The Inverse Estimation of Local Heat Transfer Coefficient in a Vertical Plate Fin with Its Base Subjected to Periodically Oscillated Temperature

Abstract

In this study, an inverse method is provided to determine the convective heat transfer coefficient of the vertical fin with its base subjected to periodically oscillated temperature. The finite-difference method is used to discretize the governing equations and then a linear inverse model is constructed to identify the undetermined heat transfer coefficients. The present approach is to rearrange the matrix forms of the differential governing equations so that the unknown heat transfer coefficients can be represented explicitly. Then, the linear least-squares-error method is adopted to find the solutions. The results show that only a few measuring points at discrete grid points are needed to estimate the unknown quantities even when measurement errors are considered. Also discussed are the effects due to the variations of the conjugate convection-conduction parameter Nc, the buoyancy parameter Ω, as well as the oscillation amplitude A and frequency ω* of the base temperature on the heat transfer coefficients. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown quantities, no initial guesses are required, no iterations in the calculating process are necessary, and the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can be easily identified.