Purpose

Aiming at finding the velocity distribution profile and other flow characteristic parameters such as the Poiseuille (Po) number, this study aims to focus on the three-dimensional forced convective flow inside rectangular ducts filled with porous media commonly used in air-based solar thermal collectors to enhance the thermal performance. The most general model for the fluid flow (i.e. the non-linear Darcy–Brinkman–Forchheimer partial differential equation subjected to slip and no-slip boundary conditions) is considered.

Design/methodology/approach

The general governing equations are solved analytically based on the perturbation technique and the results are validated against numerical simulation study based on a finite-difference solution over a non-uniform but structured grid.

Findings

The analytical velocity distribution profile based on exponential functions for the above-mentioned general case is obtained, and accordingly, expressions for the Po are introduced. It is found that the velocity distribution tends to be uniform by increasing the aspect ratio of the duct. Moreover, a criterion for considering/neglecting the nonlinear drag term in the momentum equation (i.e. the Forchheimer term) is proposed. According to the sensitivity analysis, results show that the nonlinear drag term effects on the Nusselt number are important only in porous media with high Darcy numbers.

Originality/value

A general analytic solution for three-dimensional forced convection flows through rectangular ducts filled with porous media for the general model of Darcy–Brinkman–Forchheimer and the general boundary condition including both no-slip and slip-flow regimes is obtained. An analytic expression to calculate Po number is obtained which can be practical for engineering estimations and a basis for validation of numerical simulations. A criterion for considering/neglecting the nonlinear drag term in the momentum equation is also introduced.

中文翻译：

---

多孔介质增强集热器内部强制对流：从宏观到微通道

目的

本研究旨在寻找速度分布剖面和泊肃叶 ( Po ) 数等其他流动特征参数，重点研究空气式太阳能集热器常用的填充多孔介质的矩形管道内的三维强制对流流动。以提高热性能。考虑了流体流动的最通用模型（即非线性 Darcy-Brinkman-Forchheimer 偏微分方程受滑移和无滑移边界条件的影响）。

设计/方法/方法

基于微扰技术对一般控制方程进行解析求解，并根据基于非均匀但结构化网格的有限差分解的数值模拟研究验证结果。

发现

得到了上述一般情况下基于指数函数的解析速度分布剖面，并相应地引入了Po的表达式。发现通过增加管道的纵横比，速度分布趋于均匀。此外，还提出了考虑/忽略动量方程中非线性阻力项（即 Forchheimer 项）的准则。根据敏感性分析，结果表明非线性拖曳项对 Nusselt 数的影响仅在具有高 Darcy 数的多孔介质中很重要。

原创性/价值

Darcy-Brinkman-Forchheimer 的一般模型的三维强制对流流过充满多孔介质的矩形管道的一般解析解，并获得了包括无滑移和滑移流状态的一般边界条件。得到了计算Po数的解析表达式，可用于工程估算和数值模拟验证的基础。还介绍了考虑/忽略动量方程中非线性阻力项的准则。