Analytical solutions of the heat diffusion equation for 3ω method geometry | Zendy

Jean Yves Duquesne | Zendy; D. Fournier | Zendy; Christian Frétigny | Zendy

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Analytical solutions of the heat diffusion equation for 3ω method geometry

Author(s) -

Jean Yves Duquesne,

D. Fournier,

Christian Frétigny

Publication year - 2010

Publication title -

journal of applied physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.699

H-Index - 319

eISSN - 1089-7550

pISSN - 0021-8979

DOI - 10.1063/1.3486441

Subject(s) - bessel function , thermal diffusivity , heat equation , diffusion equation , thermal conductivity , diffusion , calibration , mathematical analysis , convection–diffusion equation , mathematics , spherical geometry , geometry , physics , thermodynamics , statistics , economy , economics , service (business)

International audience“3ω” experiments aim at measuring thermal conductivities and diffusivities. Data analysis relies on integral expressions of the temperature. In this paper, we derive new explicit analytical formu- lations of the solution of the heat diffusion equation, using Bessel, Struve and Meijer-G functions, in the 3ω geometry for bulk solids. These functions are available in major computational tools. Therefore numerical integrations can be avoided in data analysis. Moreover, these expressions enable rigorous derivations of the asymptotic behaviors. We also underline that the diffusivity can be extracted from the phase data without any calibration while the conductivity measurement requires a careful one

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