Periodic heat conduction in a solid homogeneous finite cylinder

Facoltà di Ingegneria, Università di Bergamo, via Marconi 6, 24044 Dalmine (BG), Italy
International Journal of Thermal Sciences (Impact Factor: 2.56). 01/2009; 48(4):722-732. DOI: 10.1016/j.ijthermalsci.2008.05.009

ABSTRACT Analytic solution of the steady periodic, non-necessarily harmonic, heat conduction in a homogeneous cylinder of finite length and radius is given in term of Fourier transform of the fluctuating temperature field. The solutions are found for quite general boundary conditions (first, second and third kind on each surface) with the sole restriction of uniformity on the lateral surface and radial symmetry on the bases. The thermal quadrupole formalism is used to obtain a compact form of the solution that can be, with some exception, straightforwardly extended to multi-slab composite cylinders. The limiting cases of infinite thickness and infinite radius are also considered and solved.

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    ABSTRACT: The objective of this paper is to derive the mathematical model of two-dimensional heat conduction at the inner and outer surfaces of a hollow cylinder which are subjected to a time-dependent periodic boundary condition. The substance is assumed to be homogenous and isotropic with time-independent thermal properties. Duhamel’s theorem is used to solve the problem for the periodic boundary condition which is decomposed by Fourier series. In this paper, the effects of the temperature oscillation frequency on the boundaries, the variation of the hollow cylinder thickness, the length of the cylinder, the thermophysical properties at ambient conditions, and the cylinder involved in some dimensionless numbers are studied. The obtained temperature distribution has two main characteristics: the dimensionless amplitude ( $A$ ) and the dimensionless phase difference ( $\varphi $ ). These results are shown with respect to Biot and Fourier and some other important dimensionless numbers.
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    ABSTRACT: In this article, analytical modeling of two-dimensional heat conduction in a hollow sphere is presented. The hollow sphere is subjected to time-dependent periodic boundary conditions at the inner and outer surfaces. The Duhamel theorem is employed to solve the problem where the periodic and time-dependent terms in the boundary conditions are considered. In the analysis, the thermophysical properties of the material are assumed to be isotropic and homogenous. Moreover, the effects of the temperature oscillation frequency, the thickness variation of the hollow sphere, and thermophysical properties of the sphere are studied. The temperature distribution obtained here contains two characteristics, the dimensionless amplitude (A) and the dimensionless phase difference ( ${\varphi}$ ). Moreover, the obtained results are shown with respect to Biot and Fourier numbers. Comparison between the present results and the findings from a previous study for a hollow sphere subjected to the reference harmonic state show good agreement.
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