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We study the transport of heat in a three dimensional harmonic crystal ofslab geometry whose boundaries and the intermediate surfaces are connected tostochastic, white noise heat baths at different temperatures. Heat baths at theintermediate surfaces are required to fix the initial state of the slab inrespect of its surroundings. We allow the flow of energy fluxes between theintermediate surfaces and the attached baths and impose conditions that relatethe widths of the Gaussian noises of the intermediate baths. The radiated heatobeys Newton's law of cooling when intermediate baths collectively constitutethe environment surrounding the slab. We show that Fourier's law holds in thecontinuum limit. We obtain an exponentially falling temperature profile fromhigh to low temperature end of the slab and this very nature of the profile wasalready confirmed by Ingen Hausz's experiment. Temperature profile of similarnature is also obtained in the one dimensional version of this model.

Heat transport in a three dimensional slab geometry and the temperature profile of Ingen-Hausz's experiment