A three-dimensional inverse heat conduction problem approach for estimating the heat flux and surface temperature of a hollow cylinder

Abstract

This study is intended to provide a different perspective for solving the three-dimensional, inverse, steady heat conduction problem for a hollow cylinder. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary conditions. The present approach is to rearrange the matrix forms of the differential governing equations and estimate unknown conditions. Then, the linear least-squares method is adopted to find the solution. The results show that one needs only a few measuring points in order to estimate the boundary temperature and heat flux when the measurement errors are negligible. When the measurement errors are considerable, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions.

An Inverse Problem Method for Overall Heat Transfer Coefficient Estimation in a Partially Filled Rotating Cylinder

“…There are some powerful techniques for solving inverse heat transfer problems. These techniques include [24]:…”

“…29 no. 3 2008 Downloaded by [Ams/Girona*barri Lib] at 03: 11 17 November 2014 procedure in the form [24,25]:…”

“…where T exact is the solution of the direct problem with the exact overall heat transfer coefficient, 780 W/m 2 K, σ is the standard deviation of the measurement, and λ is the random variable, which is within −2.576 ≤ λ ≤ 2.576 for 99.43% confidence bound [16,[22][23][24][25]. The measuring data produced for the shell and bedside zones of cylinder with 0%, 1%, and 5% errors are given in Figures 7 and 8, respectively.…”

“…The investigation of a thermal hollow cylinder behavior undergoes analysis with inverse methodology, as reported in [23][24][25].…”

Inverse estimation of steady‐state surface temperature on a three‐dimensional body

“…Martin and Dulikravich (1996) also used BEM for two‐dimensional steady IHCPs with unknown heat sources and with unknown heat transfer coefficients (Martin and Dulikravich, 1998). Yang et al (1997) estimated surface conditions of a hollow cylinder using a least squares method with a matrix rearrangement technique. Chantasiriwan (2000) proposed an inverse method for evaluating steady‐state heat transfer coefficient in a two‐dimensional system.…”