Two-parameter integral method for laminar transpired thermal boundary-layer flow

A practical two-parameter polynomial-type integral method is developed for heat transfer associated with laminar transpired boundary-layer flow with transpiration. The method is based on the use of second- and third-order boundary-layer approximations for the distributions in shear stress and heat flux. These approximations are used to establish relationships for the distributions in velocity and temperature and to develop solutions to the integral momentum and energy equations for similar and nonsimilar flows. The accuracy of the method is generally within 3-4%, except near separation where the error can reach 15-20%. The method applies to a wide range of transpiration rates and pressure gradients, including plane and axisymmetric stagnation and separation. In addition, the method provides a fundamental basis for generalization to natural convection and turbulent flow, and a framework for the development of more accurate higher-order multiple-parameter integral methods.