Soret and Dufour effects on steady free convective MHD viscoelastic fluid flow confined between a long vertical wavy wall and parallel flat wall

Abstract

Abstract

The present paper analyzes the Soret and Dufour effects along with viscoelastic effects on a two dimensional steady free convective MHD flow of  a slow and slowly varying viscoelastic incompressible fluid between a long vertical wavy wall and a parallel flat wall. A uniform magnetic field is assumed to be applied perpendicular to the flat wall. The governing equations of the fluid and the heat transfer are solved subject to relevant boundary conditions. It is assumed that the fluid consists of two parts: a mean part and a perturbed part. To obtain the perturbed part of the solution, we perform a long wave approximation. The perturbed part of the solution is the contribution from the waviness of the wall. Expressions for the zeroth-order and first-order velocity, temperature, skin friction and heat transfer at the wall are obtained. The profiles of the velocity components are presented graphically for different combinations of parameters involved in the problem to observe the effects of the viscoelastic parameter on the governing flow taking into considerations of Soret and Dufour effects.

Keywords: MHD; Soret and Dufour effects; viscoelastic parameter; skin-friction.