TY  - JOUR
A1  - Pieper, Martin
A1  - Klein, Peter
T1  - Numerical solution of the heat equation with non-linear, time derivative-dependent source term
T2  - International Journal for Numerical Methods in Engineering
N2  - The mathematical modeling of heat conduction with adsorption effects in coated metal structures yields the heat equation with piecewise smooth coefficients and a new kind of source term. This term is special, because it is non-linear and furthermore depends on a time derivative. In our approach we reformulated this as a new problem for the usual heat equation, without source term but with a new non-linear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semi-implicit and a fully implicit finite volume method. We compared these two methods theoretically as well as numerically. Finally, as practical application, we simulated the heat conduction in coated aluminum fibers with adsorption in the zeolite coating. Copyright © 2010 John Wiley & Sons, Ltd.
Y1  - 2010
UR  - https://opus.bibliothek.fh-aachen.de/opus4/frontdoor/index/index/docId/4954
SN  - 0029-5981
VL  - 84
IS  - 10
SP  - 1205
EP  - 1221
PB  - Wiley
CY  - Chichester
ER  -