One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface
One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface
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DOI：
10.1088/1742-6596/2090/1/012140
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
H. Ishida;Koichi Higuchi;Taiki Hirahata
中科院分区：
文献类型：
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作者：
H. Ishida;Koichi Higuchi;Taiki Hirahata
在这项研究中，我们将提出一个一维方程的垂直平均温度，模拟一个垂直薄，二维热交换器与可变的顶部固-流界面，恢复二维热信息，即稳定的温度和通量分布的顶部和温度固定的底面。这些量的相对误差小于5%，高度的最大梯度保持在约0.5以下，而计算时间减少到0.1- 5%，当与直接二维计算相比时，取决于顶面的形状。通过二维热传导方程的垂直平均导出的模型方程通过热交换器在温度相对于水平坐标的二阶导数仅取决于坐标的意义上足够薄的近似来闭合。在该模型方程中，换热器上方的流体方程通过常规的顶面法向热流方程解耦。然而，在原则上，模型和流体方程的耦合是可能的，通过温度和热通量的顶部界面上，恢复的模型方程。数学建模的类型可以适用于在某些（坐标变换）方向上具有极小尺寸的各种各样的物体。
In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the maximum gradient of the height kept approximately below 0.5, while the computational time is reduced to 0.1–5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation above the exchanger is decoupled by a conventional equation for the normal heat flux on the top surface. In principle, however, the coupling of the model and the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.