Solution of Falkner- Skan Unsteady MHD Boundary Layer Flow and Heat Transfer Past a Moving Porous Wedge in a Nanofluid

Abstract

The present problem deals with the effect of various dimensionless parameters on the forced convection unsteady MHD boundary layer flow and heat transfer over a permeable wedge stretching surface in a nanofluid. The effects of Brownian motion and thermophoresis are considered. The solution for the velocity, temperature and nanoparticle concentration depends on various dimensionless parameters like Prandtl number Pr, velocity ratio parameter λ, permeability parameter K*, unsteady parameter A, pressure gradient parameter β, magnetic parameter M. The local similarity transformation is used to convert the governing partial differential equations into coupled third order non-linear ordinary differential equations. These equations are numerically solved using suitable method along with shooting technique. Numerical results are obtained for distributions of velocity, temperature and nanoparticle concentration, as well as, for the skin friction, local Nusselt number and local Sherwood number for several values of governing parameters. The numerical results are shown graphically and also in a tabular form. The velocity decreases for increasing values of velocity ratio parameter but increases for magnetic parameter, unsteady parameter, permeability parameter and pressure gradient parameter. The temperature profiles decreases for thermophoresis parameter Prandtl number and velocity ratio parameter whereas the temperature remains unchanged for Brownian motion parameter. Again, nanoparticle concentration profiles increases for Brownian motion parameter but decreases for thermophoresis parameter, Lewis number and velocity ratio parameter. Besides, the results of rate of velocity and rate of heat transfer are compared with previously published work for the validity and accuracy and found to be in good agreement.