The stability of natural convection in a vertical layer of heat-generating Darcy porous medium saturated with an Oldroyd-B fluid using a local thermal non-equilibrium (LTNE) model has been investigated numerically. The impermeable vertical walls of the porous layer are maintained at different uniform temperatures. As a consequence of LTNE model, two temperature equations representing the fluid and solid phases separately are used for the heat transport equation. A uniform volumetric heating in both fluid and solid phases is considered and the transfer of heat between the phases is considered in the basic state. The internal heating introduced asymmetry in the basic flow which led to the existence of competing modes. The intricacies of internal heat source strength in the fluid and the solid phases are clearly discerned on the stability of the system. The stress relaxation parameter $$\Lambda_{1}$$ Λ 1 , fluid-heat generation parameter $$Q_{f}$$ Q f , solid-heat generation parameter $$Q_{s}$$ Q s and the porosity-modified conductivities ratio $$\gamma$$ γ were found to exhibit destabilizing effect on the system, while the strain retardation parameter $$\Lambda_{2}$$ Λ 2 shows an opposite trend even in the presence of internal heating.

中文翻译：

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热非平衡对具有内部热源的 Oldroyd-B 流体饱和垂直多孔层中自然对流稳定性的影响

已使用局部热非平衡 (LTNE) 模型对用 Oldroyd-B 流体饱和的发热达西多孔介质垂直层中自然对流的稳定性进行了数值研究。多孔层的不可渗透垂直壁保持在不同的均匀温度。作为 LTNE 模型的结果，分别代表流体和固相的两个温度方程用于传热方程。考虑了流体和固相中的均匀体积加热，并且在基本状态下考虑了相之间的热传递。内部加热在基本流动中引入了不对称性，从而导致了竞争模式的存在。流体和固相中内部热源强度的复杂性在系统的稳定性上清晰可见。应力松弛参数 $$\Lambda_{1}$$ Λ 1 ，流体生热参数 $$Q_{f}$$ Q f ，固体生热参数 $$Q_{s}$$ Q s 和孔隙率- 修正电导率比 $$\gamma$$ γ 对系统表现出不稳定效应，而应变延迟参数 $$\Lambda_{2}$$ Λ 2 显示出相反的趋势，即使在存在内部加热的情况下。