Dynamic programming approach to a Fermat type principle for heat flow

Stanisław Sieniutycz

Abstract

We 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.
Author Stanisław Sieniutycz (FCPE / DSP)
Stanisław Sieniutycz,,
- Department of Separation Processes
Journal seriesInternational Journal of Heat and Mass Transfer, ISSN 0017-9310
Issue year2000
Vol43
No18
Pages3453-3468
Publication size in sheets0.75
DOIDOI:10.1016/S0017-9310(00)00032-6
URL http://ac.els-cdn.com/S0017931000000326/1-s2.0-S0017931000000326-main.pdf?_tid=8c681b4a-e186-11e6-b80e-00000aab0f26&acdnat=1485188047_237ae855da89fab9c191bf4d71acb9e3
Languageen angielski
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Sieniutycz S. - Dynamic programming approach....pdf 254.21 KB
Score (nominal)40
Publication indicators WoS Impact Factor: 2006 = 1.482 (2) - 2007=1.811 (5)
Citation count*14 (2015-02-24)
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