JP Journal of Heat and Mass Transfer
Volume 20, Issue 1, Pages 45 - 66
(June 2020) http://dx.doi.org/10.17654/HM020010045 |
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PREDICTION OF FREEZING IN A FINITE REGION WITH AN ADIABATIC BOTTOM BY A CONNECTION OF NEUMANN’S SOLUTION AND AN APPROXIMATE SOLUTION
M. Sugawara and M. Tago
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Abstract: This paper is concerned with a conduction freezing of superheated water in one-dimensional finite region with adiabatic bottom. The freezing path is very complex because the freezing rate does not monotonically change (i.e., a wavy freezing path) so that well-known Neumann’s solution is not applicable in long time freezing but just in the beginning. Therefore, it is very difficult to predict a long time freezing except a troublesome numerical procedure. It is possible to predict easily the thickness of all frozen by the connection of the simplest Neumann’s solution and the approximate solution in a very simple closed form so as to be available immediately in many engineering applications. Also, an idea is proposed for the freezing on fluid flow cooling that can be predicted fairly by the solutions connected under the condition of Biot number larger than 90.1. |
Keywords and phrases: freezing of water, conduction, Neumann’s solution, numerical solution, approximate solution.
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