Investigation of heat transfer coefficient in two‐dimensional transient inverse heat conduction problems using the hybrid inverse scheme

A hybrid scheme of the Laplace transform, finite difference and least-squares methods in conjunction with a sequential-in-time concept, cubic spline and temperature measurements is applied to predict the heat transfer coefficient distribution on a boundary surface in two-dimensional transient inverse heat conduction problems. In this study, the functional form of the heat transfer coefficient is unknown a priori. The whole spatial domain of the unknown heat transfer coefficient is divided into several analysis sub-intervals. Later, a series of connected cubic polynomial function in space and a linear function in time can be applied to estimate the unknown surface conditions. Due to the application of the Laplace transform, the unknown heat transfer coefficient can be estimated from a specific time. In order to evidence the accuracy of the present inverse scheme, comparisons among the present estimates, previous results and exact solution are made. The results show that the present inverse scheme not only can reduce the number of the measurement locations but also can increase the accuracy of the estimated results. Good estimation on the heat transfer coefficient can be obtained from the knowledge of the transient temperature recordings even in the case with measurement errors. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  G. Honig,et al.  A method for the numerical inversion of Laplace transforms , 1984 .

[2]  Han-Taw Chen,et al.  Estimation of two-sided boundary conditions for two-dimensional inverse heat conduction problems , 2002 .

[3]  Han-Taw Chen,et al.  Prediction of heat transfer coefficient on the fin inside one-tube plate finned-tube heat exchangers , 2005 .

[4]  Diego A. Murio,et al.  The Mollification Method and the Numerical Solution of Ill-Posed Problems , 1993 .

[5]  Han-Taw Chen,et al.  Estimation of surface absorptivity in laser surface heating process with experimental data , 2006 .

[6]  Han-Taw Chen,et al.  Investigation of natural-convection heat transfer coefficient on a vertical square fin of finned-tube heat exchangers. , 2006 .

[7]  J. P. Holman,et al.  Experimental methods for engineers , 1971 .

[8]  Somchart Chantasiriwan,et al.  Inverse heat conduction problem of determining time-dependent heat transfer coefficient , 1999 .

[9]  Harish P. Cherukuri,et al.  A non‐iterative finite element method for inverse heat conduction problems , 2003 .

[10]  J. Taler,et al.  Numerical method for the solution of non‐linear two‐dimensional inverse heat conduction problem using unstructured meshes , 2000 .

[11]  Han-Taw Chen,et al.  Estimation of Heat Transfer Coefficient in Two-Dimensional Inverse Heat Conduction Problems , 2006 .

[12]  Tahar Loulou,et al.  Estimations of a 2D convection heat transfer coefficient during a metallurgical “Jominy end-quench” test: comparison between two methods and experimental validation , 2004 .

[13]  Han-Taw Chen,et al.  Estimation of surface temperature in two-dimensional inverse heat conduction problems , 2001 .

[14]  James V. Beck,et al.  Investigation of transient heat transfer coefficients in quenching experiments , 1990 .

[15]  Han-Taw Chen,et al.  Estimation of heat transfer coefficient on the vertical plate fin of finned-tube heat exchangers for various air speeds and fin spacings , 2007 .

[16]  T. J. Martin,et al.  Inverse determination of steady heat convection coefficient distributions , 1998 .