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 Gortler-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.
Highlights
In the following, the main concerns were directed to the onset of three-dimensional instability in stagnation point flow
A literature survey related to this topic revealed that Gortler [12] was the first to study the stability problem of steady two-dimensional boundary layer flow of an Article published by EDP Sciences
It’s found that the onset conditions of thermal instability are significantly affected by the viscosity parameter and that the increase in the temperature-dependent fluid viscosity acts to increase the stability of the basic flow
Summary
The main concerns were directed to the onset of three-dimensional instability in stagnation point flow. Dimensionless Cartesian coordinates w Wall condition incompressible viscous fluid, and derived the disturbance equations for the Hiemenz flow. These equations were studied by Hammerlin [13] and demonstrated that plane stagnation flow can sustain three-dimensional disturbances. To the best of the authors’ knowledge, very little is known about the thermal instability of the stagnation point flows over heated horizontal surfaces In this regard, Chen et al [18], reveal that thermal excitation generates instabilities when the Rayleigh number exceeds some critical value. It’s found that the onset conditions of thermal instability are significantly affected by the viscosity parameter and that the increase in the temperature-dependent fluid viscosity acts to increase the stability of the basic flow
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