Temperature–Velocity Coupling of the Convective Heat Transfer Sensitivity Analysis

ABSTRACT

This article deals with sensitivity studies of the temperature–velocity coupling of convective heat transfer problems with laminar fluid flow. Sensitivity coefficients contain information about the chances of a successful inverse procedure, and they can be used in a number of inverse schemes, i.e., the Levenberg-Marquardt method. Special emphasis is given in this article to the numerical solution of the direct problem, which was obtained by the control-volume finite-element method formulation. This numerical tool was used for the sensitivity coefficients evaluation and can be used for simulation of real measurements in the full inverse algorithm. The algorithm for the sensitivity coefficients evaluation and example distributions of the sensitivity coefficients are given. A proposed full inverse procedure, allowing determination of inflow velocity based on internal temperature measurements, is also included. The inverse method employs the Levenberg-Marquardt method for stabilization purposes.

The financial assistance of the National Committee for Fundamental Research, Poland, under grant 8T10B06921, is gratefully acknowledged.

A preliminary version of this article was presented at CHT-04: An ICHMT International Symposium on Advances in Computational Heat Transfer, April 2004, G. de Vahl Davis and E. Leonerdi (eds.), CD-ROM proceedings, ISBN 1-5670-174-2, Begell House, New York, 2004.