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]
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