Instantaneous thickness of a frozen layer is a function of specific heat, heat of fusion, temperatures, the frozen layer thickness at equilibrium, the thermal conductivity, and heat transfer coefficient. The equation can be evaluated on a desk calculator

Savino, J. M.

Siegel, R.

English

NASA Technical Reports Server

August 1969
	 Brief 69-10321 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
A Method for Predicting Interfacial Freezing

of a Liquid Flowing Over a Cold Surface 
[i
A frozen layer can form in a flowing warm liquid 
when the liquid is in contact with a sufficiently cold 
surface. This occurs in some important engineering 
applications such as heat exchangers in which liquids 
are cooled by cryogenic coolants, castings formed in 
cooled molds, and in rivers where ice layers form in
winter. Common to all these applications is the need 
to know how rapidly the frozen layer forms. 
When a flowing liquid is frozen onto one side of a 
flat plate which is convectively cooled from the other 
side by another fluid, the relation between the thick-
ness of the frozen layer and time is given by the fol-
lowing equation: 
______	
R+2 1 1+R	
I 
Rx'	 ______ 
R
3 + 3R + R	 ln(Rx'+l) 
3(1 + R)2 . In (I - x') + 3R(l + R)2 
where
x 
CjTf - T)	 x	 7-hi, (T, - Tf) 
= L ,R—  , x = X., , r =
	
pLx 
h k 
and 
C,) = specific heat of frozen material 
T, T1 , T = freezing temperature and tempera-
tures of liquid and coolant 
L, k = heat of fusion and thermal conductivity of 
frozen material 
a, k. = thickness and thermal conductivity of flat 
wall on which frozen layer forms 
h,, h = convective heat transfer coefficient for 
liquid and coolant sides
x, x = instantaneous and steady state thickness of 
frozen layer 
T = time 
p = density 
The x8
 is calculated from the steady state heat balance 
where
Tf - Te 
h, (T, - Tf) = '( + a + L 
k	 k,,	 h
(continued overleal) 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19690000320 2020-03-16T18:14:14+00:00Z
Thus the instantaneous thickness of a frozen layer 
is found to be a function of specific heat, heat of 
fusion, temperatures, the frozen layer thickness at 
equilibrium, the thermal conductivity and heat trans-
fer coefficient. The equation can be evaluated on a 
desk calculator. 
The analytical predictions agree well with experi-
mental measurements of the growth of an ice layer 
when water was flowed past a cold plate. 
The method can be used to predict the (1) time 
needed to solidify plate type castings; (2) growth of 
ice covers on rivers and lakes; and (3) frozen layer 
formations in heat exchangers that tend to freeze.
Notes: 
1. Documentation is available from: 
Clearinghouse for Federal Scientific 
and Technical Information 
Springfield, Virginia 22151 
Price $3.00 
Reference: TSP69- 10321 
2. Technical questions may be directed to: 
Technology Utilization Officer 
Lewis Research Center 
21000 Brookpark Road 
Cleveland, Ohio 44135 
Reference: B69-10321 
Patent status: 
No patent action is contemplated by NASA. 
Source: J. M. Savino and R. Siegel

Lewis Research Center

(LEW-10813) 
Brief 69-10321	
Category 02


A method for predicting interfacial freezing of a liquid flowing over a cold surface

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