Time Varying Heat Conduction in Solids

Moares, Ernesto Marin

doi:10.5772/26049

Cited by 3 publications

(1 citation statement)

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“…(5), ( 9), ( 14) and (18) has a very strong non-linear dependence of T h and T c with the thermal resistance as a coefficient of the heat flux, this can be seen in the denominator of expressions inside the logarithm function. It is expected following the relationship between thermal resistance and heat conductance proposed by Marin [37], as R cond. = 1/h cond.…”

Section: Resultsmentioning

confidence: 85%

Spherical and cylindrical conductive thermal diodes based on VO2

2019

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We theoretically and comparatively study the performance of spherical and cylindrical conductive thermal diodes operating with a phase-change material, whose thermal conductivity significantly changes in a narrow interval of temperatures. Simple analytical expressions are derived for the temperature profiles, heat fluxes and optimal rectification factors of both diodes. It is shown that the diode geometry has a strong impact on the temperatures and heat fluxes, but not so much on the diode rectification factor. Optimal rectification factors of 20.8% and 20.7% are obtained for the spherical and cylindrical diodes operating with a temperature difference of 376 − 300 = 76 K and 376.5 − 300 = 76.5 K between the terminals of VO2 and a phase invariant material, respectively. These similar rectification factors could be enhanced with a material thermal conductivity exhibiting a faster phase transition and/or higher contrast than that of VO2. The obtained results can thus be useful to guide the development of phase change materials able to optimize the rectification of conductive thermal diodes with different geometries.

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Section: Resultsmentioning

confidence: 85%

Spherical and cylindrical conductive thermal diodes based on VO2

2019

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Diffusion through a half space: equivalence between different formulations of the unique solution

Mantegna¹,

Colombo²

2014

ams

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Diffusion through a half space involves a classical parabolic partial differential equation that is encountered in many fields of physics and has significant engineering applications, concerning particularly heat and mass transfer. However, in the specialized literature, the solution is usually achieved restricting the problem to particular cases and attaining apparently different formulations, thus a comprehensive overview is hindered. In this paper, the solution of the diffusion equation in a half space with a boundary condition of the first kind is worked out by means of the Fourier's Transform, the Green's function and the similarity variable, with a proof of equivalencenot found elsewhereof these different approaches. The keystone of the proof rests on the square completion method applied to Gaussian-like integrals, widely used in Quantum Field Theory.

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Heat Conduction - Basic Research

Vikhrenko¹

2011

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Time Varying Heat Conduction in Solids

Cited by 3 publications

References 44 publications

Spherical and cylindrical conductive thermal diodes based on VO2

Spherical and cylindrical conductive thermal diodes based on VO2

Diffusion through a half space: equivalence between different formulations of the unique solution

Heat Conduction - Basic Research

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