Abstract
Linear and nonlinear stability analyses of Hadley–Prats flow in a horizontal fluid-saturated porous medium with a heat source are performed. The results indicate that, in the linear case, an increase in the horizontal thermal Rayleigh number is stabilizing for both positive and negative values of mass flow. In the nonlinear case, a destabilizing effect is identified at higher mass flow rates. An increase in the heat source has a destabilizing effect. Qualitative changes appear in Rz as the mass flow moves from negative to positive for different internal heat sources.
Highlights
Thermal convection driven by an internal heat source with a horizontal mass flow has many practical applications such as underground energy transport, cooling of nuclear reactors, food processing, oil recovery, underground storage of waste products and thermal convection in clouds [1,2,3,4]
We have analyzed the instability of thermal convection in Hadley-Prats flow subject to an internal heat source using linear and nonlinear stability analysis
– An increase in the internal heat source causes a strong destabilization in all cases, as it raises the global temperature of the system
Summary
Thermal convection driven by an internal heat source with a horizontal mass flow has many practical applications such as underground energy transport, cooling of nuclear reactors, food processing, oil recovery, underground storage of waste products and thermal convection in clouds [1,2,3,4].In the last few decades, convection involving internal heat sources has attracted particular research attention. Parthiban and Patil [9] investigated thermal convection due to non-uniform heating boundaries with inclined thermal gradients in the presence of an internal heat source, followed by an extension to anisotropic porous layers by Parthiban and Patil [10]. The case of an inclined layer with internal heat source was analyzed by Barletta et al [11], where both boundaries were isothermal and kept at the same temperatures. Rionero and Straughan [12] investigated the linear and nonlinear effects in the presence of variable gravity effect and heat generation. Hill [14] investigated a porous layer with concentration based internal heat generation, with linear and nonlinear stability analyses of thermosolutal convection. Thermosolutal convection in a saturated anisotropic porous medium with internal heat generation is reported by Bhadauria [16]. Borujerdi et al [18] study the influence of Darcy number on the critical Rayleigh number in onset of
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