Free convection boundary layer flow of a nanofluid from a convectively heated vertical plate with linear momentum slip boundary condition

Abstract

Two dimensional steady laminar boundary layer flow of a nanofluid over a convectively heated vertical flat plate with linear momentum slip boundary condition has been studied numerically. The governing boundary layer equations are non-dimensionalized and transformed into a two point boundary value problem of coupled nonlinear ordinary differential equations in similarity variable before being solved numerically. The resulting equations with corresponding boundary conditions have been solved numerically by Maple 13 which uses Runge-Kutta-Fehlberg fourth- fifth order numerical algorithm for solving nonlinear ordinary boundary value problems. Our analysis reveals that the similarity solution is possible if the convective heat transfer coefficient is directly proportional to x–1/4, where x is the axial distance from the leading edge of the plate. Solutions depend on the seven parameters: Prandtl number, buoyancy ratio, Brownian motion, thermophoresis, Lewis number, momentum slip and convective heat transfer. The effects of the governing parameters on the flow and heat transfer characteristics have been shown graphically and discussed. Comparisons of the present numerical solution with the existing results in the literature are made and our results are in very good agreement. Results for the skin friction factor, the reduced Nusselt and the Sherwood numbers are provided in tabular form for various values of the convective heat transfer parameter. It is found that the skin friction coefficint reduces with the momentum slip and the buoyancy ratio parameters whilst it enhances with the convective heat transfer parameter. It is also found that mass transfer rate enhances with the Lewis number and the convective heat transfer parameter whilst it falls with the thermophoresis parameter.