RETRIEVAL OF MULTIDIMENSIONAL HEAT TRANSFER COEFFICIENT DISTRIBUTIONS USING AN INVERSE BEM-BASED REGULARIZED ALGORITHM: Numerical and experimental results

Abstract

Surface maps of heat transfer coefficients (h) are often determined by transient liquid crystal or other similar transient experimental techniques. This involves (1) conducting an experiment with an impulsively imposed convective boundary condition on an initially isothermal test object, (2) measuring the resulting timedependent surface temperature distributions, and (3) solving the onedimensional transient heat conduction equation for different points on the convective surface. 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 boundary element method(BEM)-based approach for the retrieval of spatially varying h distributions from surface temperature measurements. In this method, an efficient numerical algorithm requiring only a surface mesh is used to solve the conduction problem. At each time level, a regularized functional is minimized to estimate the time-dependent heat flux and simultaneously minimize the effect of experimental measurement uncertainties in surface temperatme values on the calculated heat flux. Newton\u27s cooling law is then invoked to compute h. Results are presented from several numerical simulations and from a laboratory experiment. The method is applicable to unsteady as well as to steady-state convective systems