Control of the boundary heat flux during the heating process of a solid material

✍ Scribed by H. Jiang; T.H. Nguyen; M. Prud'homme

• Book ID: 103830875
• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 323 KB
• Volume: 32
• Category: Article
• ISSN: 0735-1933
• DOI: 10.1016/j.icheatmasstransfer.2004.10.009

✦ Synopsis

In this paper we apply the conjugate gradient method to solve the inverse problem of determining a timedependent boundary heat flux in order to achieve a given temperature distribution at the final time. The derivation of sensitivity and adjoint equations in conjunction with the conjugate gradient algorithm are given in detail. The zeroth-order Tikhonov regularization is introduced to stabilize the inverse solution. Solutions by finite differences are obtained for various heat flux profiles. It is found that the time-dependent heat flux may be predicted only for a non-dimensional time of the order of 0.1 while the control problem can be satisfactorily solved for an arbitrary period of time.