Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Numerical solution of the heat equation with nonlinear, time derivativedependent source term
 International journal for numerical methods in engineering 84 (2010), Nr.10, S.12051221 ISSN: 00295981 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer ITWM () 
Abstract
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 nonlinear 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 nonlinear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semiimplicit 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.