TY - EJOU
AU - Sladek, J.
AU - Sladek, V.
AU - Wen, P.H.
AU - Hon, Y.C.
TI - The Inverse Problem of Determining Heat Transfer Coefficients by the Meshless Local Petrov-Galerkin Method
T2 - Computer Modeling in Engineering \& Sciences
PY - 2009
VL - 48
IS - 2
SN - 1526-1506
AB - The meshless local Petrov-Galerkin (MLPG) method is used to solve the inverse heat conduction problem of predicting the distribution of the heat transfer coefficient on the boundary of 2-D and axisymmetric bodies. Using this method, nodes are randomly distributed over the numerical solution domain, and surrounding each of these nodes, a circular sub-domain is introduced. By choosing a unit step function as the test function, the local integral equations (LIE) on the boundaries of these sub-domains are derived. To eliminate the time variation in the governing equation, the Laplace transform technique is applied. The local integral equations are nonsingular and take a very simple form. The spatial variations of the Laplace transforms of temperature and heat flux are approximated on the local boundary and in the interior of the subdomain by means of the moving least-squares (MLS) method. The truncated singular value decomposition (TSVD) is applied to solve the ill-conditioned linear system of algebraic equations obtained from the LIE after the MLS approximation. The Stehfest algorithm is then applied for the numerical Laplace inversion, in order to retrieve the time-dependent solutions. The effectiveness of the MLPG method for this inverse problem is demonstrated by some numerical examples.
KW - Transient inverse heat conduction problem
KW - Laplace transform
KW - Stehfest algorithm
KW - Singular value decomposition
KW - Meshless approximation; Moving-least-squares method
DO - 10.3970/cmes.2009.048.191