Research of the higher-order finite element arithmetic for radiation exchange

With the development of aeronautic and astronautic techniques, radiation becomes much more significant while the structure is exposed to the higher and higher temperature. Most of the current finite element software packages treat it using the net-radiation method or absorbed radiation method based on the assumption of isothermal surface with uniform radiation heat flux, which brings the conflict between the precision and the quantity of grids. Using integral method to compute the variable radiation heat flux in higher-order finite element, the precision can be improved greatly while using the same quantity of grids, because it is more consistent with the distribution of real temperature. In this paper, the integral is only processed on the same integral points as those used for solving the finite element equations, so it may be of high efficiency. In an academic testing model, the result is contrast to which get in ANSYS, proving the high precision of the method. Then an actual sandwich panel used in the thermal protection system is analyzed with the method, and the error is comparatively low to the analytical answer while the computation being of high efficiency.