Onset of Convection in a Porous Medium With Internal Heat Generation

1976 ◽  
Vol 98 (1) ◽  
pp. 49-54 ◽  
Author(s):  
R. D. Gasser ◽  
M. S. Kazimi
Keyword(s):  
Porous Medium ◽  
Heat Generation ◽  
Lower Boundary ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Rigid Surface ◽  
Onset Of Convection ◽  
Rayleigh Numbers ◽  
Upper Boundary ◽  
Small Disturbances

The conditions leading to onset of thermal convection in a horizontal porous layer are determined analytically using the method of linear stability of small disturbances. The lower boundary is treated as a rigid surface and the upper boundary as a free surface. The critical internal and external Rayleigh numbers are determined for both stabilizing and destabilizing boundary temperatures. The predicted critical external Rayleigh number in the limit of no heat generation is in agreement with the critical number predicted for a porous medium heated from below.

scholarly journals Vibrational effect on internal heated porous medium in the presence of chaos

2019 ◽  
Vol 4 (1) ◽  
pp. 13-23
Author(s):  
Palle Kiran
Keyword(s):  
Porous Medium ◽  
Heat Generation ◽  
Energy Equation ◽  
Internal Heat ◽  
Momentum Equation ◽  
Internal Heat Generation ◽  
System Parameters ◽  
Chaotic Convection ◽  
Chaotic Nature ◽  
Rayleigh Numbers

The present article investigates a chaotic convection under modulation in the presence of internal heat generation. The viscoelastic fluid saturating porous medium, heated from below is considered; a modified Darcy’s momentum equation and heat generation term used in energy equation. An autonomous system of fourth order differential equations have been deduced by using truncated Galerkin expansions. The asymptotic behavior can be stationary, periodic, or chaotic, depending upon the values of system parameters. It is found that a better combination of values of modulation parameters and scaled Rayleigh, internal Rayleigh numbers provides a way for chaos. Both a temperature and gravity modulation of the medium is to enhance or diminish the behavior of chaotic nature of the system. Due to high internal heat generation there is a chance to devolve a new kind of stable or unstable points in the system. Finally, heat transfer results are presented in terms of Nusselt number.

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