Estimation of transient wall and flow temperature distributions in a circular duct using an inverse approach

Inverse methods have become a useful tool for estimating parameters that cannot be measured or calculated directly in engineering applications. Parameters characterizing unsteady heat convection in circular duct flows are associated with numerous uncertainties. This fact renders the inverse approach appropriate for the determination of these parameters. An inverse problem for transient turbulent thermally developing and thermally developed forced-convection flow in a circular duct is formulated and discussed, and a simplified direct thermal model is presented. Parameters of the model are estimated by solving a minimization problem, using temperature data from the wall surface and/or the flow. A multivariable optimization algorithm is employed for this purpose. Furthermore, a model for the forced-convection heat-transfer coefficient is proposed and its effect on the results is discussed. The validity of the proposed method is assessed using data from two different circular duct flows. The method is shown to provide a good prediction capability in computationally demanding transient heat-data sequences of different duct flows, both in terms of duct and of flow characteristics. Results show that a hyperbolic axial distribution of the forced-convection heat-transfer coefficient in the developing region of the flow is essential for good adaptation of the method to the test data.