Study of Heat Transport in a Porous Medium Under G-jitter and Internal Heating Effects

Abstract

In this article we study the combined effect of internal heating and time-periodic gravity modulation on thermal instability in a closely packed anisotropic porous medium, heated from below and cooled from above. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the porous medium. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. The effects of various parameters such as; internal Rayleigh number, amplitude and frequency of gravity modulation, thermo-mechanical anisotropies, and Vadász number on heat transport has been analyzed. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further it is found that the heat transport can also be controlled by suitably adjusting the external parameters of the system.

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

“…The heat transport is more at higher values of R i . This confirms the results obtained most recently by Bhadauria et al [42] and Bhadauria et al [43]. Further, we have Nu Ri¼1:0 < Nu Ri¼1:1 < Nu Ri¼1:3…”

“…Therefore, the role of internal heat generation becomes very important in several applications including storage of radioactive materials, combustion and fire studies, geophysics, reactor safety analysis and metal waste form development for spent nuclear fuel. However, there are only few studies available in which the effect of internal heating on convective flow in a fluid layer has been investigated [34][35][36][37][38][39][40][41][42][43][44].…”

Linear and Weak Nonlinear Double Diffusive Convection in a Viscoelastic Fluid Saturated Anisotropic Porous Medium with Internal Heat Source

“…Later Parthiban and Patil (1995) found that the internal heat source advances the on-set of convection under the effect of non-uniform boundaries temperatures, Alex et al (2001) studied the thermal instability in porous media by taking variable gravity with internal heat source and found that the stationary longitudinal mode is favourable mode for the onset of convection, Hill (2005) studied the linear and nonlinear effect of concentration based internal heat source on the stability for double diffusive convection by using Darcy model, Saravanan (2009), Cookey et al (2010 found that the internal heat source parameter destabilizes the onset of stationary convection in a low Prandtl number, Nouri-Borujerdi et al (2007) analyses the effect of uniform heat source for the thermal nonequilibrium model, Nouri-Borujerdi et al (2008) studied the instability with uniform heat generation and including the Brinkman term, Capone et al (2011) studied the penetrative convection in the presence of internal heat source in an anisotropic porous layer with a constant through flow via internal heat source. Bhadauria et al (2011) studied the effect of internal heat source in rotating anisotropic porous layer, Bhadauria (2012) investigated the effect of internal heat source on double diffusive convection in anisotropic porous layer, Bhadauria et al (2013) analyses the effect of internal heat source in their nonlinear gravity modulation analysis and re-ported that internal heat source increases heat trans-port, Gaikwad and Kouser (2013) Viscoelastic fluids finds its application in modern industries, paint and auto-mobile industries, enhanced oil recovery, geothermal reservoirs, also some biological fluid falls in this category. Internal heat of the earth causes convection in earth's mantle, also in the solidification of metals there is a temperature difference between upper and lower layer which is caused by internal heat source.…”

Effect of Internal Heating on Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Medium

“…Capone et al [43] carried -27 -DOI: 10.5963/AMSA0301004 out the linear and nonlinear stability analysis of double-diffusive penetrative convection in an anisotropic porous layer with a constant throughflow via internal heat source. Recently Bhadauria group [44][45][46][47] have studied the problem of thermal instability in porous media with internal heating, considering various physical models. Double diffusive convection occurs in many systems in industry and nature, and in the present context, is of particular interest in the study of extraction of metals from ores where a mushy layer is formed during solidification of a metalic alloy.…”