The heat dissipation problem occurring in the lithium thionyl chloride cells discharged at relatively high rates under normal discharge conditions is examined. Four heat flow paths were identified, and the thermal resistances of the relating cell components along each flow path were accordingly calculated. From the thermal resistance network analysis, it was demonstrated that about 90 percent of the total heat produced within the cell should be dissipated along the radial direction in a spirally wound cell. In addition, the threshold value of the heat generation rate at which cell internal temperature could be maintained below 100 C, was calculated from total thermal resistance and found to be 2.9 W. However, these calculations were made only at the cell components' level, and the transient nature of the heat accumulation and dissipation was not considered. A simple transient model based on the lumped-heat-capacity concept was developed to predict the time-dependent cell temperature at different discharge rates. The overall objective was to examine the influence of cell design variable from the heat removal point of view under normal discharge conditions and to make recommendations to build more efficient lithium cells

Cho, Y. I.

Deligiannis, E.

Halpert, G.

English

NASA Technical Reports Server

tN87-11080
HEAT DISSIPATION .OF HIGH RATE Li-SOCI 2 PRIMARY CELLS
Young I. Cho and Gerald Halpert
Drexel University Jet Propulsion Laboratory
Philadelphia PA 19104 Pasadena CA 91109
INTRODUCTION
The present investigation is a part of a series of investigation being
carried out at JPL and Drexel University to better understand the heat
dissipation problem occurring in the lithium thionyl chloride cells
discharged at relatively high rates under normal discharge conditions.
The earlier work presented at the 168th Electrochemical Society Meeting
at Las Vegas(l) identified four heat flow paths, and the thermal
resistances of the relating cell components along each flow path were
accordingly calculated. From the thermal resistance network analysis,
it was demonstrated that about 90 percent of the total heat produced
within the cell should be dissipated along the radial direction in a
spirally wound cell.
In addition, the threshold value of the heat generation rate at which
cell internal temperature could be maintained below 100@C, was calcula-
ted from total thermal resistance and found to be 2.8 W. However, these
calculatons were made only at the cell components' level, and the trans-
ient nature of the heat accumulation and dissipation was not considered.
In the present study, a simple transient model based on the lumped-heat-
capacity concept has been developed to predict the time-dependent cell
temperature at different discharge rates. The overall objectives of the
study was to examine the influence of cell design variables from the
heat removal point of view under normal discharge conditions and to make
recommendations to build more efficient lithium cells.
TRANSIENT ANALYSIS OF HEAT DISSIPATION FROM THE CELL
In the present investigation, the co-called lumped-heat-capacity method
has been used instead of solving the energy equation in the cylindrical
coordinates system. As demonstrated in our previous study(l),
approximately 90 percent of thermal resistance particularly along the
radial direction occurs from the outer wall of the case can to the
environment, where heat is removed from the cell by natural
convection. In other words, the thermal resistances of cell components
along the radial as well as axial direction within the cell are so
small that heat will be diffused out quickly throughout the cell,
reaching the case can without much delay. This also implies that the
internal temperature of the cell may be assumed uniform radially and
axially and equal to the cell wall temperature as a first-order
approximation. Hence, it is an ideal problem to apply the
lumped-heat-capacity concept to estimate the transient temperature of
the cell. Of note is that a more complicated modelling work to take
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107
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into account radial and axial temperature variation is being developed
and will be reported in the future.
The governing transient heat balance equation becomes
dT(t) + hA [T(t) - T_] (I)
= pVC dt
where h is the heat transfer coefficient from the cell surface to the
environment and pVC is the so-called thermal mass of the cell.
Physically, the first term in the right hand side represents the amount
of heat stored within the cell and the second term that dissipated into
the environment. Since the amount of heat to be dissipated out by
natural convection depends on the temperature difference between the
wall and the environment, the heat transfer coefficient h is a function
of the cell temperature accordingly. However, in the present study, h
