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首页> 外文期刊>International Journal of Heat and Mass Transfer >Mathematical optimisation of laminar forced convection heat transfer through a vascularised solid with square channels
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Mathematical optimisation of laminar forced convection heat transfer through a vascularised solid with square channels

机译：层状强制对流传热的数学优化

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摘要

This paper presents a three-dimensional geometric optimisation of cooling channels in forced convection of a vascularised material with the localised self-cooling property subjected to a heat flux. A square configuration was studied with different porosities. Analytical and numerical solutions were provided. The geometrical configuration was optimised in such a way that the peak temperature was minimised at every point in the solid body. The optimisation was subject to the constraint of a fixed global volume of solid material, but the elemental volume was allowed to morph. The solid material was subject to a heat flux on one side and the cooling fluid was forced through the channels from the opposite direction with a specified pressure difference. The structure had three degrees of freedom as design variables: the elemental volume, channel hydraulic diameter and channel-to-channel spacing. A gradient-based optimisation algorithm was used to determine the optimal geometry that gave the lowest thermal resistance. This optimiser adequately handled the numerical objective function obtained from numerical simulations of the fluid flow and heat transfer. The numerical results obtained were in agreement with a theoretical formulation using scale analysis and the method of intersection of asymptotes. The results obtained show that as the pressure difference increases, the minimised thermal resistance decreases. The results also show the behaviour of the applied pressure difference on the optimised geometry. The use of the optimiser made the numerical results to be more robust with respect to the optimum internal configurations of the flow systems and the dimensionless pressure difference.
机译：本文提出了一种三维几何优化冷却通道的强制对流材料的血管化材料与局部自冷却性能受热通量。研究了具有不同孔隙率的正方形结构。提供了分析和数值解决方案。以这样的方式优化了几何构型：使固体中每个点的峰值温度最小。优化过程受固定的整体固体体积约束，但元素体积允许变形。固体材料的一侧受到热通量的作用，冷却流体从相反的方向以规定的压力差从通道中通过。该结构具有三个自由度作为设计变量：元素体积，通道水力直径和通道间距。基于梯度的优化算法用于确定给出最低热阻的最佳几何形状。该优化器充分处理了从流体流动和传热的数值模拟获得的数值目标函数。得到的数值结果与使用比例尺分析和渐近线相交方法的理论公式一致。获得的结果表明，随着压力差的增加，最小化的热阻会降低。结果还显示了在优化的几何形状上施加的压差的行为。对于流动系统的最佳内部配置和无量纲的压差，优化器的使用使数值结果更加可靠。

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