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本文研究了利用导热逆问题(IHCP)原理测算固体热扩散系数α和比热C_p的原理和方法。在最优化问题分析中,得到了α和C_p的无因次敏感度系数X_α~+和X_(C_p)~+的表达式,论证了X_α~+=-X_(C_p)~+,并揭示出它们的变化规律,为拓展IHCP方法的实施提供了理论依据。采用不锈钢或聚氨酯材质的球体或无限长圆柱试件的实验结果表明,即使测算时间r=6～1200秒,α值的测算最大偏差ε_(max)=1.97%～2.07%。但若在聚氨酯试件外壁面设置测点时,ε_(max)将高达22.09%。
In this paper, the principles and methods of calculating the thermal diffusivity α and the specific heat C_p of the solid by using the principle of inverse thermal conductivity (IHCP) are studied. In the analysis of optimization problems, we obtain the expressions of the dimensionless sensitivity coefficients α and C_p of X_α ~ + and X_ (C_p) ~ +, and demonstrate that X_α ~ + = - X_ (C_p) ~ + Their changing rules provide a theoretical basis for the implementation of IHCP method. Experimental results on stainless steel or polyurethane spheroids or infinitely long cylinder specimens show that the calculated maximum deviation of α is ε = 1.97% ~ 2.07%, even though the measurement time is from 6 to 1200 seconds. However, if the measuring point is set on the outer wall of polyurethane specimen, ε max will be as high as 22.09%.