Abstract
Flow and heat transfer in a horizontal porous layer subjected to internal heat generation and g-jitter is considered for the Dirichlet thermal boundary condition. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number. For the low amplitude, high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection when the porous layer is heated from below. When the porous layer is cooled from below and heated from above, the vibration has a destabilizing effect in the presence of internal heat generation. It is also demonstrated that when the top and bottoms walls are cooled and rigid/impermeable, the critical Rayleigh number is infinitely large and conduction is the only possible mode of heat transfer. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions.
Highlights
Gravity driven natural convection in fluid saturated porous media has been widely studied for various configurations for proposed engineering applications
This paper will not consider case 1 and case 5 which corresponds to the Neumann thermal boundary condition
For the Neumann thermal boundary condition, the formulation for Equation (11) needs to be changed to the appropriate function; that is outside the scope of the current study
Summary
Gravity driven natural convection in fluid saturated porous media has been widely studied for various configurations for proposed engineering applications. The focus of the current work is to consider the effects of vibration (g-jitter) for a porous layer with internal heat generation In principle this case corresponds to one where the basic temperature is non-constant but rather a function of the vertical z- co-ordinate. Studies around porous media subjected to internal heat generation and vibration effects for high temperature reactors should largely be driven by the safety aspects surrounding this technology [17]. The analysis in this paper uses a gas cooled porous reactor as an example, other examples for application of this work include systems involving heat extraction or storage (in porous media) using molten salts These storage systems are largely found in the concentrating solar plant (CSP), and central receiver systems using molten salts as the working fluid.
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