Abstract A hybrid numerical method for heat conduction of functionally graded plate with the variable gradient parameters under the H(t) heat source was studied. A weighted residual equation of heat conduction was considered under thermal boundary conditions. In order to calculate temperature distribution of functionally graded plate with variable gradient parameters, the Fourier transform and inverse Fourier transform were applied and the temperature field was obtained under the H(t) heat source. Results show that the influences of the gradient parameters on temperature distribution are dramatic. But with the increase of gradient parameters, the influences of parameters on the temperature distribution are gradually reduced. When the gradient parameters reach a certain critical value, the temperature does not change anymore. By comparing the temperature distribution of the upper and lower surfaces, it is seen that the temperature presents a gentle downward trend with the increase of the heat source distance, while the temperature does not change with the time in farther distance from heat source. Also, the results show that the influence of the heat source has only partial and limited influence on the temperature, which is in accordance with St. Venant’s Principle. The law of the temperature distribution of the lower surface varies with the gradient parameters, which is also discussed, an optimal gradient parameter with the thermal insulation effect of the functionally graded plate is obtained.

中文翻译：

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H(t)热源下变梯度参数功能梯度板的热传导研究

摘要 研究了H(t)热源下具有变梯度参数的功能梯度板热传导的混合数值方法。在热边界条件下考虑了热传导的加权残差方程。为了计算梯度参数变函数梯度板的温度分布，应用傅里叶变换和傅里叶逆变换，得到了H(t)热源下的温度场。结果表明，梯度参数对温度分布的影响是显着的。但随着梯度参数的增加，参数对温度分布的影响逐渐减小。当梯度参数达到某个临界值时，温度不再变化。通过对比上下表面的温度分布可以看出，随着热源距离的增加，温度呈现平缓的下降趋势，而距离热源越远，温度则不随时间变化。此外，结果表明热源的影响对温度的影响只有部分和有限，这符合圣维南原理。下表面温度分布随梯度参数变化的规律也进行了讨论，得到了具有功能梯度板绝热效果的最优梯度参数。而离热源越远，温度不随时间变化。此外，结果表明热源的影响对温度的影响只有部分和有限，这符合圣维南原理。下表面温度分布随梯度参数变化的规律也进行了讨论，得到了具有功能梯度板绝热效果的最优梯度参数。而离热源越远，温度不随时间变化。此外，结果表明热源的影响对温度的影响只有部分和有限，这符合圣维南原理。下表面温度分布随梯度参数变化的规律也进行了讨论，得到了具有功能梯度板绝热效果的最优梯度参数。