HEAT TRANSPORT IN A THREE-DIMENSIONAL SLAB GEOMETRY AND THE TEMPERATURE PROFILE OF INGEN-HAUSZ'S EXPERIMENT
| Autor: | Shiladitya Acharya, Krishnendu Mukherjee |
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| Rok vydání: | 2013 |
| Předmět: |
Materials science
Statistical Mechanics (cond-mat.stat-mech) Slab geometry Gaussian FOS: Physical sciences Statistical and Nonlinear Physics Mechanics White noise Condensed Matter Physics Thermal conduction Langevin equation symbols.namesake Fourier transform symbols Slab Condensed Matter - Statistical Mechanics |
| Zdroj: | International Journal of Modern Physics B. 27:1350057 |
| ISSN: | 1793-6578 0217-9792 |
| DOI: | 10.1142/s0217979213500574 |
| Popis: | We study the transport of heat in a three dimensional harmonic crystal of slab geometry whose boundaries and the intermediate surfaces are connected to stochastic, white noise heat baths at different temperatures. Heat baths at the intermediate surfaces are required to fix the initial state of the slab in respect of its surroundings. We allow the flow of energy fluxes between the intermediate surfaces and the attached baths and impose conditions that relate the widths of the Gaussian noises of the intermediate baths. The radiated heat obeys Newton's law of cooling when intermediate baths collectively constitute the environment surrounding the slab. We show that Fourier's law holds in the continuum limit. We obtain an exponentially falling temperature profile from high to low temperature end of the slab and this very nature of the profile was already confirmed by Ingen Hausz's experiment. Temperature profile of similar nature is also obtained in the one dimensional version of this model. 14 pages, 2 figures; typographical errors corrected ;Published in Int. J. Mod. Phys. B |
| Databáze: | OpenAIRE |
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