Heat Transfer in Porous Media
Heat Transfer in Porous Media
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DOI：
10.5772/16210
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发表时间：
2011-02
期刊：
影响因子：
--
通讯作者：
E. Languri;D. Ganji
中科院分区：
文献类型：
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作者：
E. Languri;D. Ganji
在流体在多孔介质中传输的许多问题中，换热现象起着至关重要的作用。研究热传导方程的主要应用之一是聚合物复合材料的制造过程[1]，例如液体复合材料成型。在这种技术中，复合材料是通过将预制件与注入模具入口处的树脂浸渍而成的。一些热固性树脂在充模过程中和之后可能会发生交联聚合反应，称为固化反应。因此，在LCM的充模过程中，树脂的热传递和放热聚合反应是不可忽略的。由此可见，热传导方程在多孔介质非等温流动中的重要性。通常，能量平衡方程可以用两种不同的方法推导：(1)两相或热非平衡模型[2-6]和(2)局部热平衡模型[7-18]。在两相模型中，两相(如液态复合材料成型过程中的树脂和纤维)分别存在两个不同的能量平衡方程，两个方程之间的换热通过换热系数来实现。在热平衡模型中，我们假设各相(如树脂和纤维)达到局部热力学平衡。因此，只需要一个能量方程作为热控制方程[3，5]。首先，我们考虑了各向同性多孔介质简单情况下的热传导控制方程。假定辐射效应、粘性耗散和压力所做的功可以忽略不计。我们通过假定S的局部热平衡fT==进一步简化，其中S T和fT分别是固体和液体相温度。进一步的假设是，在固体和流体中存在平行的传导换热。取多孔介质的平均转速，我们有以下关于固体和液体相的公式，
Heat transfer phenomena play a vital role in many problems which deals with transport of flow through a porous medium. One of the main applications of study the heat transport equations exist in the manufacturing process of polymer composites [1] such as liquid composite molding. In such technologies, the composites are created by impregnation of a preform with resin injected into the mold’s inlet. Some thermoset resins may undergo the cross-linking polymerization, called curing reaction, during and after the mold-filling stage. Thus, the heat transfer and exothermal polymerization reaction of resin may not be neglected in the mold-filling modeling of LCM. This shows the importance of heat transfer equations in the non-isothermal flow in porous media. Generally, the energy balance equations can be derived using two different approaches: (1) two-phase or thermal non-equilibrium model [2-6] and (2) local thermal equilibrium model [7-18]. There are two different energy balance equations for two phases (such as resin and fiber in liquid composite molding process) separately in the two-phase model, and the heat transfer between these two equations occur via the heat transfer coefficient. In the thermal equilibrium model, we assume that the phases (such as resin and fiber) reach local thermodynamic equilibrium. Therefore, only one energy equation is needed as the thermal governing equation, [3,5]. Firstly, we consider the heat transfer governing equation for the simple situation of isotropic porous media. Assume that radioactive effects, viscous dissipation, and the work done by pressure are negligible. We do further simplification by assuming the thermal local equilibrium that s f T T T = = where s T and f T are the solid and fluid phase temperature, respectively. A further assumption is that there is a parallel conduction heat transfer taking place in solid and fluid phases. Taking the average over an REV of the porous medium, we have the following for solid and fluid phases,