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# 9. Advanced Topics in Engineering: Nonlinear Models

1. Jacques Janssen,
2. Oronzio Manca and
3. Raimondo Manca
1. Jacques Janssen,
2. Oronzio Manca and
3. Raimondo Manca

Published Online: 4 APR 2013

DOI: 10.1002/9781118578339.ch9

## 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

#### Publication History

1. Published Online: 4 APR 2013
2. Published Print: 4 MAR 2013

#### ISBN Information

Print ISBN: 9781848212497

Online ISBN: 9781118578339

## SEARCH

### Keywords:

• diffusive problem;
• heat conduction;
• integral method;
• nonlinear model

### Summary

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.