Determination of local heat transfer coefficient from the solution of the inverse heat conduction problem

The aim of this paper is to present two techniques for simply and accurately determining space-variable heat transfer coefficient, given measurements of temperature at some interior points in the body. The fluid temperature is also measured as part of the solution. The methods are formulated as linear and non-linear least-squares problems. The unknown parameters associated with the solution of the inverse heat conduction problem (IHCP) are selected to achieve the closest agreement in a least squares sense between the computed and measured temperatures using the Levenberg-Marquardt method (method I) or the singular value decomposition (method II). The methods presented in the paper are used for determining the local heat transfer coefficient on the circumference of the vertical smooth tube placed in the tube bundle with a staggered tube arrangement. Good agreement between the results is obtained. The uncertainties in the estimated heat transfer coefficients are calculated using the error-propagation rule of Gauss. The main advantage of the presented methods is that they do not require any complex simulation of flow and temperature field in the fluid.