Application of the hybrid method to inverse heat conduction problems

Abstract

The hybrid method involving the combined use of the Laplace transform method and the finite element method is considerably powerful for solving one-dimensional linear heat conduction problems. In the present method, the time-dependent terms are removed from the problem using the Laplace transform method and then the finite element method is applied to the space domain. The transformed temperature is inverted numerically to obtain the result in the physical quantity. The estimation of the surface heat flux or temperature from transient measured temperatures inside the solid agrees well with the analytical solution of the direct problem without Beck's sensitivity analysis and a least square criterion. Due to no time step, the present method can directly calculate the surface conditions of an inverse problem without step by step computation in the time domain until the specific time is reached. In addition, it is also not necessary to compute all the nodal temperatures at each time step when the present method is applied to an inverse problem. It is worth mentioning that a little effect of the measurement location on the estimates is shown in the present method. Thus, it can be concluded that the present method is straightforward and efficient for such problems.