Unsteady flow and heat transfer of a viscous fluid in the stagnation region of a three-dimensional body with a magnetic field

Abstract

The unsteady incompressible flow and heat transfer of a viscous electrically conducting fluid in the vicinity of a stagnation point of a general three-dimensional body have been studied when the velocity in the potential flow varies arbitrary with time. The magnetic field is applied normal to the surface. The effects of viscous dissipation and Ohmic heating are included in the analysis. Both nodal-point region (0⩽ c⩽1, where c= b/ a is the ratio of the velocity gradients in y and x directions in the potential flow) and saddle-point region (−1⩽ c<0) are considered. The semi-similar solution of the Navier–Stokes equations and the energy equation are obtained numerically using an implicit finite difference scheme. Also a self-similar solution is found when the velocity in the potential flow, the magnetic field and the wall temperature vary with time in a particular manner. The asymptotic behaviour of the self-similar equations for large η is obtained which enables us to find the upper limit of the unsteady parameter λ. One interesting result is that the magnetic field tends to delay or prevent flow reversal in y-component of the velocity. The surface shear stresses in x and y directions and the surface heat transfer increase with the magnetic field as well as with the accelerating free stream velocity.