Effects of Internal Heat Generation and Variable Viscosity on Onset of Rayleigh-Benard Convection

Gangadharaiah Y H,Suma S P

doi:10.24297/ijct.v5i3.3521

Abstract

In the present study, onset of stationary Rayleigh-Benard convective instability in a fluid layer, with internal heating and thermally dependent viscosity has been investigated by means of linear stability analysis. The dependence of viscosity is assumed to be exponential. The resulting eigen value problem is solved using a regular perturbation technique with wave number a as a perturbation parameter. The viscosity parameter and the presence of internal heat source play a decisive role on the stability characteristics of the system. It is observed that both stabilizing and destabilizing factors can be enhanced because of the simultaneous presence of a volumetric heat source and variable viscosity so that a more precise control (suppress or augment) of thermal convective instability in a fluid layer is possible.

Highlights

Convective flow in a thin layer of fluid, free at the upper surface and heated from below, is of fundamental importance and becomes a prototype to a more complex configuration in experiments and industrial processes
The mechanism of internal heating in a flowing fluid is relevant to the thermal processing of liquid foods through ohmic heating, where the internal heat generation serves for the pasteurization/sterilization of the food Ruan et al (2004)
It is noted that the appearance of newly formed sub layer, which first occurs at the maximum critical Rayleigh number Rc with associated viscosity parameter, continues to manifest itself after becoming dominant at the critical state

Summary

Introduction

Convective flow in a thin layer of fluid, free at the upper surface and heated from below, is of fundamental importance and becomes a prototype to a more complex configuration in experiments and industrial processes. The mechanism of internal heating in a flowing fluid is relevant to the thermal processing of liquid foods through ohmic heating, where the internal heat generation serves for the pasteurization/sterilization of the food Ruan et al (2004). Other important applications of flows with internal heat generation are relative to nuclear reactors, as well as to the geophysics of the earth’s mantle. In both cases, the internal heating is due to the radioactive decay. Due to the wide range of industrial and geophysical applications, extensive literature has been recently produced on this subject; see e.g. (Carr 2004, Carr and Putter 2003, Hill 2004, Straughan 2008, Straughan and Walker 1996, Tse and Chasnov 1998, and Zhang and Schubert 20020)

Methods

Results

Conclusion