352
P. Sathavara et al.
References
1. Weisz-Patrault D, Ehrlacher A, Legrand N (2014) Temperature and heat flux fast estimation
during rolling process. Int J Therm Sci 75:1–20
2. Cui M, Yang K, Liu YF, Gao XW (2012) Inverse estimation of transient heat flux to slab
surface. J Iron Steel Res Int 19(11):13e18
3. Zhou J, Zhang Y, Chen JK, Feng ZC (2010) Inverse heat conduction using measured back
surface temperature and heat flux. J. Thermophys. Heat Transfer 24(1):262
4. Yu XC, Bai YG, Cui M, Gao XW (2013) Inverse analysis of thermal conductivities in transient
non-homogeneous and non-linear heat conductions using BEM based on complex variable
differentiation method. Sci. China Phys. Mech. Astron. 56(5):966–973
5. Lin DTW, Yang CY, Li JC, Wang CC (2011) Inverse estimation of the unknown heat flux
boundary with irregular shape fins. Int J Heat Mass Transf 54(25–26):5275–5285
6. Lin SM (2011) A sequential algorithm and error sensitivity analysis for the inverse heat conduction problems with multiple heat sources. Appl Math Model 35(6):2607–2617. https://doi.org/
10.1016/j.apm.2010.11.015
7. Liu FB (2011) A hybrid method for the inverse heat transfer of estimating fluid thermal
conductivity and heat capacity. Int J Therm Sci 50(5):718–724
8. Li HQ, Lei J, Liu QB (2012) An inversion approach for the inverse heat conduction problems. Int
J Heat Mass Transf 55(15–16):4442–4452. https://doi.org/10.1016/j.ijheatmasstransfer.2012.
04.014
9. Czel B, Grof G (2012) Inverse identification of temperature-dependent thermal conductivity
via genetic algorithm with cost function-based rearrangement of genes. Int J Heat Mass Transf
55(15–16):4254–4263. https://doi.org/10.1016/j.ijheatmasstransfer.2012.03.067
10. Cheng W, Fu CL, Qian Z (2007) A modified Tikhonov regularization method for a spherically
symmetric three-dimensional inverse heat conduction problem. Math Comput Simul 75(3–
4):97–112. https://doi.org/10.1016/j.matcom.2006.09.005
11. Liu FB (2012) inverse estimation of wall heat flux by using particle swarm optimization algorithm with Gaussian mutation. Int J Thermal Sci 54(4):62–69, 265–273. https://doi.org/10.
1016/j.ijthermalsci.2011.11.013. https://doi.org/10.1016/j.ijheatmasstransfer.2012.10.036
12. Bideau PL, Ploteau JP, Glouannec P (2009) Heat flux estimation in an infrared experimental
furnace using an inverse method. Appl Therm Eng 29(14–15):2977–2982. https://doi.org/10.
1016/j.applthermaleng.2009.03.014
13. Deng S, Hwang Y (2007) Solution of inverse heat conduction problems using Kalman filterenhanced Bayesian back propagation neural network data fusion. Int J Heat Mass Transf 50(11–
12):2089–2100. https://doi.org/10.1016/j.ijheatmasstransfer.2006.11.019
14. Chang C-L, Chang M (2006) Non-iteration estimation of thermal conductivity usingfinite
volume method. Int Commun Heat Mass Transfer 33(8):1013–1020
15. Alifanov OM (1974) Solution of an inverse problem of heat conduction by iteration methods.
J Eng Phys 26:471±476
16. Ozisik MN, Orlande H, Kassab AJ (2002) Inverse heat transfer: fundamentals and applications.
Appl Mech Rev 55(1):B18
17. Panchal M, Saraswat A, Verma S, Chaudhuri P (2019) Estimation of effective thermal conductivity for lithium meta-titanate (Li 2 TiO 3 ) pebble beds using steady state and axial heat flow
