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.

中文翻译：

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具有内热源和反应效应的局部热非平衡多孔介质中双扩散对流的稳定性分析

研究了内部热源和反应对局部热非平衡多孔介质中热溶对流开始的影响，其中流体和固体骨架的温度可能不同。边界条件固定的 Darcy-Brinkman 型线性不稳定性和非线性稳定性理论是在层从下方加热和盐化的情况下进行的。这 D 2 {D^{2}} Chebyshev tau 技术用于计算受两种理论边界条件约束的相关方程组。考虑了三种不同类型的内部热源函数，第一种跨层增加，而第二种减少，第三种加热和冷却方式不均匀。图形描述了不同参数对瑞利数的影响。此外，结果表明，利用内部热源、反应和非平衡对确定对流稳定性和不稳定性阈值有显着影响。