Explicit series solutions for supersonic flat-plate boundary layer flows

Abstract

This paper describes explicit series solutions for supersonic flat-plate boundary layer flows that are convergent in the whole spatial domain for Mach numbers of up to 50. These series solutions are achieved by means of the homotopy analysis method (HAM), an analytic technique for highly nonlinear problems. Unlike the analytic approximations given by perturbation methods or other approaches, our explicit series solutions are guaranteed to converge with arbitrary physical parameters because of the so-called “convergence-control parameter” in the HAM framework. Explicit analytic expressions for the local surface skin-friction coefficient and the local heat-transfer coefficient of the supersonic boundary layer flow are also derived. These analytical solutions are found to be in perfect agreement with the corresponding numerical results, allowing the effects of physical parameters on supersonic boundary layer flows to be discussed in detail. The explicit series solutions described in this paper provide a benchmark for supersonic flat-plate boundary layer flows with Mach numbers in the range 0.8≤Ma≤50. To the best of our knowledge, no such explicit series solutions for supersonic flat-plate boundary layer flows have previously been reported. To enable relevant applications, a corresponding Mathematica package is provided to enable convenient access to explicit series solutions for supersonic flat-plate boundary layer flows.