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Hybrid Methods in Engineering

ISSN Imprimir: 1099-2391
ISSN En Línea: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v1.i3.20
18 pages

ALTERNATE APPLICATION OF REGULAR AND MODIFIED CONJUGATE GRADIENT METHOD TO TWO-DIMENSIONAL INVERSE HEAT CONDUCTION

Woo-Seung Kim
Department of Mechanical Engineering, Hanyang University, 1271 Sa-1 dong, Sangnok-gu, Ansan, Kyeonggi-do, 425-791, Korea
M. N. Ozisik
Mechanical and Aerospace Engineering Department North Carolina State University, Raleigh, N. C. 27607
Eui-Rak Choi
Department of Mechanical Engineering, Hanyang University, Seoul 133-791, Korea

SINOPSIS

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, (X*, Y), and timewise varying unknown strength, G(τ), of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method (RCGM) and the modified conjugate gradient method (MCGM), with adjoint equation, are used alternately to estimate the unknown strength G(τ) of the source term, while the parameter estimation approach is used to estimate the unknown location (X*, Y*) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e., τ = 0 and τ = τf) and hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength G(τ) is chosen in the form of rectangular, triangular, and sinusoidal functions.


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