An Analytic Investigation of the Steady-State Natural Convection Boundary Layer Flow on a Vertical Plate for a Wide Range of Prandtl Numbers

Natural convection boundary-layer flow on a vertical plate is considered under isothermal boundary conditions. Fundamental flow is supposed to be governed by steady-state boundary-layer equations. An analytic approximation of the coupled nonlinear differential equations system of the basic flow is made with the aid of the numerical results of Bejan's similarity method. An ad hoc formula of the dimensionless velocity profile is proposed in order to verify approximately the equilibrium of the coupled system in which the analytic formula of the dimensionless temperature profile is derived. A comparison with the numerical results is given for all spatial regions and a wide range of Prandtl numbers. A new Nusselt number expression is obtained and compared with the experimental measurements and theoretical studies for a wide range of Prandtl number values.