Analysis of transient heat conduction within semi-infinite medium surrounding heated conical shell

The probe method is an in-situ method used for measuring the thermal properties of the surrounding medium. The conical probe is a new configuration, which still lacks heat transfer analysis. To obtain a model of the conical probe configuration, we investigate the temperature evolution within and around the conical probe, allowing for contact thermal conductance between the conical shell and the surrounding medium. The governing differential equations written in a special coordinate system are obtained by considering a differential element of the conical shell and balancing heat energy. Assuming that the heat flux component parallel to the surface of the conical shell can be neglected, we simplify the equations. The solution of the simplified model is obtained by Laplace transforms. This solution is verified based on the comparison between the present analytical results and numerical computations with the finite element method (FEM). We discuss the causes of errors, including the neglected ed heat flux component, axial and radial boundaries and non-ideal heat source. The analytical solution of the simplified model is well fitted in the regions where boundary effects can be neglected. In this study, a material selection guideline for conical probes different from cylindrical thermal probes is proposed. The analytical solution presented greatly reduces the computation time and has strong potential for solving the inverse problem.