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Identification of temperature‐dependent thermophysical properties in a partial differential equation subject to extra final measurement data
Authors:Chein‐Shan Liu
Affiliation:Department of Mechanical and Mechatronic Engineering, Taiwan Ocean University, Keelung 20224, TaiwanDepartment of Mechanical and Mechatronic Engineering, Taiwan Ocean University, Keelung 20224, Taiwan
Abstract:We consider an inverse problem for estimating the two coefficient functions c and k in a parabolic type partial differential equation c(u)ut = ?[k(u)ux]/?x with the aid of the measurements of u at two different times. The first‐ and second‐order one‐step group preserving schemes are developed. Solving the resultant algebraic equations with a closed‐form, we can estimate the unknown temperature‐dependent thermal conductivity and heat capacity. The new methods possess threefold advantages: they do not require any a priori information on the functional forms of thermal conductivity and heat capacity; no initial guesses are required; and no iterations are required. Numerical examples are examined to show that the new approaches have high accuracy and efficiency, even there are rare measured data. When the measured temperatures are polluted by uniform or normal random noise, the estimated results are also good. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
Keywords:inverse problem  one‐step group preserving scheme  inverse heat conduction problem  estimation of thermophysical properties
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