Dynamic programming approach to a Fermat type principle for heat flow
AbstractWe consider nonlinear heat conduction satisfying a variational principle of Fermat type in the case of stationary heat flow. We review origins of a physical theory and transform it into a formalism consistent with irreversible thermodynamics, where the theory emerges as a consequence of the theorem of minimum entropy production. Applications of functional equations and the Hamilton–Bellman–Jacobi equation are effective when Bellman’s method of dynamic programming is applied to propagation of thermal rays. Potential functions describing minimum resistance are obtained by analytical and numerical methods. For the latter, approximation schemes are developed. Differences between propagation of thermal and optical rays are discussed and it is shown that while simplest optical rays can be described by Riemmanian geometry, it is rather Finslerian geometry that is valid for thermal rays.
|Journal series||International Journal of Heat and Mass Transfer, ISSN 0017-9310|
|Publication size in sheets||0.75|
|Publication indicators||: 2006 = 1.482 (2) - 2007=1.811 (5)|
|Citation count*||14 (2015-02-24)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.