Uniqueness in a melting slab with space- and time-dependent heating
Author:
Bruno A. Boley
Journal:
Quart. Appl. Math. 27 (1970), 481-487
DOI:
https://doi.org/10.1090/qam/254434
MathSciNet review:
254434
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Abstract: Conditions for uniqueness of solution are derived for a slab which melts under an applied heat input dependent both on time and on the melted depth, the melted material being instantaneously removed. Some examples are constructed in which more than one solution is exhibited as well as one in which no melting solution exists. A theorem demonstrating monotonic dependence of solution on boundary data under certain conditions is proved.
- Bruno A. Boley, A method of heat conduction analysis of melting and solidification problems, J. Math. and Phys. 40 (1961), 300–313. MR 141376
- Bruno A. Boley, Upper and lower bounds in problems of melting or solidifying slabs, Quart. J. Mech. Appl. Math. 17 (1964), 253–269. MR 165844, DOI https://doi.org/10.1093/qjmam/17.3.253
- Ting-shu Wu and Bruno A. Boley, Bounds in melting problems with arbitrary rates of liquid removal, SIAM J. Appl. Math. 14 (1966), 306–323. MR 213105, DOI https://doi.org/10.1137/0114028
S. J. Citron, Heat conduction in melting slab, J. Aero. Sci. 27, 219–228 (1960)
G. W. Sutton, The hydrodynamics and heat conduction of a melting surface, J. Aero. Sci. 25, 29–32, 36 (1958)
N. J. Hoff, Structures and materials for finite lifetime, Advances Aero. Sci., 2, Pergamon Press, 1958
B. A. Boley, The analysis of problems of heat conduction and melting, in High temperature structures and materials, Proc. Symp. on Naval Structural Mechanics, Pergamon Press, New York, pp. 260–315, 1964
- Bruno A. Boley, Upper and lower bounds for the solution of a melting problem, Quart. Appl. Math. 21 (1963), 1–11. MR 147124, DOI https://doi.org/10.1090/S0033-569X-1963-0147124-3
---, Estimate of errors in approximate temperature and thermal stress calculations, Proc. XI Int. Congr. Appl. Mech., Munich, 586–596, Springer-Verlag, Berlin, 1964
---, A general starting solution for melting and solidifying slabs, Int. J. Eng. Sci. 6, 89–111 (1968)
- Mauro Picone, Sul problema della propagazione del calore in un mezzo privo di frontiera, conduttore, isotrope e omogeneo, Math. Ann. 101 (1929), no. 1, 701–712 (Italian). MR 1512562, DOI https://doi.org/10.1007/BF01454870
B. A. Boley, A method of heat-conduction analysis of melting and solidifying slabs, J. Math. Phys. 40, 300–313 (1961)
---, Upper and lower bounds in problems of melting or solidifying slabs, Quart. J. Mech. Appl. Math. 17, 253–269 (1964)
T. S. Wu and B. A. Boley, Bounds in melting problems with arbitrary rates of liquid removal, SIAM J. Appl. Math. 14, 306–323 (1966)
S. J. Citron, Heat conduction in melting slab, J. Aero. Sci. 27, 219–228 (1960)
G. W. Sutton, The hydrodynamics and heat conduction of a melting surface, J. Aero. Sci. 25, 29–32, 36 (1958)
N. J. Hoff, Structures and materials for finite lifetime, Advances Aero. Sci., 2, Pergamon Press, 1958
B. A. Boley, The analysis of problems of heat conduction and melting, in High temperature structures and materials, Proc. Symp. on Naval Structural Mechanics, Pergamon Press, New York, pp. 260–315, 1964
---, Upper and lower bounds for the solution of a melting problem, Quart. Appl. Math. 21, 1–11 (1963)
---, Estimate of errors in approximate temperature and thermal stress calculations, Proc. XI Int. Congr. Appl. Mech., Munich, 586–596, Springer-Verlag, Berlin, 1964
---, A general starting solution for melting and solidifying slabs, Int. J. Eng. Sci. 6, 89–111 (1968)
M. Picone, Sul problema della progagazione del calore in un mezzo privo di frontiera, conduttore, isotropo e omogeneo, Math. Ann. 101, 701 (1929)
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Article copyright:
© Copyright 1970
American Mathematical Society
