B.: Calculation of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

An approximate method for the development of flow and thermal "boundary layers in the laminar regime on cylinders with arbitrary cross section and transpiration!cooled walls is obtained Ъу the use of von Karman's integrated momentum equation and an analogous heat!flow equa! tion. Incompressible flow with constant property values throughout the boundary layer is assumed. The velocity and temperature profiles within the boundary layer are approximated by expressions composed of trigo! nometric functions. Shape parameters for these profiles and functions necessary for the solution of the boundary!layer equations are presented as graphs so that the calculation for any specific case is reduced to the solution of two first!order differential equations. The method is applied to determine local heat!transfer coefficients and surface temperatures in the laminar flow region of transpiration! cooled turbine blades for a given coolant flow rate, or!to calculate the coolant flow distribution which is necessary in order to keep the blade temperature uniform along the surface