is assumed to be constant for the mathematical simplicity.
Using the initial boundary condition, T = T= at t = O, the solution
of the above equation becomes
T(t) - T_ = _ [i - e
hA
] (2)
where _ is the heat generation rate to be determined by the discharge
rate of the cell. Since hA is the inverse of the thermal resistance
RSV between the case can and the environment, it becomes
hA __ i - 0.0352 W/°C (3)
RSV
Note that the heat transfer coefficient h for the present D-size cell
becomes 4.4 W/m2°C, which is a typical value (2) for the case of
heat dissipation to the room temperature by natural convection. Also
note that for the adiabatic boundary condition which occurs in many
military applications of the lithium cells, the second term of the
right hand side in Eq. (i) disappears and the corresponding solution
becomes
T(t) - T_ - p_C t (4)
As shown in Eqs. (2) and (4), the thermal mass of the cell PVC is an
important parameter in the calculation of the transient cell
temperature T. Therefore, the thermal mass of each cell component was
calculated based on the JPL's first generation D-size cell
specification and shown in Table I. Values of mass of each cell
component, pV, are the data experimentally measured at JPL and the
}_ 3¸.r!!¸
108
specific heats of lithium, nickel and stainless steel were taken from
Ref. (3). The specific heat of the electrolyte (i.e., 1.8 M LiAICI 4
in SOC12, received from Lithium Corporation of America, Lithcoa) was
estimated from the work by Venkatasetty(4) and founded to be
1215 J/KgK.
Table 1 shows that about 54 percent of the total thermal mass can be
attributed to the electrolyte at the beginning of the discharge. Of
note is that near the end of normal discharge, i.e., 80 percent DOD,
approximately half of the electrolyte is consumed, thus reducing the
thermal mass of the cell correspondingly. In this regard, of note is
that a flooded cell may be safer than a starved cell from the heat
transfer point of view since the percentage loss of thermal mass in the
flooded cell due to the electrolyte consumption is relatively small
compared to the case of the starved cell. However, in the present
study, the time-dependent effect of the electrolyte consumption was not
considered. A complete model to take into account the transient
nature of the thermal mass of the electrolyte as well as the heat
transfer coefficient h will be developed and reported in the future.
The cell temperature was predicted from Eq. (2) in which the heat
generation rate, _, was calculated from the discharge characteristics
curve experimentally obtained at C/2, i.e., see Fig. i. The resulting
cell temperature vs. time is shown in Fig. 2, which also gives the
percentage depth of discharge along the abscissa. This figure clearly
demonstrates that the cell temperature increases gradually to IO0°C for
the first 95 min and then suddenly jumps to about 200 250°C within the
next 15 min. The horizontal dashed line indicates the maximum
allowable cell temperature of IO0°C, which is below the melting points
of cell components such as sulfur (I12°C) and lithium (179°C). The
corresponding DOD to the cell temperature of 100°C was approximately
80 percent with the discharge rate of C/2. This indicates that the
present cell may be discharged safely at C/2 rate up to 80 percent
DOD. Although the time-dependent temperature prediction with the
lumped-heat-capacity method was carried out with the constant values of
the heat transfer coefficient h and the initial thermal mass pVC, the
resulting temperature showed the actual trend observed in the test of
the lithium cell. An IBM-PC based computer code to calculate thermal
resistance of cell components and to predict the transient cell
temperature including the effect of electrolyte consumption and the
temperature-dependent heat transfer coefficient h will be developed and
reported accordingly with a detail comparison with experimental data.
FIN ANALYSIS
When the lithium cells are in contact with the environment during the
normal discharge, one way to improve heat dissipation from the cell is
to add fins around the cell. In so doing, it is important to recognize
the conditions for which the finned surface has advantages over the
unfinned surfaces. Particularly for aerospace applications, the weight
109
added, the space needed and the cost of adding fins are of the greatest
importance. Also note that the installation of fins on a heat transfer
surface will not necessarily increase the heat transfer rate. In
general, if the value of 2k/ht is larger than 5, it is advantageous to
use fins around the heat transfer surface. Here, k is the thermal
conductivity of a fin material, h is the heat transfer coefficient
between the fin surface and the environment, and t is the fin thickness.
For the _resent application, h is relatively small, being approximately
4 7 W/mZ°C and k is large, being 16.3 W/m°C for stainless steel and
204 W/m°C for aluminum. Hence, it is clearly advantageous to install
