ON THE CONDUCTION OF HEAT IN A MELTING SLAB
COLUMBIA UNIV NEW YORK INST OF FLIGHT STRUCTURES
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A new method for the solution of the problem of heat conduction in a melting slab, where the molten material is immediately removed upon formation, is presented. No restrictions are placed on the boundary conditions which may be imposed on the slab and the material properties are allowed to be temperature dependent. The problem of determining the temperature distribution in the slab and the amount of material melted is reduced to finding the solution of an ordinary differential equation on the amount of material melted. This reduction from a partial differential equation problem is accomplished by determining a Taylors series expansion in space for the temperature distribution. The equation so obtained for the determination of the amount of material melted is of a form readily solved numerically. Comparisons with known results for a slab insulated on one face and subjected to a constant heat input on the other face are given.
- Electricity and Magnetism