Study on heat conduction of functionally graded plate with the variable gradient parameters under the H(t) heat source

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.

Keywords:

• Functionally graded plate
• heat conduction
• H(t) heat source
• hybrid numerical method

Additional information

Funding

The research is supported by the National Natural Science Foundation of China [No. 11302159], Basic Research Plan of Natural Science in Shannxi Province [No. 2018JM5099], and Scientific Research Program Funded by Shaanxi Provincial Education Department [No. 19JK0412].