**Abstract**

A mathematical model for convective heat and mass transfer of two immiscible fluids in a vertical channel of variable width with thermo-diffusion, diffusionthermal effects is presented. The governing boundary layer equations generated for momentum, angular momentum, energy and species concentration are solved with appropriate boundary conditions using Galeriken finite element method. The effects of the pertinent parameters are studied in detail. Furthermore, the rate of heat transfer, mass transfer and shear stress near both walls is analyzed.

**Keywords:** vertical channel, immiscible fluids, finite element method, heat and mass transfer
