Effect of Prandtl Number on Transient Free Convection from Vertical Plate

Numerical study of the transient laminar free convection from vertical plate is presented in this paper. The problem is simplified by the Boussinesq and boundary layer approximations. The resulting governing equations are solved using finite difference method and the calculations are made to continue until the results (velocity and temperature profiles and local Nusselt number) approach the steady state solution. The steady state solution is found also using the similarity method, and the fourth order Runge-Kutta method is used for solving the resulting ordinary differential equations. The dimensionless time required to approach the steady state condition is found to increase with increasing the Prandtl number. A simple correlation is found to represent the relation between this time and the Prandtl number.