Article
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).
04/2009;
48(4):722732.
DOI: 10.1016/j.ijthermalsci.2008.05.009

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ABSTRACT: An extension to the classical quadrupole method is proposed which allows computing temperature and heat fluxes anywhere inside a multilayer material containing localized and/or distributed heat sources. The distributed heat sources are not limited to being uniform in each layer. By using the superposition principle and through a treatment which depends on the relative position of the heat sources and the observation point, we get a closedform analytical expression for the temperature/flux vector which yields stable results over an arbitrary time scale. This sourcesampled quadrupole method is based on the transfer formulation related to a Tscheme twoport network representation. We propose another approach based on the impedance formulation related to the same Tscheme twoport network representation; it leads to a global impedance matrix formulation which provides first the heat flux vector and then the temperature vector. Alternatively we also propose an approach based on the admittance formulation related to a Πscheme twoport network representation with admittances; it leads to a global admittance matrix formulation which provides first the temperature vector and then the heat flux vector. Both impedance and admittance matrix formulations are easier to program than the sourcesampled quadrupole method but their computing time is slightly higher. The three proposed methods are illustrated on two fourlayer slabs, one with a uniform heat source distribution in each layer and the other one with exponential heat source profiles.International Journal of Thermal Sciences 07/2014; 81:38–51. DOI:10.1016/j.ijthermalsci.2014.02.007 · 2.56 Impact Factor 
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ABSTRACT: The objective of this paper is to derive the mathematical model of twodimensional heat conduction at the inner and outer surfaces of a hollow cylinder which are subjected to a timedependent periodic boundary condition. The substance is assumed to be homogenous and isotropic with timeindependent 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.International Journal of Thermophysics 02/2013; 34(2). DOI:10.1007/s107650131418y · 0.62 Impact Factor 
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ABSTRACT: In this article, analytical modeling of twodimensional heat conduction in a hollow sphere is presented. The hollow sphere is subjected to timedependent periodic boundary conditions at the inner and outer surfaces. The Duhamel theorem is employed to solve the problem where the periodic and timedependent 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.International Journal of Thermophysics 01/2011; 33(1). DOI:10.1007/s1076501111362 · 0.62 Impact Factor
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