Viscous heating in free convection along a plate in presence of magnetic field

Abstract

The steady free convection boundary layer flow along a semi-infinite isothermal vertical plate in presence of transverse magnetic field, taking the frictional heat into account, is reported here. The governing equations have been solved by taking series expansion or stream function and the temperature function in powers of Brinkman number (<i>Br</i>)<i>. </i>The resulting

ordinary non-linear coupled differential equations with boundary conditions have been solved numerically using computer by Newton's shooting technique. The velocity and temperature profiles are drawn for different values of Prandtl number, magnetic field parameter and Brinkman number. The expressions for the skin-friction and Nusselt number have been

obtained and the numerical values of <i>f</i>₀′′(0),<i> </i>θ′₀ (0), <i>f</i>₁′′(0)and θ′₁ (0), which correspond to local skin-friction and rate or surface heat transfer, are also described. The effects or magnetic field, Prandtl number and frictional heating have been discussed in detail.