2d Transient Natural Convection Generated by Isothermal Active Walls in Parallelogrammic Enclosures

Baı̈ri, A.; Nguyen, Nam C.; Baïri, I.; Laraqi, Najib; María, Juan; Alilat, Nacim

doi:10.1615/ichmt.2008.cht.1970

Cited by 1 publication

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“…The pure transient or periodic heat conduction and simple or complex combinations of these two are encountered in the heat treatment of metals, air conditioning, and food processing [1,2]. Transient heat transfer problems are very common in engineering applications, e.g., hydrocooling of spherical food products [1,3] or fast transient heat conduction in a sphere subjected to sudden and violent thermal effects on its surface used in many engineering fields such as aeronautics, electronics, metallurgy, or food processing [4,5]. Transient heat conduction is studied in a sphere by using Laplace transforms [6,7] or in polar coordinates with multiple layers in the radial direction [8].…”

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confidence: 99%

Analysis of Transient Heat Conduction in a Hollow Sphere Using Duhamel Theorem

Abdous

Avval²,

Ahmadi

et al. 2011

Int J Thermophys

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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 (ϕ). 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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