Shiladitya Acharya, Krishnendu Mukherjee
We study the transport of heat in a three dimensional harmonic crystal of slab geometry whose boundaries and 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 energy fluxes flown between the intermediate surfaces and the attached baths and impose conditions that relate the widths of the Gaussian noises of the intermediate baths. We show that under these conditions 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 nature was already confirmed by Ingen Hausz's experiment. Profile indicates that transport in the steady state involves the process of conduction and radiation of heat.
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http://arxiv.org/abs/1211.1929
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