Abstract Forced convection heat transfer is analytically performed in a channel partially filled with porous media located at two inner walls under local thermal non-equilibrium (LTNE) condition. A constant heat flux is imposed at the channel walls. The Brinkman extended Darcy model is applied in the porous region and the stress jump and continuity conditions are employed at the interface. Exact solutions are obtained for velocity, pressure drop, the fluid and solid temperatures and Nusselt number. The effects of pertinent parameters on the fluid flow and heat transfer are conducted. Furthermore, the solution for the Nusselt number is compared to that by applying the local thermal equilibrium (LTE) assumption and the validity of the LTE is examined. It is shown that by applying LTNE model for different solid to fluid effective thermal conductivity ratios (K) and Biot numbers (Bi), the variations of Nusselt number with hollow ratio include three types of curves, which are: a maximized Nusselt number occurs at a small optimum hollow ratio, Nusselt number monotonically decreases by increasing hollow ratio and a minimized Nusselt number occurs at a small hollow ratio, respectively. For high K, a small critical value of S at which the Nusselt number reaches to LTE Nusselt number occurs and it lowers with the increase of Bi number and the decrease of Darcy number; while for low K, the LTNE Nu number versus hollow ratio is almost the same with LTE Nu number and therefore the LTE is valid. The stress jump at the interface is found to have negligible effect on the Nusselt number and the pressure drop, except in a high Darcy number with a low stress jump coefficient where the calculation of pressure drop need to account for the stress jump effect at the interface and the Nusselt numbers for both LTE and LTNE models slightly differs from the case of stress continuity interface condition.

中文翻译：

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使用 LTNE 模型求解具有应力跳跃和连续性界面条件的部分多孔通道中的流体流动和传热的解析解

摘要 在局部热非平衡 (LTNE) 条件下，在位于两个内壁的部分填充多孔介质的通道中，对强制对流换热进行了分析。在通道壁上施加恒定的热通量。多孔区域采用 Brinkman 扩展达西模型，界面采用应力跳跃和连续性条件。可以获得速度、压降、流体和固体温度以及努塞尔特数的精确解。进行了相关参数对流体流动和传热的影响。此外，通过应用本地热平衡 (LTE) 假设将 Nusselt 数的解决方案与解决方案进行比较，并检查 LTE 的有效性。结果表明，应用LTNE模型对不同固液有效热导率(K)和毕奥数(Bi)，努塞尔数随空心比的变化包括三种曲线，即： 最大努塞尔数出现在一个小的最佳空心比，努塞尔特数随着空心比的增加而单调减少，而最小的努塞尔数分别出现在一个小的空心比。对于高K，出现Nusselt数达到LTE Nusselt数的小临界值S，并且随着Bi数的增加和Darcy数的减少而降低；而对于低K，LTNE Nu数对空心比与LTE Nu数几乎相同，因此LTE是有效的。发现界面处的应力跳跃对努塞尔数和压降的影响可以忽略不计，