Solution of inverse free convection problems by conjugate gradient method:effects of Rayleigh number

A study is made of the inverse free convection problem (IFCP) by adjoint eq uations and conjugate gradient (CG), to determine an unknown space and time dependent boundary heat flux on the side of an enclosure, from temperature measurements by sensors within the flow. The direct, sensitivity and adjoi nt set of equations for a Boussinesq fluid are solved by control volumes. S olutions are presented for different types of boundary conditions and a wid e range of Rayleigh numbers, for a square enclosure. It is found that by pl acing sensors close enough to the active boundary, solutions may be achieve d for Rayleigh numbers higher than in previous studies. Noisy data solution s are regularized by stopping the iterations according to the discrepancy p rinciple of Alifanov, before the high frequency components of the random no ises are reproduced. The accuracy of the solutions is shown to depend stron gly on the Rayleigh number, the sensor's position and the type of boundary conditions imposed. (C) 2001 Elsevier Science Ltd. All rights reserved.