Stability Analysis of Double Diffusive Convection in Local Thermal Non-equilibrium Porous Medium with Internal Heat Source and Reaction Effects

Abstract

The internal heat source and reaction effects on the onset of thermosolutal convection in a local thermal non-equilibrium porous medium are examined, where the temperature of the fluid and the solid skeleton may differ. The linear instability and nonlinear stability theories of Darcy–Brinkman type with fixed boundary condition are carried out where the layer is heated and salted from below. The D 2 {D^{2}} Chebyshev tau technique is used to calculate the associated system of equations subject to the boundary conditions for both theories. Three different types of internal heat source function are considered, the first type increases across the layer, while the second decreases, and the third type heats and cools in a nonuniform way. The effect of different parameters on the Rayleigh number is depicted graphically. Moreover, the results detect that utilizing the internal heat source, reaction, and non-equilibrium have pronounced effects in determining the convection stability and instability thresholds.

Magnetic and chemical reaction effects on double‐diffusive convection with the effect of heat and salt flux boundary conditions

“…There is extensive literature on penetrative convection via an internal heat source, see, for example, Carr, 41 Capone et al, 42,43 Gangadharaiah et al, 44 Shivakumara and Dhananjaya, 45 Goluskin and van der Poel, 46 Mahajan and Nandal, 47 and Mahajan et al 48 Recently, Gangadharaiah et al 49 investigated the effect of the internal heat source of double‐diffusive convection where the fluid layer is overlying a porous layer using a linear instability analysis. Furthermore, Noon and Haddad 50 investigated the stability analysis of double‐diffusive convection when the reaction and internal heat source effects are present, in which the layer has been salted and heated from the bottom for the Darcy–Brinkman model in local thermal nonequilibrium (LTNE) porous material. There are three various functions of the internal heat sources that are taken into account: increasing through the layer, decreasing through the layer, and the layer being heated and cooled irregularly.…”

Effects of LTNE on Two-Component Convective Instability in a Composite System with Thermal Gradient and Heat Source

“…A stability assessment of Brinkman-Bènard convection was studied by Siddabasappa et al [21]. Thermosolutal convection in an LTNE porous medium was examined by Noon and Haddad [22]. Corcione and Quintino [23] examined the dual-component effects for water-based nanofluids using Rayleigh-Bènard convection.…”