Soret and Dufour Effects on Hydromagnetic Flow of H2O-Based Nanofluids Induced by an Exponentially Expanding Sheet Saturated in a Non-Darcian Porous Medium

Abstract

Diffusion-thermo effect (Dufour effect) and thermal-diffusion effect (Soret effect) on an MHD flow through porous medium taking nanoparticles may be considered to be useful in many engineering problems when there is a species concentration along with the solid nanoparticles. To study such an attracting problem, it is necessary to consider the flow to be single-phase. In the present investigation, the hydromagnetic flow of H2O-based nanofluids due to an exponentially expanding sheet saturated in non-Darcian porous material is examined with Dufour and Soret effects. In addition, temperature and species concentration along the surface in flow distribution are considered to be variable exponentially. Two sorts of nanofluids are considered, to be specific, Cu–H2O and Ag–H2O. Use of proper similarity transformations transfers the governing PDEs to coupled ODEs. Then the solutions of the coupled equations are computed by very efficient shooting method. Non-dimensionless velocity species concentration and temperature are introduced in graphical mode for several values of involved parameters. Out of several obtained outcomes, it is noticeable that similar to the magnetic parameter and permeability parameter, due to increase in non-Darcy Forchheimer parameter velocity diminishes and while temperature and species concentration increments are witnessed. Due to presence of Dufour effect, temperature enhances and similarly, the concentration increases for Soret effect. While due to Dufour effect, the concentration initially decreases, but away from surface it increases and similar behaviour is found for temperature in the case of Soret effect. Also, it is obtained that skin-friction coefficient for Cu–H2O nanofluid is larger than it value for Ag–H2O nanofluid. Dufour effect turns into the reason for the reduction of Nusselt number and increment of Sherwood number for both nanofluids, but Soret effect affects the two nanofluids reversely. The analysis and its findings provide some tools which may be applied in engineering and industrial problems.