Initial Unsteady Free Convective Flow Past an Infinite Vertical Plate with Radiation and Mass Transfer Effects

Abstract

Abstract An exact solution and analysis of an initial unsteady two dimensional free convection flow, heat and mass transfer in the presence of thermal radiation along an infinite fixed vertical plate when the plate temperature is instantaneously raised, is presented. The fluid considered is a gray, absorbing emitting radiation but a nonscattering medium. Three cases have been discussed, in particular, namely, (i) when, the plate temperature is instantaneously raised to a higher constant value, (ii) when, the plate temperature varies linearly with time and (iii) when, the plate temperature varies non-linearly with time. A close form general solution for all the cases has been obtained in terms of repeated integrals of error functions. In two particular cases, the solutions in terms of the repeated integrals of error functions have been further simplified to forms containing only error functions. It is observed that for an increase in the radiation parameter N or a decrease in the Grashof number Gr or Gm, there is a fall in the velocity or temperature, but compared to the no radiation case or no diffusing species, there is a rise in the velocity and temperature of the fluid.