Abstract In this paper, we address the influence of the thermal non-equilibrium state on double-diffusive convection in a porous enclosure, subject to constant heat and solute fluxes at the vertical walls, while other walls of the enclosure are adiabatic. For this, Darcy model has been adopted. The governing equations are solved numerically by the ADI method and analytically by using parallel flow assumption valid for the slender enclosure. A comparative study has been made in between buoyancy aiding flow(i.e., buoyancy ratio, N > 0 ) and buoyancy opposed flow(i.e., buoyancy ratio, N 0 ). It was found that same as LTE (local thermal equilibrium) state particular oscillations and multiple solutions have also been observed on considering local thermal non-equilibrium (LTNE) state between the fluid and solid phase, for a certain range of interphase heat transfer coefficient (H) and conductivity ratio of fluid and solid ( γ ), when both buoyancy forces are opposite in nature (buoyancy ratio, N 0 ). The range of the interval for buoyancy ratio, I NM , (in which multiple solutions exists) increases on increasing the value of H as well as γ , while the range of the interval for buoyancy ratio, I NO , (in which oscillation exits) vary in a subtle way. In general, same as LTE state, here also I NO is found to be a subset of I NM for most of the values of H as well as γ considered in this study. Apart from this, in case of buoyancy aiding flow, the enhancement of aspect ratio (A) enhances the heat transfer rate for both the phases, up to a threshold value A 0 of A, beyond that threshold value the impact of the same is negligible, while Sh acts in other way.

中文翻译：

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由于外壳壁上的热量和溶质的横向通量，热溶质自然对流的热非平衡方法：多解和振荡

摘要 在本文中，我们讨论了热非平衡状态对多孔外壳中双扩散对流的影响，受垂直壁处恒定的热量和溶质通量影响，而外壳的其他壁是绝热的。为此，采用了达西模型。控制方程通过 ADI 方法进行数值求解，并通过使用对细长外壳有效的平行流动假设进行解析。对助浮力流（即浮力比，N > 0 ）和反浮力流（即浮力比，N 0 ）进行了对比研究。发现与LTE（局部热平衡）状态相同，在考虑流体和固相之间的局部热非平衡（LTNE）状态时，也观察到了特定的振荡和多种解决方案，对于一定范围的相间传热系数（H）和流体与固体的传导率（γ），当两者的浮力性质相反（浮力比，N 0 ）时。浮力比区间 I NM 的范围（其中存在多个解）随着 H 和 γ 的值的增加而增加，而浮力比区间 I NO 的范围（其中存在振荡）以微妙的方式变化。通常，与 LTE 状态相同，对于本研究中考虑的大多数 H 和 γ 值，这里也发现 I NO 是 I NM 的子集。除此之外，在浮力辅助流动的情况下，纵横比 (A) 的增强提高了两相的传热速率，达到 A 的阈值 A 0 ，超过该阈值，相同的影响可以忽略不计，而 Sh 则以其他方式行事。