Abstract
A new method of deriving a self-similar solution of the compressible laminar boundary layer equations is obtained for air as calorically or thermally perfect gas and where the viscosity is a power function of the temperature. Modified Levy-Mangier and Dorodnitsyn-Howarth transformations are introduced to solve the flow in a thin laminar boundary layer with no external pressure gradient and on a smooth flat plate. These transformations describe the similarity variable in terms of a power of the density that takes into account the viscosity-temperature power law relation. This results in an explicit relation between the stream function and the temperature fields described by a closed coupled system of nonlinear ordinary differential equations. Solutions are presented for boundary layer flows with Mach number of the external flow up to 4. The influence of the flow Prandtl number, wall to freestream temperature ratio, and power of the viscosity-temperature law is investigated. The present methodology also provides a simple way of comparing results according to various assumptions about the viscosity-temperature relations. (Author)
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