methods. J Coupled Syst Multiscale Dyn 6(4):257–265
P. Sathavara et al.
References
1. Weisz-Patrault D, Ehrlacher A, Legrand N (2014) Temperature and heat flux fast estimation
during rolling process. Int J Therm Sci 75:1–20
2. Cui M, Yang K, Liu YF, Gao XW (2012) Inverse estimation of transient heat flux to slab
surface. J Iron Steel Res Int 19(11):13e18
3. Zhou J, Zhang Y, Chen JK, Feng ZC (2010) Inverse heat conduction using measured back
surface temperature and heat flux. J. Thermophys. Heat Transfer 24(1):262
4. Yu XC, Bai YG, Cui M, Gao XW (2013) Inverse analysis of thermal conductivities in transient
non-homogeneous and non-linear heat conductions using BEM based on complex variable
differentiation method. Sci. China Phys. Mech. Astron. 56(5):966–973
5. Lin DTW, Yang CY, Li JC, Wang CC (2011) Inverse estimation of the unknown heat flux
boundary with irregular shape fins. Int J Heat Mass Transf 54(25–26):5275–5285
6. Lin SM (2011) A sequential algorithm and error sensitivity analysis for the inverse heat conduction problems with multiple heat sources. Appl Math Model 35(6):2607–2617. https://doi.org/
10.1016/j.apm.2010.11.015
7. Liu FB (2011) A hybrid method for the inverse heat transfer of estimating fluid thermal
conductivity and heat capacity. Int J Therm Sci 50(5):718–724
8. Li HQ, Lei J, Liu QB (2012) An inversion approach for the inverse heat conduction problems. Int
J Heat Mass Transf 55(15–16):4442–4452. https://doi.org/10.1016/j.ijheatmasstransfer.2012.
04.014
9. Czel B, Grof G (2012) Inverse identification of temperature-dependent thermal conductivity
via genetic algorithm with cost function-based rearrangement of genes. Int J Heat Mass Transf
55(15–16):4254–4263. https://doi.org/10.1016/j.ijheatmasstransfer.2012.03.067
10. Cheng W, Fu CL, Qian Z (2007) A modified Tikhonov regularization method for a spherically
symmetric three-dimensional inverse heat conduction problem. Math Comput Simul 75(3–
4):97–112. https://doi.org/10.1016/j.matcom.2006.09.005
11. Liu FB (2012) inverse estimation of wall heat flux by using particle swarm optimization algorithm with Gaussian mutation. Int J Thermal Sci 54(4):62–69, 265–273. https://doi.org/10.
1016/j.ijthermalsci.2011.11.013. https://doi.org/10.1016/j.ijheatmasstransfer.2012.10.036
12. Bideau PL, Ploteau JP, Glouannec P (2009) Heat flux estimation in an infrared experimental
furnace using an inverse method. Appl Therm Eng 29(14–15):2977–2982. https://doi.org/10.
1016/j.applthermaleng.2009.03.014
13. Deng S, Hwang Y (2007) Solution of inverse heat conduction problems using Kalman filterenhanced Bayesian back propagation neural network data fusion. Int J Heat Mass Transf 50(11–
12):2089–2100. https://doi.org/10.1016/j.ijheatmasstransfer.2006.11.019
14. Chang C-L, Chang M (2006) Non-iteration estimation of thermal conductivity usingfinite
volume method. Int Commun Heat Mass Transfer 33(8):1013–1020
15. Alifanov OM (1974) Solution of an inverse problem of heat conduction by iteration methods.
J Eng Phys 26:471±476
16. Ozisik MN, Orlande H, Kassab AJ (2002) Inverse heat transfer: fundamentals and applications.
Appl Mech Rev 55(1):B18
17. Panchal M, Saraswat A, Verma S, Chaudhuri P (2019) Estimation of effective thermal conductivity for lithium meta-titanate (Li 2 TiO 3 ) pebble beds using steady state and axial heat flow
methods. J Coupled Syst Multiscale Dyn 6(4):257–265