Stability Analysis of Double Diffusive Convection in Local Thermal Non-equilibrium Porous Medium with Internal Heat Source and Reaction Effects
Najat J. Noon, Shatha A. Haddad
Abstract
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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi mathvariant="italic">D</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> {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.