The Effect of Induced Magnetic Field and Convective Boundary Condition on MHD Stagnation Point Flow and Heat Transfer of Nanofluid Past a Stretching Sheet

Abstract

This study examines the effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer due to nanofluid over a stretching sheet. It takes into account the effect of Brownian motion and thermophoresis parameters. The nonlinear governing equations and their associated boundary conditions are reduced into dimensionless form by similarity variables. The resulting systems of equations are then solved numerically using fourth-order Runge-Kutta method along with shooting technique. The solution for the problem depends on parameters: magnetic M, velocity ratio B, Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, thermophoresis Nt, and reciprocal of magnetic Prandtl number A. Numerical results of the study are obtained for velocity, temperature, induced magnetic field, and concentration profiles as well as skin friction coefficient, the local Nusselt number, and Sherwood number. It is found that the skin friction coefficient, the local Nusselt number, and Sherwood number decrease with an increase in B and M parameters. However, the local Nusselt number -θ'(0) increases with an increase in Bi, and local Sherwood number -φ'(0) decreases with an increase in convective parameter Bi. The study indicated that the flow velocity and the skin friction coefficient on stretching sheet are strongly influenced by velocity ratio (B <; 1) and magnetic parameters. It is also observed that the skin friction coefficient -f"(0) is an increasing function of magnetic parameter and a decreasing function of velocity ratio parameter B. The study also shows that the local heat transfer rate -θ'(0) is an increasing function of the convective parameter Bi, but it is a decreasing function of magnetic parameter M, velocity ratio parameter B, and thermophoresis parameter Nt. The obtained results are displayed both in graphical and tabular form to show the effect of the governing parameters on the dimensionless velocity, induced magnetic field, temperature and concentration. The numerical results are compared and found to be in good agreement with the previously published results on special cases of the problem.