fins around the cell.
The proposed fin dimensions in the present study as shown in Fig. 3 are
as follows; t(thickness) = 0.04 cm, L(length) = 0.44 cm and H(height) =
5.69 cm same as the height of the D-size cell. The proposed total
number of fins is 32. Therefore, the value of 2k/ht for stainless
steel fins becomes 18,500, which demonstrates the usefulness of
installation of these types of fins. A valid method of evaluating fin
performance is to compare heat transfer with the fin to that which
would be obtained without the fin. The ratio of the two for a single
fin becomes
<_> with fin _ tanh mL (5)
<_> without fin V_-AIkP
where < > indicates a value for a single fin and m is _hP/kA. Of
note is that when the value of L/(t/2) is equal to or larger than
unity, the fin is considered long, in which the heat loss from the fin
end surface is negligibly small. In the present study, the value of
L/(t/2) becomes 285, which is far beyond the threshold value of one.
Hence, the simple solution, Eq. (5), which was derived for the case
with an insulated fin end, is valid for the present analysis. Applying
the proposed fin dimensions, the ratio in Eq. (5) for a single fin was
calculated to be
<_> with fin
<_> without fin
= 21.65 for a stainless steel fin (6)
Next, the total heat dissipated from the cell with 32 fins was
calculated and compared with that without fins. The ratio of the two
becomes
total heat dissipated from the cell with 32 fins
= 3.4 (7)
total heat dissipated without fins
This indicates that the heat transfer from the cell could be enhanced
by a factor of 3.4 when compared with that without fins. This implies
that the thermal resistance will be decreased to the one-third of the
ii0
present value of 28.4 °C/W. This is a considerable improvement in the
heat dissipation from the lithium cell when heat is removed from the
cell to the environment by natural convection.
Use of aluminum (k = 204 W/m°C) or copper (k = 385 W/m°C) as a fin
material was also examined to see if those materials may further
increase the heat dissipation from the cell. However, the fins
considered in the present study are too short to show any improvement
over the fins made with stainless steel (k = 16.3 W/m°C). For
reference, the ratio in Eq. (6) for copper fins was found to be 21.96.
Also, when the thickness of fins is doubled to 0.08 cm, the
corresponding ratio in Eq. (7) was calculated to be 3.35. Therefore,
the heat transfer enhancement with thicker fins (i.e., t = 0.08 cm) is
essentially the same that with thinner fins (i.e., t = 0.04 cm).
SUMMARY AND CONCLUSIONS
A simple transient model to predict the time-dependent cell temperature
was developed based on the lumped-heat-capacity method. The transient
cell temperature predicted from the model for the case of C/2 discharge
rate with the JPL's D-size cell indicated a gradual increase of the
cell temperature for the first 95 min. Then, for the next 15 min,
there was a sharp increase of the cell temperature to about 200_250°C,
as was observed in many of experimental test results. This suggests
that the present cell may be discharged safely at C/2 discharge rate up
to 80 percent DOD while the cell temperature remains below 100°C.
As a practical way of the heat transfer enhancement, the feasibility of
installing fins was considered. With the proposed fins in the present
study, it was demonstrated that about three times more heat could be
removed from the cell. Additionally, the use of aluminum or copper
fins, and thicker fins than the present ones was also discussed.
As a final remark, the present analysis is based on the assumption that
the cell is in contact with air. Therefore, in some of aerospace
applictions of these cells where there is no air, the heat dissipation
analysis based on the radiation heat transfer should be carried out.
111
REFERENCES
i. Y. Cho, S. Subbarao, J.J. Rowlette and G. Halpert, Thermal
assessment of high rate Li-SOCI 2 primary cells, presented at the
168th Electrochemical Society Meeting, Las Vegas, Oct. 1985.
(Extended Abstracts, ,Vol. 85-2, pp. 169-170).
2. J.P Holman, "Heat Transfer," McGraw-Hill, New York (1981).
3. Handbook of Tables for Applied Engineering Science, R.E Bolz and
G.L. Tuve, Editors, CRC, Cleveland (1970).
4. H.V. Venkatasetty, Final Report to Naval Ocean Systems Center,
E47992, Dec. (1982).
112
Table 1. THERMAL MASS OF CELL COMPONENTS
pVC
(w.s/*c) %
Lithium
Nickel
Stainless Steel
Electrolyte
Others
19.5
6.7
19.2
53.0
0
20
6.8
20
54
0
Total 98.4 100%
113
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C,/2 (5 AMP) DISCHARGE RATE
I i I I
20 40 60 80 100 12(
J i I J I i I J I J I
0 20 40 60 80 100
100°C
TIME (m|n)
DOD (%)
Figure 2. CELL TEMPERATURE PREDICTION FROM THE TRANSIENT MODEL, EQ. (1)
115
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116


Heat dissipation of high rate Li-SOCl sub 2 primary cells

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