Self-similar analysis of the time-dependent compressible and incompressible boundary layers including heat conduction

TL;DR

This paper analyzes self-similar solutions of time-dependent compressible and incompressible boundary layers with heat conduction, providing analytic solutions for incompressible cases and deriving ODE systems for compressible layers.

Contribution

It introduces a self-similar analytical approach to boundary layers including heat conduction, with detailed parameter analysis and derivation of ODE systems for compressible flows.

Findings

Analytic solutions for incompressible boundary layers expressed with special functions.

Parameter dependencies of solutions are thoroughly studied.

Derived ODE systems for compressible boundary layers.

Abstract

We investigate the incompressible and compressible heat conducting boundary layer with applying the two-dimensional self-similar Ansatz. Analytic solutions can be found for the incompressible case which can be expressed with special functions. The parameter dependencies are studied and discussed in details. In the last part of our study we present the ordinary differential equation (ODE) system which is obtained for compressible boundary layers.