Retrieval of Multidimensional Heat Transfer Coefficient Distributions Using an Inverse BEM-Based Regularized Algorithm: Numerical and Experimental Results

The surface distribution of heat transfer coefficients (h) is often determined point by point using surface temperature measurements of the tested object, initially at a uniform temperature and impulsively imposed with a convective boundary condition, and the solution to the transient heat conduction equation for a semi-infinite medium. There are many practical cases where this approach fails to adequately model the temperature field and, consequently, leads to erroneous h values. In this paper, we present an inverse BEM-based approach for the retrieval of spatially varying h distributions from surface temperature measurements. In this method, a convolution BEM marching scheme is used to solve the conduction problem. At each time level, a regularized functional is minimized to estimate the current heat flux and simultaneously smooth out uncertainties in calculated h values due to experimental uncertainties in measured temperatures. Newton's cooling law is then invoked to compute h. Results are presented from a numerical simulation and from an experiment. It is also shown that the method can be readily applied to steady-state.