TY - JOUR
T1 - Estimation of surface conditions for nonlinear inverse heat conduction problems using the hybrid inverse scheme
AU - Chen, Han Taw
AU - Wu, Xin Yi
N1 - Funding Information:
Received 30 April 2006; accepted 16 June 2006. The authors gratefully acknowledge the financial support provided by the National Science Council of the Republic of China under Grant NSC 90-2212-E-145-001. Address correspondence to Han-Taw Chen, Department of Mechanical Engineering, National Cheng Kung University, Tainan City, Taiwan 701, Republic of China. E-mail: [email protected]
PY - 2007/5/1
Y1 - 2007/5/1
N2 - A hybrid numerical method involving the Laplace transform technique and finite-difference method in conjunction with the least-squares method and actual experimental temperature data inside the test material is proposed to estimate the unknown surface conditions of inverse heat conduction problems with the temperature-dependent thermal conductivity and heat capacity. The nonlinear terms in the differential equations are linearized using the Taylor series approximation. In this study, the functional form of the surface conditions is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis subtime intervals and then the unknown estimates on each subtime interval can be predicted. In order to show the accuracy and validity of the present inverse scheme, a comparison among the present estimates, direct solution, and actual experimental temperature data is made. The effects of the measurement errors, initial guesses, and measurement location on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.
AB - A hybrid numerical method involving the Laplace transform technique and finite-difference method in conjunction with the least-squares method and actual experimental temperature data inside the test material is proposed to estimate the unknown surface conditions of inverse heat conduction problems with the temperature-dependent thermal conductivity and heat capacity. The nonlinear terms in the differential equations are linearized using the Taylor series approximation. In this study, the functional form of the surface conditions is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis subtime intervals and then the unknown estimates on each subtime interval can be predicted. In order to show the accuracy and validity of the present inverse scheme, a comparison among the present estimates, direct solution, and actual experimental temperature data is made. The effects of the measurement errors, initial guesses, and measurement location on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.
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U2 - 10.1080/10407790600878734
DO - 10.1080/10407790600878734
M3 - Article
AN - SCOPUS:33847115401
SN - 1040-7790
VL - 51
SP - 159
EP - 178
JO - Numerical Heat Transfer, Part B: Fundamentals
JF - Numerical Heat Transfer, Part B: Fundamentals
IS - 2
ER -