Abstract. The present work deals with the cooling of a flat plate having an initial non-homogeneous temperature distribution, which undergoes a sudden temperature drop at its surfaces. Hence, starting from an arbitrary steady-state temperature distribution, the two surfaces of the slab are suddenly cooled down to the value 0, resulting in a strong perturbation of the initial temperature distribution. A general analytical solution is provided by adopting the variable separation technique to the Fourier equation in transient conditions, thus obtaining a general solution in terms of a very fast converging series, which includes a definite integral of the initial steady-state distribution. Common engineering applications are investigated and the related results, obtained thanks to an extremely low computational effort, are presented and discussed.

An analytical approach to the cooling of a flat plate / Pagliarini, Luca; Spiga, Marco; Vocale, Pamela. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - (2021), pp. 012003.1-012003.8. [10.1088/1742-6596/1868/1/012003]

An analytical approach to the cooling of a flat plate

Luca Pagliarini
Membro del Collaboration Group
;
Marco Spiga
Membro del Collaboration Group
;
Pamela Vocale
Membro del Collaboration Group
2021-01-01

Abstract

Abstract. The present work deals with the cooling of a flat plate having an initial non-homogeneous temperature distribution, which undergoes a sudden temperature drop at its surfaces. Hence, starting from an arbitrary steady-state temperature distribution, the two surfaces of the slab are suddenly cooled down to the value 0, resulting in a strong perturbation of the initial temperature distribution. A general analytical solution is provided by adopting the variable separation technique to the Fourier equation in transient conditions, thus obtaining a general solution in terms of a very fast converging series, which includes a definite integral of the initial steady-state distribution. Common engineering applications are investigated and the related results, obtained thanks to an extremely low computational effort, are presented and discussed.
2021
An analytical approach to the cooling of a flat plate / Pagliarini, Luca; Spiga, Marco; Vocale, Pamela. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - (2021), pp. 012003.1-012003.8. [10.1088/1742-6596/1868/1/012003]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2886994
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