Rapid calculation for convective heat transfer in laminar boundary layer by Gaussian quadratures

Summary The integral of the form, which arises in the convective heat transfer with constant wall temperature, is integrated by using Gauss-Laguerre and Gauss-Legendre Quadrature formulae. It is shown that the Nusselt number can be expressed explicitly in terms of the Prandtl number and the method proposed in this paper is valid for wide range of Prandtl numbers. Examples are given for the cases of flow over a semi-infinite plate and two-dimensional and axisymmetrical stagnations. The results are compared with the exact solutions for Prandtl numbers ranging from 0.006 to 100 (flat plate) and 0.01 to 50 (two-dimensional and axisymmetrical stagnation flows).