Similarity solutions for buoyancy-induced flows over a non-isothermal curved surface in a thermally stratified porous medium

Abstract

A generalized similarity transformation procedure was proposed for the analysis of buoyancy-induced flows over a curved heated surface embedded in a thermally stratified porous medium. The analysis considers two-dimensional and axisymmetric non-isothermal smooth bodies of arbitrary geometrical configuration. A generalized similarity variable which adjusts its vertical scaling according to the geometry as well as the surface temperature variation was introduced to show that, for any two-dimensional or axisymmetric smooth body shape, there exists a certain class of the surface and ambient temperature distributions which admit similarity solutions. Subsequently, the set of the governing partial differential equations were transformed into a single ordinary differential equation, which was, then, solved by a standard shooting procedure based on the Runge-Kutta method, for numerous sets of parameters. The results presented here may readily be translated for the problem of free convection over any particular two-dimensional or axisymmetric smooth body within a porous medium. The effects of the surface temperature and thermal stratification on the temperature profile and isotherms were also discussed in connection with the local surface heat flux.