A pseudosimilarity approach to a steady free convection flow

TL;DR

This paper explores new exact solutions for steady free convection flows using a pseudosimilarity approach, addressing cases where traditional similarity solutions do not exist, and analyzing their existence and asymptotic behavior.

Contribution

It introduces a pseudosimilarity method to find exact solutions for steady free convection problems where classical similarity solutions are absent.

Findings

Existence of new exact solutions for specific boundary conditions.

Asymptotic behavior of these solutions analyzed.

Addresses cases previously considered unsolvable with classical methods.

Abstract

In this communication we deal with the exact solutions called "pseudosimilarity" of a steady free convection problem studied by by Kumaran and Pop (2006). They showed that there is no similarity solution for the case of a wall temperature as $T_{w}(x)\sim x^{-{1/2}}$ (resp. a wall heat flux as $q_{w}(x)\sim x^{-{3/2}},$ and a dimensionless heat transfer coefficient $h_{w}(x)\sim x^{-1}$). We shall present some results about existence and asymptotic behaviour of new exact solutions of the resulting boundary value problem for each case.