Heat Transfer and Friction in a Thin Air Laminar Boundary Layer over Semi-Sphere Surface

A qualitative solution to the problem of calculating convective heat transfer can be obtained only by numerically integrating the differential equations of the boundary layer, which is associated with overcoming a number of computational problems. Consequently, it is important to develop relatively simple, but fairly high-precision calculation methods. As a first approximation to solving this problem, we can consider the use of the effective length method. From the practical point of view, this method is characterized by satisfactory accuracy of calculating convective heat transfer, which has led to its widespread use in aeronautical design engineering. However, this method is also characterized by a relatively high complexity, although it is much lower than that in numerical integration of the differential equations of the boundary layer. The most effective approach to solving heat transfer and friction problems in engineering practice is to use simple algebraic formulae obtained on the basis of approximating the results of rigorous numerical calculations, or experimental studies. Unfortunately, there is no information in literary sources about the accuracy of these formulae under various conditions of product functioning. This problem is solved on the basis of a systematic numerical calculation of the equations of the boundary layer in the most rigorous theoretical calculation, as well as a detailed analysis of the accuracy of the obtained algebraic formulae and their literary analogues

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