governing equations is solved analytically with appropriate initial and boundary conditions. The accuracy of the analytical method is ensured by obtaining numerical solutions with PDEPE of MATLAB and comparing with the analytical results. Perturbation method is first adopted to decouple the system of equations that arise as a result of coupling Soret and Dufour effects. Laplace Transform Technique is then applied to solve the system. The expressions for velocity, temperature, concentration, Skin-friction, Nuselt and Sherwood numbers are obtained. In the course of discussions, the effects of main parameters are described. It is observed that increase in Soret number reduces the temperature while increasing the velocity and concentration. Moreover, Soret effect is more significant on the concentration than on the temperature. Similarly, the Dufour parameter causes the temperature and velocity to increase while the concentration decreases and the effect is more significant on the temperature than on the concentration. However, there is no significant difference on the effects of Dufour and Soret parameters on the velocity. The velocity, temperature and concentration profiles are presented graphically for $$Pr = 0.71$$ and $$Sc = 0.78$$ as well as for arbitrary values of other parameters.