Inverse Forced Convection Problem of Simultaneous Estimation of Two Boundary Heat Fluxes in Irregularly Shaped Channels

Abstract

This article deals with the use of the conjugate gradient method of function estimation for the simultaneous identi cation of two unknown boundary heat uxes in channels with laminar ows. The irregularly shaped channel in the phy sical domain is transformed into a parallel plate channel in the computational domain by using an elliptic scheme of numerical grid generation. The direct problem, as well as the auxiliary problems and the gradient equations, required for the solution of the inverse problem with the conjugate gradient method are formulated in terms of generalized boundary-tted coordinates. Therefore, the solution approach presented here can be readily applied to forced convection boundary inverse problems in channels of any shape. Direct and auxiliary problems are solved with nite volumes. The numerical solution for the direct problem is validated by comparing the results obtained here with benchmark solutions for smoothly expanding channels. Simulated temperature measurement s containing random errors are used in the inverse analysis for strict cases involving functional forms with discontinuities and sharp corners for the unknown functions. The estimation of three different types of inverse problems are addressed in the paper: ( i) time-dependent heat uxes; ( ii) spatially dependent heat uxes; and ( iii) time and spatially dependent heat uxes.

Direct and inverse solutions with non-Fourier effect on the irregular shape

“…In general, inverse operation method is usually applied when analyzing simple shape (see [2][3][4][8][9][10]13]). This paper is theoretically based on linear least-squares error method [14], but changes with the finite element method in spatial discretion to solve spatial stiffness matrix of irregular shape, and adds sequential algorithm concept to build a universal solving process.…”

Problemas Inversos em Transferência de Calor

“…As equações desenvolvidas acima podem ser arranjadas em um conveniente algoritmo computacional descrito nas referências [6,7,[16][17][18][19][20][21][22][23][24][25][26].…”

Inverse natural convection problem of simultaneous estimation of two boundary heat fluxes in irregular cavities

“…. However, with few exceptions [26][27][28]30], the above papers have addressed the estimation of one single unknown quantity.…”