Transient free-convective flow in a vertical channel due to symmetric heating

This paper presents a closed form solution for a transient free convective flow of a viscous and incompressible fluid in a vertical channel due to symmetric heating of channel walls. The Laplace transform technique has been used to obtain the expression for the velocity and temperature fields by solving the governing differential equations. The influence of the physical parameters on the velocity field, skin-friction, rate of heat transfer and volumetric flux of the fluid are carefully analysed. A correlation between the steady state time and the Prandtl number has been developed. It is observed that the nature of correlation is linear when the Prandtl number is greater than one while cubic for the Prandtl number is less than one.