Extensions of Merk's method to the calculation of laminar boundary layer heat transfer from a non-isothermal surface

The Merk's method for calculating non-similar boundary layer heat transfer from an isothermal surface is extended to the case with non-isothermal surface and the reliability of the method is checked in detail. It is shown that except for some small ranges of β (pressure gradient parameter) and γ (wall temperature distribution parameter), the present method yields accurate heat transfer results. Examples of application of the present method are given for a flow around a circular cylinder and for that past a flat plate. The calculations are performed in the limits Pr→∞ and Pr→0, and the results are compared with those derived from the exact asymptotic theories for these limits.