Estimation of unknown boundary functionsin an inverse heat conduction problem using a mollified marching scheme
- 145 Downloads
In this article, a one-dimensional inverse heat conduction problem with unknown nonlinear boundary conditions is studied. In many practical heat transfer situations, the heat transfer coefficient depends on the boundary temperature and the dependence has a complicated or unknown structure. For this reason highly nonlinear boundary conditions are imposed involving both the flux and the temperature. A numerical procedure based on the mollification method and the space marching scheme is developed to solve numerically the proposed inverse problem. The stability and convergence of numerical solutions are investigated and the numerical results are presented and discussed for some test problems.
KeywordsInverse heat conduction Nonlinear boundary condition Mollification Space marching method
Unable to display preview. Download preview PDF.
- 1.Cannon, J.R.: The one-Dimensional Heat Equation. Addison-Wesley (1984)Google Scholar
- 2.Özisik, M.N.: Heat Conduction. John Wiley & Sons INC (1993)Google Scholar
- 13.Garshasbi, M., Damirchi, J., Reihani, P.: Parameter estimation in an inverse initial-boundary value problem of heat equation. J. Adv. Res. Diff. Equ. 2, 49–60 (2010)Google Scholar
- 15.Murio, D.A.: Mollification and space marching. In: Woodbury, K (ed.) Inverse Engineering Handbook. CRC Press (2002)Google Scholar
- 16.Mejia, C.E., Murio, D.A., Zhan, S.: Some applications of the mollification method. In: Lassonde, M. (ed.) App. Opti. Math Eco., pp. 213–222. Physica-Verlag (2001)Google Scholar