Identification of the timewise thermal conductivity in a 2D heat equation from local heat flux conditions

References

• Cannon JR, Yin HM. A class of nonlinear nonclassical parabolic equations. J Differ Equ. 1989;79:266–288. doi: 10.1016/0022-0396(89)90103-4
   Google Scholar
• Cannon JR, Matheson AL. A numerical procedure for diffusion subject to the specification of mass. Int J Eng Sci. 1993;31:347–355. doi: 10.1016/0020-7225(93)90010-R
   Google Scholar
• Cannon JR, Lin Y, Wang S. An implicit finite difference scheme for the diffusion equation subject to mass specification. Int J Eng Sci. 1990;28:573–578. doi: 10.1016/0020-7225(90)90086-X
   Google Scholar
• Ivanchov MI. Some inverse problems for the heat equation with nonlocal boundary condition. Ukrainian Math J. 1993;45:1066–1071. doi: 10.1007/BF01070965
   Google Scholar
• Ivanchov MI. On an inverse problem of heat conduction with nonlocal overdetermination condition. Visnyk L'vivskogo Universytetu Ser Mech Mat. 1994;40:12–15.
   Google Scholar
• Ivanchov MI. Inverse problems for equations of parabolic type. Liviv: VNTL; 2003.
   Google Scholar
• Huntul MJ, Lesnic D. Reconstruction of the timewise conductivity using a linear combination of heat flux measurements. J King Saud Univ Sci. 2020;32:928–933. doi: 10.1016/j.jksus.2019.05.006
   Google Scholar
• Huntul MJ, Lesnic D. An inverse problem of finding the time-dependent thermal conductivity from boundary data. Int Commun Heat Mass Transfer. 2017;85:147–154. doi: 10.1016/j.icheatmasstransfer.2017.05.009
   Google Scholar
• Huntul MJ, Hussein MS, Lesnic D, et al. Reconstruction of an orthotropic thermal conductivity. Int J Math Model Numer Optim. 2020;10:102–122.
   Google Scholar
• Alifanov OM, Budnik SA, Nenarokomov AV, et al. Estimation of thermal properties of materials with application for inflatable spacecraft structure testing. Inverse Probl Sci Eng. 2012;20:677–690. doi: 10.1080/17415977.2012.665909
   Google Scholar
• Huang CH, Huang CY. An inverse problem in estimating simultaneously the effective thermal conductivity and volumetric heat capacity of biological tissue. Appl Math Model. 2007;31:1785–1797. doi: 10.1016/j.apm.2006.06.002
   Google Scholar
• Mera NS, Elliott L, Ingham DB, et al. An iterative BEM for the Cauchy steady state heat conduction problem in an anisotropic medium with unknown thermal conductivity tensor. Inverse Prob Eng. 2000;8:579–607. doi: 10.1080/174159700088027748
   Google Scholar
• Reddy SR, Dulikravich GS. Simultaneous determination of spatially varying thermal conductivity and specific heat using boundary temperature measurements. Inverse Probl Sci Eng. 2019;27:1635–1649. doi: 10.1080/17415977.2019.1578352
   Google Scholar
• Reddy SR, Dulikravich GS, Zeidi SMJ. Non-destructive estimation of spatially varying thermal conductivity in 3D objects using boundary thermal measurements. Int J Thermal Sci. 2017;118:488–496. doi: 10.1016/j.ijthermalsci.2017.05.011
   Google Scholar
• Hussein MS, NSEP Kinash, Lesnic D, et al. Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor. Appl Anal. 2017;96:1–15. doi: 10.1080/00036811.2016.1232401
   Google Scholar
• Sagaydak R. Large on existence and uniqueness of solution for the inverse problem of determination major coefficients in two-dimensional parabloic equation. Visnyk L'vivskogo Universytetu Ser Mech Mat. 2005;64:236–244.
   Google Scholar
• Barakat HZ, Clark AJ. On the solution of the diffusion equations by numerical methods. J Heat Transfer. 1966;88:421–427. doi: 10.1115/1.3691590
   Google Scholar
• Campbell LJ, Yin B. On the stability of alternating-direction explicit methods for advection-diffusion equations. Numer Meth Partial Differ Equ. 2007;23:1429–1444. doi: 10.1002/num.20233
   Google Scholar
• Ozisik MN. Finite difference methods in heat transfer. Boca Raton (FL): CRC Press; 1994.
   Google Scholar
• Mathworks. Documentation optimization toolbox-least squares (model fitting) algorithms; 2016. Available from: www.mathworks.com
   Google Scholar
• Coleman TF, Li Y. An interior trust region approach for nonlinear minimization subject to bounds. SIAM J Optim. 1996;6:418–445. doi: 10.1137/0806023
   Google Scholar
• Cannon JR. The one-dimensional heat equation. Menlo Park (CA): Addison-Wesley; 1984.
   Google Scholar