Abstract
Double-diffusive Hadley–Prats flow with a concentration based heat source is investigated through linear and non-linear stability analyses. The resultant eigenvalue problems for both theories are solved numerically using Shooting and fourth order Runga–Kutta methods, with the critical thermal Rayleigh number being evaluated with respect to various flow governing parameters such as the magnitudes of the heat source and mass flow. It is observed, in the linear case, that an increase in the horizontal thermal Rayleigh number is stabilising for both positive and negative values of the solutal Rayleigh number. In the non-linear case, a destabilising effect is identified at higher mass flow rates. An increase in both the heat source and mass flow results in destabilisation.
Highlights
Double-diffusive convection in a fluid-saturated porous media has received much attention during the last few decades, due to its many real-world applications such as underground energy transport (Nagano et al [1]), food processing, oil recovery, the spreading of pollutants etc. (Bendrichi and Shemilt [2]; Reddy et al [3]) and multiple environmental processes (Xi and Li[4] and Kwon et al [5])
If the flow is subjected to horizontal mass flow along with inclined thermal gradients, the resultant flow is known as Hadley-Prats flow (Barletta and Nield [17])
Our goal in this study is to bring out the effect of a concentration based heat source on the double-diffusive Hadley-Prats flow in porous media
Summary
Double-diffusive convection in a fluid-saturated porous media has received much attention during the last few decades, due to its many real-world applications such as underground energy transport (Nagano et al [1]), food processing, oil recovery, the spreading of pollutants etc. (Bendrichi and Shemilt [2]; Reddy et al [3]) and multiple. The motivation of the present work is to investigate double-diffusive Hadley flow in porous media induced by the active absorption of radiation, as demonstrated by Krishnamurti [18] for a viscous fluid in the absence of Hadely circulation and Hill [19] for flows through porous media. Their model has received much attention in recent years as it provides an accurate model of cumulus convection as it occurs in the atmosphere. We organize the paper in the following manner: section 2 constructs the governing equations of the model under consideration; in sections 3 & 4 we discuss the basic-state solution and perturbation equations; in sections 5 & 6 linear and non-linear analyses are performed, respectively, with the results and conclusions being discussed in sections 7 and 8, respectively
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