Convection heat transfer coefficient estimation in ducts using the reciprocity functional method

Abstract

In this work, we present an original inverse problem approach, based on the Reciprocity Functional Method coupled with the Classical Integral Transform Technique. This results in a fully analytical estimation approach, which is applied to a three-dimensional inverse problem to estimate the internal heat transfer coefficient distribution in ducts, using temperature measurements taken on the external boundary of the duct. The methodology allows the use of both steady-state and transient external wall temperature measurements as input data. To estimate the heat transfer coefficient in a duct, according to the proposed technique, two auxiliary problems are required: the first is related to the estimate of the heat flux and the second to the estimate of the internal wall temperature. The convection heat transfer coefficient is therefore calculated, since the heat flux and the internal wall temperature are known. Such innovative methodology, avoiding the solution of linear systems, reduces the computational cost that is considerable when traditional approaches are applied to three-dimensional problems. The proposed procedure is first verified adopting synthetic temperature data and then validated using real temperature measurements acquired by an infrared camera. The results highlighted that the presented methodology is able to recover the unknown functions in a very short computational time and with a good accuracy, even when the noisy temperature measurements are used.