Abstract

Freezing processes taking place in a plate, a cylinder and a sphere are investigated by using the improved quasi-steady analysis model developed in the present study. In the improved quasi-steady analysis, an additional term is added to the temperature profile to simulate the transient effect on the temperature distribution in the solid phase. This additional term is based on the ratio of the heat flux at the phase boundary to that at the cooling surface, and physically, presents the thermal capacity effect in the frozen region. The maximum relative error of the moving phase front location obtained from the improved quasi-steady analysis is about 3% in comparison with that obtained from the exact solution of the freezing process in a plate. Since there is no exact solution available for the freezing process taking place in a cylinder or a sphere, the results obtained from the improved quasi-steady analysis are compared with results from references. The maximum relative errors of the improved quasi-steady analysis for the cylindrical and spherical cases are less than 4% while the maximum relative errors of the quasi-steady approximation are higher than 42%. It is evident that the improved quasi-steady analysis developed in the present study maintains the simplicity of the quasi-steady approximation while greatly increasing its accuracy.

Issue Section:
Melting and Solidification
Keywords:
Analytical, Cylinder, Heat Transfer, Plate, Solidification, Sphere, solidification, freezing, temperature distribution, digital simulation
Topics:
Approximation, Cylinders, Freezing, Solidification, Temperature distribution, Errors
1.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Oxford University Press, London, Chap. XI.
2.
Lunardini, V. J., 1981, Heat Transfer in Cold Climates, Van Nostrand Reinhold Co., New York, Chap. 8.
3.
London
,
A. L.
, and
Seban
,
R. A.
,
1943
, “
Rate of Ice Formation
,”
Trans. ASME
,
65
, pp.
771
–
778
.
4.
Mennig
,
J.
, and
Ozisik
,
M. N.
,
1985
, “
Coupled Integral Approach for Solving Melting or Solidification
,”
Int. J. Heat Mass Transfer
,
28
, pp.
1481
–
1485
.
5.
Caldwell
,
J.
, and
Kwan
,
Y. Y.
,
2003
, “
On the Perturbation Method for the Stefan Problem With Time-Dependent Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
46
, pp.
1497
–
1501
.
6.
Riley
,
D. S.
,
Smith
,
F. I.
, and
Poots
,
G.
,
1974
, “
The Inward Solidification of Spheres and Circular Cylinders
,”
Int. J. Heat Mass Transfer
,
17
, pp.
1507
–
1516
.
7.
Poots
,
G.
,
1962
, “
On the Application of Integral Methods to the Solution of Problems Involving the Solidification of Liquid Initially at Fusion Temperature
,”
Int. J. Heat Mass Transfer
,
5
, pp.
525
–
531
.
8.
Beckett, P. M., 1971, Ph.D. thesis, Hull University, England.
9.
Allen
,
D. N. de G.
, and
Severn
,
R. T.
,
1962
, “
The Application of the Relaxation Method to the Solution of Non-Elliptic Partial Differential Equations
,”
Q. J. Mech. Appl. Math.
,
15
, p.
53
53
.
10.
Tao
,
L. C.
,
1967
, “
Generalized Numerical Solutions of Freezing a Saturated Liquid in Cylinders and Spheres
,”
AIChE J.
,
13
(
1
), p.
165
165
.
11.
Pedroso
,
R. I.
, and
Domoto
,
G. A.
,
1973
, “
Perturbation Solutions for Spherical Solidification of Saturated Liquids
,”
ASME J. Heat Transfer
,
95
(
1
), pp.
42
–
46
.
Copyright © 2003
 by ASME
You do not currently have access to this content.