Abstract
The linear instability and nonlinear stability analyses are performed for the model of bidispersive local thermal non-equilibrium flow. The effect of local thermal non-equilibrium on the onset of convection in a bidispersive porous medium of Darcy type is investigated. The temperatures in the macropores and micropores are allowed to be different. The effects of various interaction parameters on the stability of the system are discussed. In particular, the effects of the porosity modified conductivity ratio parameters, and , with the inter-phase momentum transfer parameters and, on the onset of thermal Convection are also considered. Furthermore, the nonlinear stability boundary is found to be below the linear instability threshold. The numerical results are presented for free-free boundary conditions.
Highlights
Thermal convection in a bidispersive porous medium is one of much current interest due to its practical applications in various fields, such as in heat pipes technologies, catalytic chemistry, methane recovery from coal deposits, and thermal insulation see e.g., Szczygieł [1], Lin et al [2], Shi and Durucan [3], Nield and Bejan [4], Straughan [5], and the referencesIraqi Journal of Science, 2022, Vol 63, No 2, pp: 702-722 therein
Important work discussed the problem of thermal convection in a bidispersive porous medium is done by Gentile and Straughan in
The papers by Franchi et al [19] present the effect of local thermal non-equilibrium on a bidispersive porous medium
Summary
Thermal convection in a bidispersive porous medium is one of much current interest due to its practical applications in various fields, such as in heat pipes technologies, catalytic chemistry, methane recovery from coal deposits, and thermal insulation see e.g., Szczygieł [1], Lin et al [2], Shi and Durucan [3], Nield and Bejan [4], Straughan [5], and the references. The papers by Franchi et al [19] present the effect of local thermal non-equilibrium on a bidispersive porous medium. These authors work on development a theory of double porosity material, where the solid skeleton, and the fluid in the micro and macropores may have different temperatures. Gaikwad et al [28] explained the combined effect of rotation and local thermal non-equilibrium on the double diffusive convection using linear instability and nonlinear stability methods. We investigate in details the thermal convection in a bidisperse porous medium where two different temperature fields for the porous solid and for the saturating fluid are assumed in order to model the local thermal non-equilibrium. To obtain the decay of u f and up , we have to employ the arithmetic geometric mean inequality in (10) and (10)
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