An Analysis of Free-Convection about a Vertical Plate

Abstract

With the use of the integrated momentum and energy equations, an approximate calculation was carried out for the flow and heat transfer in the laminar and turbulent free-convection boundary layer on a vertical flat plate. The velocity profiles employed for laminar layer are of a polinomial of the fifth order and an exponential function of y, which satisfy the following boundary condition in addition to the usual ones : [numerical formula] The calculated results agree practically well, over the entire range of P_r, with the Ostrach's. The method of attack for turbulent flow is similar in principle to that of Eckert and Jackson, though some different profiles are used for temperature and velocity fields. When the turbulent region coexists with the laminar region near the leading edge, the average Nusselt number was proved to be [numerical formula] where G_rc is the critical Grashof number, at which the transition from laminar to turbulent occurs.