Linear Stability Analysis on the Onset of Rayleigh-Bénard Convection in A Second-Order Fluid with Maxwell-Cattaneo Law under the Effect of Non-Uniform Temperature Gradient

Abstract

Abstract

A Linear stability analysis is performed to study the effect of non-uniform temperature gradient on the onset of Rayleigh-Bénard convection in a second order fluid with Maxwell-Cattaneo law. The eigenvalue is obtained for general boundary condition on velocity and temperature using Galerkin technique. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on the onset of convection is discussed. It is observed that the Cattaneo number and Prandtl number advances the onset of convection but the Viscoelastic parameter delays the onset of convection.

Keywords: Maxwell-Cattaneo law, Non-Uniform Temperature Gradient, Galerkin Technique, Second order fluid, Biot Number

Cite this Article

Keerthana S, Smita S Nagouda. Linear Stability Analysis on the Onset of Rayleigh-Bénard Convection in A Second-Order Fluid with Maxwell-Cattaneo Law Under the Effect of Non-Uniform Temperature Gradient. Recent Trends in Fluid Mechanics. 2018; 5(1): 18–30p.