Upper and lower bounds for the solution of a melting problem
Author:
Bruno A. Boley
Journal:
Quart. Appl. Math. 21 (1963), 1-11
MSC:
Primary 80.49
DOI:
https://doi.org/10.1090/qam/147124
MathSciNet review:
147124
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Abstract: A slab, melting under an arbitrary heat input on one face and insulated on the other is studied. Variable material properties are taken into account. After preliminary general considerations, it is shown that the solution to the stated problem is unique. It is then proved that higher rates of melting and higher temperatures will result from higher heating rates; from this intuitively plausible result upper and lower bounds for the solution are easily constructed. An example is worked out in detail.
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- Stephen J. Citron, Heat conduction in a melting slab, J. Aero/Space Sci. 27 (1960), 219–228. MR 111468
T. R. Goodman, Aerodynamic ablation of melting bodies, Proc. 3rd U. S. Nat. Congress Appl. Mech., New York, 1958, p. 735
G. W. Sutton, The hydrodynamics and heat conduction of a melting Surface, J. Aeron. Sci. 25 (1958) 29
N. J. Hoff, Structures and materials for finite lifetime, Advances in aeronautical science, Vol. 2. Pergamon Press, New York, 1958, p. 928
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- H. G. Landau, Heat conduction in a melting solid, Quart. Appl. Math. 8 (1950), 81–94. MR 33441, DOI https://doi.org/10.1090/S0033-569X-1950-33441-3
- H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford, at the Clarendon Press, 1947. MR 0022294
B. A. Boley, The analysis of a problem of heat conduction and melting, Proc. 3rd Symp. on Naval Structural Mechanics, Int. Conf. on Elevated Temperature Mechanics, Pergamon Press, New York, 1963.
B. A. Boley, A method of heat conduction analysis of melting and solidification problems, Journal of Math. and Physics. 40 (1961) 300
S. J. Citron, Heat conduction in a melting slab, Journal of the Aero/Space Sciences. 27 (1960) 219
T. R. Goodman, Aerodynamic ablation of melting bodies, Proc. 3rd U. S. Nat. Congress Appl. Mech., New York, 1958, p. 735
G. W. Sutton, The hydrodynamics and heat conduction of a melting Surface, J. Aeron. Sci. 25 (1958) 29
N. J. Hoff, Structures and materials for finite lifetime, Advances in aeronautical science, Vol. 2. Pergamon Press, New York, 1958, p. 928
M. Picone, Sul problema della propagazione del calore in un mezzo privo di frontiera, conduttore, isotropo e omogeneo, Mathematische Annalen, 101 (1929) 701
B. A. Boley and J. H. Weiner, Theory of thermal stresses, J. Wiley and Sons, New York, 1960.
H. G. Landau, Heat conduction in a melting solid, Quart. Appl. Math., 18 (1950) 81.
H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids, Clarendon Press, Oxford, Second Edition, 1959.
B. A. Boley, The analysis of a problem of heat conduction and melting, Proc. 3rd Symp. on Naval Structural Mechanics, Int. Conf. on Elevated Temperature Mechanics, Pergamon Press, New York, 1963.
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Article copyright:
© Copyright 1963
American Mathematical Society