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首页> 外文期刊>Mathematical Problems in Engineering: Theory, Methods and Applications >Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media
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Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media

机译：简化积分方案的扩展，以计算具有非散射介质的3D矩形外壳中的直接交换面积

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摘要

The evaluation of direct exchange areas (DEA) in zonal method is the most important task due to the heavy computer cost of multi-integrals together with the existing of singularities. A technique of variable transformation to reduce the fold of integrals, which was developed originally by Erkku (1959) to calculate the DEAs of uniformly zonal dividing cylindrical system, was extended by Tian and Chiu (2003) for nonuniformly zonal dividing cylindrical system with large thermal gradients. In this paper, we further extend the reduced integration scheme (RIS) to calculate the DEAs in three-dimensional rectangular system. The detail deductions of six-, five-, and fourfold integrals to threefold ones are presented; the DEAs in a rectangular system with assumption of gray medium are computed by the Gaussian quadrature integration (GQI) and the RIS comparatively. The comparisons reveal that the RIS can provide remarkable higher accuracy and efficiency than GQI. More interestingly and practicably, the singularities of DEAs can be decomposed and weakened obviously by RIS.
机译：由于多积分的巨大计算机成本以及奇异性的存在，采用区域方法评估直接交换区域（DEA）是最重要的任务。由Erkku（1959）最初开发的用于减小积分折叠的变量变换技术，用于计算均匀带状分割圆柱体系统的DEA，Tian and Chiu（2003）扩展了大热不均匀带状分割圆柱体系统的技术。渐变。在本文中，我们进一步扩展了简化积分方案（RIS），以计算三维矩形系统中的DEA。给出了六，五和四倍积分到三倍积分的详细推论;假设采用灰色介质的矩形系统中的DEA分别通过高斯积分（GQI）和RIS计算得出。比较表明，RIS可以提供​​比GQI更高的准确性和效率。更有趣和实用的是，RIS可以明显分解和削弱DEA的奇异性。

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