Computation of internal heat source, viscous dissipation and mass flow effects on mono-diffusive thermo-convective stability in a horizontal porous medium

Rafeeq, MKV; Reddy, GJ; Matta, A; Beg, OA

Abstract

A mathematical model is developed to investigate the combined effects of internal heat source and viscous dissipation
on the Hadley-Prats flow in an infinite parallel horizontal
porous layer with the inclined temperature gradient. Darcy’s
model is deployed for the porous medium which is considered to be isotropic and homogenous. Following nondimensionalization of the model, a linear instability analysis
is conducted and the basic steady state solution is derived.
Transverse or longitudinal roll disturbances are examined.
The dimensionless emerging eigenvalue problem is solved
numerically with Runge-Kutta and shooting methods to determine the eigenvalues as the vertical values of the thermal
Rayleigh number for both cases of disturbances i. e. longitudinal and transverse rolls. The critical wave number and
critical vertical thermal Rayleigh number are identified
for different thermo physical parameters. The conceptual
study is constructed to comprehend the consequence of the
viscous dissipation of the mono-diffusive instability analysis
of Hadley-Prats flow thermal convection in the fluid saturated infinite horizontal porous layer. The simulations show
that increased internal heat generation causes efficient destabilisation in all areas, since it raises the overall temperature of the system. For higher value of Gebhart number a significant destabilizing effect of Hadley-Prats flow is computed. Internal heat generation also strongly modifies the critical
vertical Rayleigh number. Higher values of horizontal Rayleigh number , generally result in a decrease in critical
vertical Rayleigh number and therefore flow destabilization
in the porous medium. Extensive interpretation of the solutions relating to the onset of convection is provided. The
study is relevant to geophysical flows and materials fabrication systems.

Citation

Rafeeq, M., Reddy, G., Matta, A., & Beg, O. (2024). Computation of internal heat source, viscous dissipation and mass flow effects on mono-diffusive thermo-convective stability in a horizontal porous medium. ˜An œinterdisciplinary journal of discontinuity, nonlinearity, and complexity (Online), 13(3), 517-529. https://doi.org/10.5890/DNC.2024.09.010

• Journal Article Type: Article
• Acceptance Date: Nov 28, 2022
• Publication Date: 2024-04
• Deposit Date: Jan 10, 2023
• Publicly Available Date: May 1, 2026
• Journal: Discontinuity, Nonlinearity, and Complexity
• Print ISSN: 2164-6376
• Electronic ISSN: 2164-6414
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 3
• Pages: 517-529
• DOI: https://doi.org/10.5890/DNC.2024.09.010
• Publisher URL: https://www.lhscientificpublishing.com/Journals/DNC-Default.aspx
• Additional Information: Projects : Computational fluid dynamics simulation of hydrodynamic stability in geothermal systems