Heat transfer through a constant-property laminar boundary layer Part 1 - calculations based on Lighthill's method Part 2 - calculations based on Stratford's method

Abstract

Part I. Two methods are derived for calculating the heat transfer through a constant-property laminar boundary layer, that depend respectively on approximations valid at low and high values of σ, the Prandtl number. The high σ approach is a development of an earlier method, due to Lighthill; an additional term is now retained in the assumed form of the velocity profile near the wall. The low σ approach is effectively an extension to Prandtl numbers of order unity of the limiting solution of Morgan et al, valid as σ -> 0. A certain amount of empirical fitting ensures good agreement with the 'similar' solutions When the methods are used to calculate heat transfer in flow past a circular cylinder, a comparison with experiment suggests that the high a approximation is at least as good as other methods of calculating heat transfer, and that the low σ approximation may be even better. Part II. The now well-known technique of Stratford is used to calculate heat-transfer rates through a constant-property laminar boundary layer with an arbitrary adverse pressure gradient. The velocity profiles are assumed to have been calculated by Stratford's method, linking solutions valid respectively in the inner and outer parts of the boundary layer, and a similar division is made in analysing the temperature profiles. A particularly simple formula is obtained for the heat-transfer rate at the wall. The accuracy of the method, estimated by comparison with such exact solutions as are available, is found to be reasonable.