9542267d-a1f6-46b5-8eb0-8b24ae1553d120210914063750809naun:naunmdt@crossref.orgMDT DepositInternational Journal of Mechanics1998-444810.46300/9104http://www.naun.org/cms.action?id=2828128202112820211510.46300/9104.2021.15https://www.naun.org/cms.action?id=23280M. R.ShahnazariK. N. Toosi University of technology, Tehran, IranF. RoohiShaliK. N. Toosi University of technology, Tehran, IranA.SaberiK. N. Toosi University of technology, Tehran, IranM. H.MoosaviK. N. Toosi University of technology, Tehran, IranSolving the inverse problems, especially in the field of heat transfer, is one of the challenges of engineering due to its importance in industrial applications. It is well-known that inverse heat conduction problems (IHCPs) are severely ill-posed, which means that small disturbances in the input may cause extremely large errors in the solution. This paper introduces an accurate method for solving inverse problems by combining Tikhonov's regularization and the genetic algorithm. Finding the regularization parameter as the decisive parameter is modelled by this method, a few sample problems were solved to investigate the efficiency and accuracy of the proposed method. A linear sum of fundamental solutions with unknown constant coefficients assumed as an approximated solution to the sample IHCP problem and collocation method is used to minimize residues in the collocation points. In this contribution, we use Morozov's discrepancy principle and Quasi-Optimality criterion for defining the objective function, which must be minimized to yield the value of the optimum regularization parameter.96202196202115115817https://www.naun.org/main/NAUN/mechanics/2021/a342003-017(2021).pdf10.46300/9104.2021.15.17https://www.naun.org/main/NAUN/mechanics/2021/a342003-017(2021).pdf10.1016/j.ijheatmasstransfer.2013.07.054Zhang, B., et al., Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer. International Journal of Heat and Mass Transfer, 2013. 66: p. 507-516. Hadamard, J., Sur les problèmes aux dérivées partielles et leur signification physique. Princeton university bulletin, 1902: p. 49-52. 10.1115/1.3679871Stolz, G., Numerical solutions to an inverse problem of heat conduction for simple shapes. Journal of heat transfer, 1960. 82(1): p. 20-25. Tikhonov, A.N. and V.I. 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Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 27, 2, 2008, 33-38. doi: 10.30492/ijcce.2008.6995. 10.1615/jpormedia.v8.i2.20Shahnazari, M. R, ZiaBasharHagh M., Theoretical and experimental investigation of the channeling effect in fluid flow through porous media, Journal of Porous Media, 10.1615/JPorMedia.v8.i2.20. 10.1080/10407780117384Colaco, M. and H. Orlande, Inverse forced convection problem of simultaneous estimation of two boundary heat fluxes in irregularly shaped channels. Numerical Heat Transfer: Part A: Applications, 2001. 39(7): p. 737-760. 10.1016/j.ijheatmasstransfer.2011.11.010Liu, D., J. Yan, and K. Cen, On the treatment of non-optimal regularization parameter influence on temperature distribution reconstruction accuracy in participating medium. International Journal of Heat and Mass Transfer, 2012. 55(5-6): p. 1553-1560. 10.1016/j.apm.2013.10.019Pourgholi, R., H. Dana, and S.H. Tabasi, Solving an inverse heat conduction problem using genetic algorithm: sequential and multi-core parallelization approach. Applied Mathematical Modelling, 2014. 38(7-8): p. 1948-1958. 10.1016/j.ijheatmasstransfer.2015.05.015Mulani, K., et al., Performance analysis and feasibility study of ant colony optimization, particle swarm optimization and cuckoo search algorithms for inverse heat transfer problems. International Journal of Heat and Mass Transfer, 2015. 89: p. 359-378. 10.1016/j.applthermaleng.2016.01.017Sun, S., et al., Inverse geometry design of two-dimensional complex radiative enclosures using krill herd optimization algorithm. Applied Thermal Engineering, 2016. 98: p. 1104-1115. 10.1615/ihtc16.cip.021812Li, Ran, and Zhongwei Huang. "AN IMPROVED SPACE MARCHING METHOD INCORPORATING FUTURE TEMPERATURES IN LEAST SQUARE MANNER FOR LINEAR AND NONLINEAR IHCP." International Heat Transfer Conference Digital Library. 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