This study proves the possibility of predicting the existence of a cavity inside a homogenous body based on the geometrical parameters and the position of cavity by means of the boundary element method. Regarding the extensive use of steel plates in heavy and huge industries, this project focuses on two-dimensional plates and studies the thermal effects of shape and position of the existing cavity by solving the two-dimensional Laplace’s equation on conduction heat transfer over the body. The thermal changes on some boundaries affected by shape and position of cavity give an appropriate estimate of cavity. Considering the bulky and big amount of calculation and iteration and also the type of boundary conditions the fast and accurate numerical method proper to the mentioned problem, Boundary Element Method, is applied to simulate the experiments. The conclusion is taken due to the results of simulation. Based on the theory of Boundary Element method, the problem is simulated as a rectangular plate with two constant temperature and two constant flux boundary conditions while the cavity is inside, so concerning the position of cavity the variation of decreasing temperature on the boundaries with constant flux rate is changing. In order to reach the idea, the proper programming code has been written in Visual Fortran programming language and the results of the program output has been compared and interpreted.
A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements