Pool-boiling serves as the physical model problem for electronics cooling by means of phase-change heat-transfer. The key for optimal and reliable cooling capacity is better understanding of the conditions that determine the critical heat-flux (CHF). Exceeding CHF results in the transition from efficient nucleate-boiling to inefficient film-boiling. This transition is intimately related to the formation and stability of multiple (steady) states on the fluid-heater interface. To this end, the steady-state behavior of a three-dimensional pool-boiling system has been studied in terms of a representative mathematical model problem. This model problem involves only the temperature field within the heater and models the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. The steady-state behavior is investigated via a bifurcation analysis with a continuation algorithm based on the treatment of the model with the method of separation of variables and a Fourier-collocation method. This revealed that steady-state solutions with homogeneous interface temperatures may undergo bifurcations that result in multiple solutions with essentially heterogeneous interface temperatures. These heterogeneous states phenomenologically correspond with vapor patches (“dry spots”) on the interface that characterize transition conditions. The findings on the model problem are consistent with laboratory experiments.

1.
Mudawar
,
I.
, 2001, “
Assessment of High-Heat-Flux Thermal Management Schemes
,”
IEEE Trans. Compon. Packag. Technol.
1521-3331,
24
, pp.
122
141
.
2.
Thome
,
J. R.
, 2003, “
Boiling
,”
Handbook of Heat Transfer
,
A.
Bejan
and
A. D.
Krause
, eds.,
Wiley
,
Hoboken
.
3.
Dhir
,
V. K.
, 1998, “
Boiling Heat Transfer
,”
Annu. Rev. Fluid Mech.
0066-4189,
30
, pp.
365
401
.
4.
Auracher
,
H.
, and
Maquardt
,
W.
, 2004, “
Heat Transfer Characteristics and Mechanisms Along Entire Boiling Curves Under Steady-State and Transient Conditions
,”
Int. J. Heat Fluid Flow
0142-727X,
25
, pp.
223
242
.
5.
Speetjens
,
M.
,
Reusken
A.
, and
Marquardt
,
W.
, 2008, “
Steady-State Solutions in a Three-Dimensional Nonlinear Pool-Boiling Heat-Transfer Model
,”
Commun. Nonlinear Sci. Numer. Simul.
1007-5704,
13
, pp.
1518
1537
.
6.
Van Ouwekerk
,
H.
, 1972, “
Burnout in Pool Boiling The Stability of Boiling Mechanisms
,”
Int. J. Heat Mass Transfer
0017-9310,
15
, pp.
25
33
.
7.
Blum
,
J.
,
Lüttich
,
T.
, and
Marquardt
,
W.
, 1999, “
Temperature Wave Propagation as a Route From Nucleate to Film Boiling?
,”
Proceedings of the Second International Symposium on Two-Phase Flow Modelling and Experimentation, Rome
,
G. P.
Celata
,
P.
DiMarco
, and
R. K.
Shah
, eds.,
Edizioni ETS
,
Pisa
.
8.
Speetjens
,
M.
,
Reusken
A.
, and
Marquardt
,
W.
, 2008, “
Steady-State Solutions in a Nonlinear Pool-Boiling Model
,”
Commun. Nonlinear Sci. Numer. Simul.
1007-5704,
13
, pp.
1475
1494
.
9.
Kovalev
,
S. A.
, 1966, “
An Investigation of Minimum Heat Fluxes in Pool Boiling of Water
,”
Int. J. Heat Mass Transfer
0017-9310,
9
, pp.
1219
1226
.
10.
Kreyszig
,
E.
, 1999,
Advanced Engineering Mathematics
,
Wiley
,
Chichester
.
11.
Canuto
,
C.
,
Hussaini
,
M. Y.
,
Quarteroni
,
A.
, and
Zang
,
T. A.
, 1987,
Spectral Methods in Fluid Dynamics
,
Springer
,
Berlin
.
12.
Here an in-house continuation algorithm of the Chair of Process Systems Engineering, RWTH Aachen, has been used that is based on techniques described in Ref. 14. Elaboration on this algorithm is beyond the scope of this Communication.
13.
Ott
,
E.
, 2002,
Chaos in Dynamical Systems
,
2nd ed.
,
Cambridge University Press
,
Cambridge
.
14.
Govaerts
,
W. J. F.
, 2000,
Numerical Methods for Bifurcations of Dynamical Equilibria
,
SIAM
,
Philadelphia, PA
.
15.
Speetjens
,
M.
,
Reusken
,
A.
,
Maier-Paape
,
S.
, and
Marquardt
,
W.
, 2008, “
Stability Analysis of Two-Dimensional Pool-Boiling Systems
,”
SIAM J. Appl. Dyn. Syst.
1536-0040,
7
, pp.
933
961
.
16.
Auracher
,
H.
, and
Maquardt
,
W.
, 2002, “
Experimental Studies of Boiling Mechanisms in all Boiling Regimes Under Steady-State and Transient Conditions
,”
Int. J. Therm. Sci.
1290-0729,
41
, pp.
586
598
.
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