Recent Advances in Heat Flux Estimation: An inverse approach

This paper reviews some of the recent advances in acquiring transient heat flux from a time domain viewpoint. The time domain view in semi-infinite media leads to an integral relationship between heat flux, q’’ and temperature, T (and more importantly the heating rate, dT/dt). This formulation isolates the cause of the ill posedness and suggests, through the combination of mathematics and physics of diffusion, ways of stabilizing a projective process. As with all ill-posed problems, regularization of some sort is required. Unique to our view is that regularization isaccomplished through the data itself with the aid of the physics of diffusion. This integrated viewpoint captures and resolves a major hurdle associated with inverse studies. The resolved inverse problem using this view is less sensitive to the regularization parameter then most other common approaches. That is, the interrogation of the data in the frequency domain used in conjunction with the subtle understanding of the physical significance of the time rate of change of temperature contrasts the conventional and often purely mathematical view in which the prediction is often highly sensitive to the chosen regularization parameter. Additionally, the computational method imposes laboratory constraints into the algorithm for assuring additional stability. Integrating experimental and analytical observations leads to an increase in stability and predictive accuracy while reducing complexity in the numerical algorithms. This paper presents a classical inverse heat conduction problem using this integrated viewpoint.

Keywords:

heat flux , inverse , constraints , sensors