Existence and multiplicity of solutions of an equation from pool boiling on wires

Author:
Shin-Hwa Wang

Journal:
Quart. Appl. Math. **58** (2000), 331-354

MSC:
Primary 34B15; Secondary 80A20

DOI:
https://doi.org/10.1090/qam/1753403

MathSciNet review:
MR1753403

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the existence and multiplicity of steady states of the equation

**[1]**P. J. Berenson,*Experiments on pool-boiling heat-transfer*, Internat. J. Heat Mass Transfer**5**, 985-999 (1962)**[2]**A. E. Bergles,*Poolboiling, Two-Phase Flows and Heat Transfer in the Power and Process Industries*, Hemisphere Publishing Corporation, Chapter 7, 1981, pp. 191-225**[3]**L. A. Bromley,*Heat transfer in stable film boiling*, Chem. Engrg. Progress**46**, 221-227 (1950)**[4]**R. Creighton Buck,*Advanced calculus*, 3rd ed., McGraw-Hill Book Co., New York-Auckland-Bogotá, 1978. With the collaboration of Ellen F. Buck; International Series in Pure and Applied Mathematics. MR**0476931****[5]**J. G. Collier,*Convective Boiling and Condensation*, second edition, McGraw-Hill, New York, 1981, pp. 121-133**[6]**E. J. Doedel, G. Joly, and J.-P. Kernévez,*Continuation of a steep temperature front in nonlinear heat transfer*, Semigroups, theory and applications, Vol. I (Trieste, 1984) Pitman Res. Notes Math. Ser., vol. 141, Longman Sci. Tech., Harlow, 1986, pp. 96–109. MR**876932****[7]**G. Joly, J.-P. Kernévez, and M. Llory,*Thermal instability in pool boiling on wires at constant pressure*, SIAM J. Appl. Math.**43**(1983), no. 6, 1294–1309. MR**722943**, https://doi.org/10.1137/0143087**[8]**G. Joly,*Analyse des solutions multiples dans les systèmes distribués*, thèse, Compiènge, 1982**[9]**Theodore Laetsch,*The number of solutions of a nonlinear two point boundary value problem*, Indiana Univ. Math. J.**20**(1970/1971), 1–13. MR**0269922**, https://doi.org/10.1512/iumj.1970.20.20001**[10]**N. Madsen,*A graphical method for analyzing pool-boiling systems*, Internat. J. Heat Mass Transfer**15**, 513-517 (1973)**[11]**S. Nukiyama,*The maximum and minimum value of the heat Q transmitted from metal to boiling water under atmospheric pressure*, Journal Japan Society of Mechanical Engineers**37**, 367-374 (1934). Translation in International Journal of Heat and Mass Transfer**9**, 1419-1433 (1966)**[12]**Renate Schaaf,*Global solution branches of two-point boundary value problems*, Lecture Notes in Mathematics, vol. 1458, Springer-Verlag, Berlin, 1990. MR**1090827****[13]**Shin-Hwa Wang and Nicholas D. Kazarinoff,*Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable*, J. Austral. Math. Soc. Ser. A**52**(1992), no. 3, 343–355. MR**1151291****[14]**A. Watson,*Influence of axial wall conditions in variable property convection, with particular references to subcritical pressure fluids*, Internat. J. Heat Mass Transfer**20**, 65-71 (1967)**[15]**T. Yanagida,*Couple map lattice model for boiling*, Physics Letter**165A**, 405-408 (1992)

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
34B15,
80A20

Retrieve articles in all journals with MSC: 34B15, 80A20

Additional Information

DOI:
https://doi.org/10.1090/qam/1753403

Article copyright:
© Copyright 2000
American Mathematical Society