Heat-Transfer Coefficient of Inviscid Fluid Freezing Onto a Moving Heat Sink

[+] Author and Article Information
H. Bueckner

Mathematics Research Center, U. S. Army, University of Wisconsin, Madison, Wis.

G. Horvay

General Electric Research Laboratory, Metallurgy and Ceramics Department, Schenectady, N. Y.

J. Heat Transfer 85(3), 246-256 (Aug 01, 1963) (11 pages) doi:10.1115/1.3686087 History: Received February 06, 1962


When a cold slab travels at speed U through a liquid metal bath, it freezes out metal at the rate of V. It is shown that the problem of determining the heat-transfer coefficient h at the interface of the liquid and solid phases is equivalent—under certain simplifying assumptions—to solving the (time-independent) wave equation in a sector. For the case of α ≡ arctan V/U < π/4, treated in the present paper, the problem is reduced, through suitable changes of variables and a Fourier sine transform, to the solution of Dirichlet’s problem for the Laplace equation. The temperature field T(X, Y) is expressed as an inverse sine transform, involving a single integration (in the transform variable). One finds that at the entrance cross section to the bath, X = 0, the heat-transfer coefficient is zero, then it rapidly approaches the asymptotic (“fully developed”) value h = γcV cos α. The heat-transfer coefficient is determined in closed form for α = π/6, π/4, and asymptotic expressions of it are derived for very small and very large distances from the origin when α is arbitrary (0 < α < π/4). Numerical evaluation of the heat-transfer coefficient at the solid-liquid interface is carried out for α = π/36, π/12, π/4. Plots of the temperature field T for these angles are also shown, along rays ϑ = π/6, π/3, π/2 to the horizontal.

Copyright © 1963 by ASME
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