An inverse method for the estimation of a long-duration surface heat flux on a finite solid

- Sequential inverse method is proposed for long-duration heat flux estimation.
- Rescaled time is optimized to minimize the error of direct solution.
- Closed-form temperature solution is used for inverse analysis and converges fast.
- The increase of rescaled time step size stabilizes the estimated heat flux.

The nonlinear inverse heat conduction problem (IHCP) is resolved for the estimation of surface heat flux from two temperature measurements inside a finite domain. An improvement is achieved in this study by optimizing the rescaled time used to linearize the heat conduction equation with temperature-dependent thermal properties. A closed-form solution of the transient temperature is derived, considering the inhomogeneous boundary conditions. The direct solution is further incorporated into a sequential technique for inverse analysis, and the uncertainty of inverse solution with respect to input parameters is obtained. The results from a representative example show that the method is computationally efficient and the inverse solution can be stabilized by increasing the rescaled time step size. Thus, the effect of the real time step on the ill-posedness can be reduced and the increase of sampling rate in experiment is possible. The present method is useful for the prediction of long-duration heat flux in thermal engineering.