Development of flow and heat transfer on a wedge with a magnetic field

Abstract

The development of the flow and heat transfer of an incompressible laminar viscous electrically conducting fluid on a stationary infinite wedge with an applied magnetic field has been studied when the fluid in the external stream is set into motion impulsively and at the same time, the surface temperature is suddenly raised from its ambient temperature. The effects of the induced magnetic field, viscous dissipation and Ohmic heating have been taken into account. The mathematical problem has been formulated in such a way that at time t = 0, it reduces to Rayleigh type of equation and as time t → ∞, it tends to Falkner-Skan type of equation. The scale of time has been chosen such that the traditional infinite region of integration becomes finite which considerably reduces the computational time. The singular parabolic partial differential equations governing the flow have been solved numerically using an implicit finite difference scheme. There is a smooth transition from the Rayleigh solution at ξ = 0 (t^* = 0) to Falkner-Skan type of solution at ξ = 1 (t → ∞ when the steady state is reached). The surface shear stress and the surface heat transfer increase or decrease with time when the pressure gradient parameter is greater or less than a certain value. However, the x component of the induced magnetic field at the surface decreases as time increases.