Semi-analytical solution for steady-periodic heat transfer of attached underground engineering envelope

The solution for steady-periodic heat transfer of attached underground engineering can be expressed by complex temperature. The solution involves two parts: steady temperature and complex amplitude of the annual temperature fluctuations. Using a mathematical model of heat transfer of attached underground engineering, the calculation area is divided into eight rectangular blocks according to the interzone temperature profile estimation (ITPE) technology, and the solutions are obtained for all the parts using the separation of variables method. During the solution, the Fourier coefficients are determined based on the continuity of the heat flux and boundary conditions; as a result, a system of 14N linear equations with 14N unknowns is obtained, where N is the truncation point of the Fourier series. The linear equations can be easily solved with a standard method (e.g. Gauss–Jordan elimination). The semi-analytical solution obtained by the ITPE can provide rapid and accurate solution for calculation of heat transfer as well as the basis for analysis of the influential factors of the heat transfer.