非定指数抛物线型热平衡积分法：分析和基准练习
The heat-balance integral method by a parabolic profile with unspecified exponent: Analysis and Benchmark Exercises
摘要：
本文对Goodman的热平衡积分法进行了深入的分析，并将其应用于指数随边界条件变化的抛物型面。如果采用所讨论的特定抛物线分布，则定义规定温度分布的时间相关系数的经典Goodman边界条件在热层的前部不有效地工作。基于物理假设的附加约束增强了热平衡积分方法，并形成了定义抛物线指数的鲁棒算法。与Veinik方法的计算结果进行了比较，Veinik方法与Goodman方法有很大的不同，但也假设了热层的形成。该方法已被证明通过详细的解决方案的4个一维热传导问题的笛卡尔坐标，包括一个球的问题（通过改变变量）和过指定的边界条件的热层的脸。
英文摘要：
The heat-balance integral method of Goodman has been thoroughly analyzed in the case of a parabolic profile with unspecified exponent depending on the boundary condition imposed. That the classical Good man's boundary conditions defining the time-dependent coefficients of the prescribed temperature profile do not work efficiently at the front of the thermal layers if the specific parabolic profile at issue is employed. Additional constraints based on physical assumption enhance the heat-balance integral method and form a robust algorithm defining the parabola exponent . The method has been compared by results provided by the Veinik's method that is by far different from the Good man's idea but also assume forma tion of thermal layer penetrating the heat body. The method has been demonstrated through detailed solutions of 4 1-D heat-conduction problems in Cartesian co-ordinates including a spherical problem (through change of vari ables) and over-specified boundary condition at the face of the thermal layer.
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