9. Advanced Topics in Engineering: Nonlinear Models
Published Online: 4 APR 2013
Copyright © 2013 by John Wiley & Sons, Inc.
Applied Diffusion Processes from Engineering to Finance
How to Cite
Janssen, J., Manca, O. and Manca, R. (2013) Advanced Topics in Engineering: Nonlinear Models, in Applied Diffusion Processes from Engineering to Finance, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118578339.ch9
- Published Online: 4 APR 2013
- Published Print: 4 MAR 2013
Print ISBN: 9781848212497
Online ISBN: 9781118578339
- diffusive problem;
- heat conduction;
- integral method;
- nonlinear model
This chapter discusses nonlinear model in heat conduction. The diffusion problems can be nonlinear when, at least, the governing equations have nonlinearity or the boundary conditions are nonlinear. Some problems can present both the governing equation and nonlinear boundary conditions. Moreover, it is important to classify partial differential equations (PDEs) as linear and nonlinear because the mathematical methods to solve these types of equations are often completely different. Linear or nonlinear can be defined in terms of a PDE operator given, in a three-dimensional problem. Nonlinearities are often present in diffusion or heat conduction problems and, as observed previously, they can be found in the governing equations and/or in boundary conditions. In the hypothesis that thermal properties of the solid present significant temperature dependence or if the involved temperature range is large, the diffusive (conductive) problem is nonlinear. The integral method can be applied to solve nonlinear problems.