Effect of temperature dependent viscosity on the thermal instability of two-dimensional stagnation point flow

¹ Laboratoire de Mécanique, Matériaux et Energétique (L2ME), Faculté de Technologie, Université de Bejaia, Route de Targua Ouzemour, 06000 Bejaia, Algérie
² Laboratoire de Physique Théorique (LPT), Faculté des Sciences Exactes, Université de Bejaia, Route de Targua Ouzemour, 06000 Bejaia, Algérie

^a Corresponding author: mfatsah@hotmail.fr

Received: 31 March 2014
Accepted: 30 December 2014

Abstract

This paper presents numerical study of thermal instability of a two-dimensional stagnation point flow when the fluid viscosity is assumed to vary as a linear function of temperature. Similarity transformation was used to reduce the partial differential boundary layer equations to a non linear system of coupled ordinary differential equations before solving it numerically using the fourth order Runge-Kutta method with shooting technique. The linear stability of the basic flow to three-dimensional disturbances is then investigated by making use of the normal mode decomposition within the Görtler-Hammerlin framework. The equations of linear stability theory create an eigenvalue problem which is solved numerically by means of a pseudo spectral collocation method using Laguerre’s polynomials. The numerical experiment reveals that temperature-dependent viscosity affects significantly the onset of thermal instability. It is found that the increase in the temperature-dependent fluid viscosity acts to increase the stability of the basic flow.