A novel hybrid flux finite element model to steady heat conduction in porous materials

Abstract

A new hybrid finite-element model was developed for heat flux and temperature analyses in porous material. The model in this paper was based on an assumed heat flux hybrid finite-element method, which is a two-field functional. An independent heat flux field that meets a priori inner thermal equilibrium was assumed inside the element, and a temperature field was assumed on the cell boundary. Temperature was used as the Lagrange multiplier to introduce the continuous condition of heat flux at the hole edge into the functional, and a modified complementary energy functional was obtained. The element flux field that was built up of polynomial terms and reciprocal terms from the stream function and that can consider the shape of pores in location coordinates was raised for the first time. Several numerical examples are discussed and compared with conventional finite-element methods to validate the accuracy and efficiency of the proposed approach.

Keywords:

• Effective conductivity coefficient
• heat flux
• hybrid finite-element model
• temperature

Disclosure statement

The authors declared that they have no conflicts of interest to this work.

Data availability

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (grant No. 12062007).