Numerical simulation of laminar flow and free convection heat transfer from an isothermal vertical flat plate

In this modest work, we present a numerical study of the phenomenon of laminar natural convection in a vertical plate, whose wall was maintained at a constant temperature.It was assumed that the boundary layer problem was initially given in a two-dimensional flow even though the physical properties of the fluid were considered to be constant except for the density change with the temperature.The governing equations of the model have been transformed and simplified into a non-linear system of ordinary differential equations (ODE) through the use of similarity variables which we were able to solve numerically using the Runge-Kutta method. This method has better opted for the numerical resolution of this system which was developed in FORTRAN code on the computer. The numerical results of the model were presented in tabular form and the velocity and temperature profiles for various Prandtl numbers were analyzed and depicted graphically. Also, the expressions of the mean heat transfer rate and the average Nusselt number for the whole plate were obtained in the analysis. The results were compared at the end with the numerical results obtained in the literature, showing that they were in good agreement.