Freezing over a cylinder with finite heat transfer at the wall
01 May 1983-Vol. 17, Iss: 3, pp 181-186
TL;DR: In this paper, a simple and straightforward implicit numerical technique for phase change problems in cylindrical geometry is proposed, which isolates the nonlinearity associated with the moving interface as well as that of any nonlinear wall boundary condition and permits the simultaneous evaluation of the unknown interface location and the wall temperature at the new time level.
Abstract: A simple and straightforward implicit numerical technique for phase change problems in cylindrical geometry is proposed. When implicit schemes are used the moving interface along with the convective or radiative boundary condition pose a problem because of the requirement to calculate the interface location and boundary temperature implicitly. Due to this difficulty some of the methods available in literature used approximations near the wall and the rest used iterative methods. The present technique isolates the nonlinearity associated with the moving interface as well as that of any nonlinear wall boundary condition and permits the simultaneous evaluation of the unknown interface location and the wall temperature at the new time level. Thereafter the temperatures at the other nodes are obtained without nodal iterations. Numerical results are obtained for outward solidification with both finite and infinite heat transfer rates at the wall. Good agreement is obtained between the present numerical results and the results available in literature for the limiting cases.
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TL;DR: Synthese des travaux publies et bibliographie mondiale sur le transfert de chaleur pour l'annee 1983 as discussed by the authors.
16 citations
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TL;DR: In this paper, an analytical study is presented of the inward freezing of a sphere or a circular cylinder, initially molten and at the fusion temperature, when the outside surface is suddenly cooled.
166 citations
"Freezing over a cylinder with finit..." refers background or methods in this paper
...Most of the approximate methods available in literature [ 1-4 ] used a restrictive condition that the phase change medium is initially at its saturation temperature and thereby considered only one region for analysis....
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...Further, references [1, 2 ] considered only infinite heat transfer at the wall....
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TL;DR: In this paper, a numerical method and graphs of generalized solutions are presented for a moving interface problem of freezing a saturated liquid inside a cylindrical or a spherical container with a constant heat transfer coefficient, as well as melting a saturated solid.
Abstract: A numerical method and graphs of generalized solutions are presented for a moving interface problem of freezing a saturated liquid inside a cylindrical or a spherical container with a constant heat transfer coefficient, as well as melting a saturated solid. The frozen solid phase has a constant heat capacity.
149 citations
"Freezing over a cylinder with finit..." refers result in this paper
...The earlier studies reported in literature [ 7-9 ] used only explicit difference schemes because of their simplicity....
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TL;DR: In this article, the change of variable method introduced by Landau for the one-dimensional problem is extended to the multi-dimensional using an independent variable which takes constant values at the boundary and the freezing front.
Abstract: This paper presents a simple numerical method for solving two and three-dimensional freezing problems with arbitrary geometries. The change of variable method introduced by Landau for the one-dimensional problem is extended to the multi-dimensional using an independent variable which takes constant values at the boundary and the freezing front. Example calculations were performed for the Stefan type freezing problem in regular squares, triangles, and ellipses. Then some of the results were compared with the experimental ones that were obtained for the constant cooling rate.
108 citations
TL;DR: In this article, the authors present a technique for the analysis of unsteady, two-dimensional diffusive heat-or mass-transfer problems characterized by moving irregular boundaries, including an immobilization transformation and a numerical scheme.
75 citations
"Freezing over a cylinder with finit..." refers methods in this paper
...Goodling and Khader [ 10 ] used an iterative technique which again require considerable computing time....
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67 citations