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ISSN Online: 2377-424X

International Heat Transfer Conference 12
August, 18-23, 2002, Grenoble, France

Inverse problem of turbulent forced convection inside parallel-plate ducts using a reduced model

Get access (open in a dialog) DOI: 10.1615/IHTC12.1230
6 pages

Abstract

Inverse Heat Convection Problems have received attention only recently. In this numerical study, the possibility to quickly solve such a problem with a low order model is analysed. The objective could be then to use this approach in industrial applications, control command processes for example. Turbulent forced convection is considered, with a hydrodynamically fully developed, thermally developing, incompressible, constant property, turbulent flow inside a parallel-plate duct. Axial conduction in the flow is neglected. A model involving turbulent velocity distribution and eddy diffusivity for heat is taken as turbulent model, making heat transfer equation linear. This linearity assumption is needed to apply the reduction method. The system is submitted to three different thermal inputs: the known fluid inlet temperature and two unknown wall heat flux densities varying with time, respectively applied on the upper and lower plates. Both heat flux densities are estimated through the inverse procedure from the knowledge of simulated transient temperature measurements inside the fluid. Heat transfer is described with the finite volume method, taking into account the wall thermal capacitance. This Detailed Model (DM) is formulated in the State Space Representation, which expresses the linear relationship between inputs and temperature data set. The Modal Identification Method is applied to build a Reduced Model (RM) of the system. When solving the inverse problem with RM instead of DM, drastic reduction of computing time is obtained (up to 11000 in the present study), without significant loss of accuracy. The inversion procedure is sequential and requires no iterations. Future time steps with a function specification are used as regularisation procedure. Effects of functional form of the unknowns, sensor number and position, magnitude of measurement error, on the accuracy of estimates are examined.