Boundary Heat Flux Estimation in one-dimensional Heat Conduction Problem
Keywords:
finite volume method, CGM, heat fluxAbstract
A numerical model is developed to estimate the boundary heat flux in a 1D heat conduction problem using CGM. No prior information is used for the functional form of the space-wise varying heat flux. The energy equations are discretized using the finite volume method. The direct problem is first solved with a known heat flux at the boundary and the temperature field of the domain is determined. The inverse method is then applied to predict this heat flux with some of the additional temperature data inside the solution domain obtained from the direct problem. The prediction of boundary heat flux by the present algorithm is found to be quite reasonable.
References
G. Jr. Stolz, “Numerical solutions to an inverse problem of heat conduction for simple shapes,” Journal Heat Transfer, vol. 82, pp. 20–26, 1960.
O.M. Alifanov, “Solution of an inverse problem of heat conduction by iteration methods,” Journal of Engineering Physics, vol. 26, pp. 471–476, 1974.
U.C. Chen, W.J. Chang, J.C. Hsu, “Two-dimensional inverse problem in estimating heat flux of pin fins,” International Communications in Heat and Mass Transfer, vol. 28, no. 6, pp. 793–801, 2001.
M. Prud’homme, T.H. Nguyen, “On the iterative regularization of inverse heat conduction problems by conjugate gradient method,” International Communications in Heat and Mass Transfer, vol. 25, no. 7, pp. 999–1008, 1998.
C.H. Huang, S.P. Wang, “A three-dimensional inverse heat conduction problem in estimating surface heat flux by conjugate gradient method,” International Journal of Heat and Mass Transfer, vol. 42, pp. 3387–3403, 1999.
H.T. Chen, S.M. Chang, “Application of the hybrid method to inverse heat conduction problems,” International Journal of Heat and Mass Transfer, vol. 33, pp. 621–628, 1990.
H.T. Chen, S.Y. Lin, L.C. Fang, “Estimation of surface temperature in two-dimensional inverse heat conduction problems,” International Journal of Heat and Mass Transfer, vol. 44, pp. 1455–1463, 2001.
C.H. Huang, M.N. Ozisik, “Inverse problem of determining the unknown strength of an internal plane heat source,” Journal of the Franklin Institute, vol. 329, no. 4, pp. 751–764, 1992.
A.J.S. Neto, M.N. Ozisik, “Two-dimensional inverse heat conduction problem of estimating the time-varying strength of a line heat source,” Journal of Applied Physics, vol. 71, pp. 5357–5362, 1992.
A.J.S. Neto, M.N. Ozisik, “Inverse problem of simultaneously estimating the timewise-varying strengths of two plane heat sources,” Journal of Applied Physics, vol. 73, no. 5, pp. 2132–2137, 1993.
N. Tian, J. Sun, W. Xu, C. Lai, “Estimation of unknown heat source function in inverse heat conduction problems using quantum-behaved particle swarm optimization,” International Journal of Heat and Mass Transfer, vol. 54, pp. 4110–4116, 2011.
F.B. Liu, “A modified genetic algorithm for solving the inverse heat transfer problem of estimating plane heat source,” International Journal of Heat and Mass Transfer, vol. 51, pp. 3745–3752, 2008.
F.S. Lobato, Jr. V. Steffen, A.J.S. Neto, “Simultaneous estimation of location and timewise varying strength of a plane heat source using differential evolution,” Proceedings 2nd International Conference on Engineering Optimization, Lisbon, Portugal, 2010.
G. Karami, M.R. Hematiyan, “A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources,” Communications in Numerical Methods in Engineering, vol. 16, pp. 191–203, 2000.
A.J.S. Neto, M.N. Ozisik, “Simultaneous estimation of location and timewise varying strength of a plane heat source,” Numerical Heat Transfer, vol. 24, pp. 467–477, 1993.
R.A. Khachfe, Y. Jarny, “Determination of heat sources and heat transfer coefficient for two-dimensional heat flow: numerical and experimental study,” International Journal of Heat and Mass Transfer, vol. 44, no. 7, pp. 1309–1322, 2001.
F. Lefèvre, C.L. Niliot, “Multiple transient point heat sources identification in heat diffusion: Application to experimental 2D problems,” International Journal of Heat and Mass Transfer, vol. 45, pp. 1951–1964, 2002.
F. Lefèvre, C.L. Niliot, “The BEM for point heat sources estimation: application to multiple static sources and moving sources,” International Journal of Thermal Sciences, vol. 41, pp. 526–545, 2002.
F. Lefèvre, C.L. Niliot, “A boundary element inverse formulation for multiple point heat sources estimation in a diffusive system: Application to a 2D experiment,” Inverse Problems in Engineering, vol. 10, no. 6, pp. 539–557, 2002.
C.L. Niliot, F. Lefèvre, “A parameter estimation approach to solve the inverse problem of point heat sources identification,” International Journal of Heat and Mass Transfer, vol. 47, pp. 827–841, 2004.
C.L. Niliot, F. Lefèvre, “Multiple transient point heat sources identification in heat diffusion: application to numerical two- and three-dimensional problems,” Numerical Heat Transfer, Part B, vol. 39, pp. 277–301, 2001.
B. Sawaf, M.N. Ozisik, Y. Jarny, “An inverse analysis to estimate linearly temperature dependent thermal conductivity components and heat capacity of an orthotropic medium,” International Journal of Heat and Mass Transfer, vol. 38, no. 16, pp. 3005–3010, 1995.
B. Sawaf, M.N. Ozisik, “Determining the constant thermal conductivities of orthotropic materials by inverse analysis,” International Communication in Heat and Mass Transfer, vol. 22, no. 2, pp. 201–211, 1995.
M. Raudensky, A.W. Keith, J. Kral, “Genetic algorithm in solution of inverse heat conduction problems,” Numerical Heat Transfer Part B, vol. 28, no. 3, pp. 293–306, 1995.
S. Parthasarathy, C. Balaji, “Estimation of parameters in multimode heat transfer problems using Bayesian inference—effect of noise and a priori,” International Journal of Heat and Mass Transfer, vol. 51, pp. 2313–2334, 2008.
N. Gnanasekaran, C. Balaji, “A Bayesian approach for the simultaneous estimation of surface heat transfer coefficient and thermal conductivity from steady state experiments on fins,” International Journal of Heat and Mass Transfer, vol. 54, pp. 3060–3068, 2011.
N. Gnanasekaran, C. Balaji, “Markov Chain Monte Carlo (MCMC) approach for the determination of thermal diffusivity using transient fin heat transfer experiments,” International Journal of Thermal Sciences, vol. 63, pp. 46–54, 2013.
Downloads
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.