An approximate solution procedure for laminar free and forced convection heat transfer problems

Laminar convective heat transfer in forced convective flow over a nonisothermal wedge and in free convective flow over a vertical flat plate immersed in a thermally stratified fluid is investigated analytically using integral approximation methods. It is shown that similar solutions can be found for these two cases because they are specified by two configurational parameters associated with the external and wall conditions. The conservation equations are reduced to a simple algebraic relationship of boundary-layer thickness ratio, Prandtl number, and the configuration parameters, allowing the calculation of the Nusselt number. Sample results are presented in graphic form and compared to those computed from the exact solutions; good agreement is found over a wide range of Prandtl numbers. This approach permits local heat-transfer rates through thermal boundary layers to be quickly and accurately estimated.