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Free Convection in a Trench with Radiative Wall Conditions
Author(s) -
De Socio L. M.,
Misici L.
Publication year - 1980
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19800600106
Subject(s) - trench , uniqueness , radiative transfer , convection , mechanics , natural convection , perturbation (astronomy) , mathematical analysis , free surface , physics , mathematics , geometry , materials science , optics , layer (electronics) , quantum mechanics , composite material
Abstract Free convection is considered in a rectangular trench with an assigned temperature distribution at the bottom and radiative vertical walls. Following a domain perturbation technique, the problem reduces to the Stokes' equation. After proving the existence and uniqueness of the solution, from a functional point of view, the stream function is expressed in closed form via a bi‐harmonic series and the shape of the free surface is also given. An application follows in order to show the convergence characteristics of the solution and the flow structure.