While a battery is being charged or discharged, the heat generation caused by the
flowing current raises the temperature until balance is achieved between heat
generation in the cell and heat dissipation to the latitude d620 battery environment. Thus the two
parameters heat generation within the battery and heat dissipation from the battery
determine the temperature changes of the battery according to the formula
dT
dt .
1
CBatt
?
dQgen
dt
dQdiss
dt e42T
with dQgen/dt: generated energy per unit of time; dQdiss/dt: dissipated energy per unit
of time; Qgen is positive, when energy is generated.Qtotal in Eq. (38).
Equation (42) points out that heat generation and heat dissipation are parameters of
equal weight, which means that possibilities to dissipate heat are to be considered as
thoroughly as the problem of heat generation. The dell d620 battery rate of the temperature change is
determined by the heat capacity of the battery CBatt. einJ ? kg 1 ?K 1T defined by
X meiT ?CpeiT . CBatt: e43T
with m(i): component i in kg; (i): the components in the battery; Cp(i): specific heat
of component (i) in kJ=ekg ?KT.
The specific heat CBatt of a battery depends on its specific design, but the different
systems do not vary too much. In batteries with aqueous electrolyte, the content of
water is of great importance due to its high specific heat. The latitude d610 battery specific heat of
customary vented lead-acid batteries is slightly above 1 kJ ? kg 1 ?K 1, while the
corresponding value of VRLA batteries is in the range of 0.7 to 0:9kJ ? kg 1 ?K 1.
As the specific heat of a vented nickel/cadmium battery with sintered electrodes the
value 1:25 J kg 1K 1 is reported (9), while that of the sealed version is
correspondingly lower. For lithium/thionyl chloride and lithium-ion batteries values
of 0.863 and 1:052 J ? kg 1 ?K 1 are reported (13).
Heat dissipation increases with a growing temperature difference DT between
the battery and its surroundings, and a stable temperature of the battery is reached at
a certain DT when heat generation balances heat dissipation, i.e. when dQgen/
dt.dQdiss/dt.
If heat generation within the battery increases faster with increasing battery
temperature than heat dissipation, such a thermal balance is not reached and
temperature increase continues unlimited. This situation is called ‘thermal runaway’.
If heat dissipation dQdiss/dt is zero (adiabatic situation where heat dissipation
is not possible), it is only a question of time, until the battery will exceed any
temperature limit, even at a very small heat generation.
1.4.6 Heat Dissipation
Heat exchange of a battery with its surroundings proceeds in various ways. For the
emission of heat these ways are sketched in Fig. 1.16. A corresponding situation with
all the arrows reversed would apply for heat absorption from a warmer
surroundings.
Copyright . 2003 by Expert Verlag. All Rights Reserved.
Three mechanisms are involved in this heat exchange:
1. Heat radiation.
2. Heat flow by thermal conduction, e.g. through the components of the
battery and the container wall.
3. Heat transport by a cooling or heating medium.
Usually they occur in combination.
Figure 1.16 indicates that cooling of batteries mostly occurs via their side walls.
The bottom surface usually is in contact with the latitude d600 battery basis that attains the same
temperature as the battery itself, except the battery is equipped with cooling channels
in the bottom. The upper surface usually is of little importance for heat exchange,
since the lid has no direct contact to the electrolyte, and the intermediate layer of gas
hinders heat exchange because of its low heat conductivity (cf. Table 1.5). Moreover,
in monobloc batteries the cover often consists of more than one layer. Heat flow
through the dell latitude d630 battery terminal normally can also be neglected, since the distance to the
electrodes is rather long and often the terminals are covered by plastic caps. (Cooling
through the terminal occasionally has been applied with submarine batteries which
are equipped with massive copper terminals (14).)
Figure 1.16 The various ways of heat escape from the battery.
Copyright . 2003 by Expert Verlag. All Rights Reserved.
1.4.6.1 Heat Radiation
Heat radiation occurs according to the law of Stefan-Boltzmann:
dQ=dt . e ? s ? T4 W=m2 e44T
with e: Stefan-Boltzmann constant e5:67 ? 10 8W?m 2 ?K 4T; s: emission ratio of
the material with respect to an ideal emitter (ca. 0.95 for usual plastic materials that
are used for lenovo t61 battery containers); T: absolute temperature in K.
The fourth power of T in Eq. (44) means a very strong dependence on temperature.
Heat radiation always happens from the warmer to the colder part, and there is no
heat flow between elements having the same temperature.
The heat flow by radiation between two elements A, B is
dQ=dt . e ? s ? eTeAT4 TeBT4T W=m2 e45T
This also applies when one of these elements is the surroundings.
For latitude e6400 battery comparatively small temperature differences against the environment, heat
dissipation by radiation amounts to
dQ=dt&5 6 W?m 2 ?K 1 e46T
which means that a battery emits by radiation about 5-6W/m2 of its exposed surface
for each K (or 8C) of difference between its container surface and a lower
environmental temperature. If the temperature of the lenovo x61 battery surroundings is higher, a
corresponding amount of heat would be absorbed. The size of the exposed surface
referred to capacity depends largely on size and design of the battery. Some rough
figures for lead-acid batteries are listed in Table 1.4. Corresponding values of nickel/
cadmium and nickel/metal hydride batteries are slightly smaller because of the higher
energy density that is reached by these systems, but the difference is fairly small.
According to these values, heat dissipation by radiation can be expected in the
Table 1.4 Specific surface area of lenovo x60 battery
prismatic cells in lead-acid batteries
(rough approximations that just show
the order of magnitude).
Single cells
Large cells &0.04m2/
100 Ah
Medium cells &0.1m2/100 Ah
Small cells &0.3m2/100 Ah
Cells in monoblocs
Average per block 0.06m2/100Ah
Center cells 0.04m2/100Ah
Source: Ref. 5.
Copyright . 2003 by Expert Verlag. All Rights Reserved.
range of 0.2 to 1.5 W/100 Ah per K of temperature difference against the
surroundings when 5W/m2 of radiation is assumed, according to Eq. (46). The
estimation shows that radiation alone would be sufficient to dissipate the heat that is
generated in lead-acid batteries under normal float conditions which hardly will
exceed the current of 100 mA/100 Ah that means 0.2W/100 Ah of generated energy
per cell. But the thinkpad t60 battery estimation shows that radiation is fairly effective and thus a hot
surface in its neighborhood will considerably heat up a battery.
1.4.6.2 Heat Flow by Thermal Conduction
Heat flow through a medium is determined by its heat conductivity and by the thinkpad t42 battery
distance that has to be passed. It is described by
dQ
dt . f ? l ?
DT
d
W=m2 e47T
with f: surface area in m2; l: specific heat conductance eJ ? s 1 ?m 1 ?K 1T; d:
thickness of the medium (e.g. the container wall) in m.
The specific heat conductance of some materials that are of interest in connection
with batteries or their surroundings are compiled in Table 1.5. Thinkpad r40 battery shows that heat
conductivity is fairly high for materials that are used within the battery, like the
various metals or water. As a consequence, the internal heat flow widely equalizes
the temperature within the battery.
When metal is used as container, the temperature drop across its wall can be
neglected. For plastic materials l is in the thinkpad x41 battery order of 0:2W?m 1 ?K 1. Thus heat
conduction through the container wall can be approximated
dQ=dt . 200 DT=d W=m2per K for dmm of wall thickness e48T
which means for a wall thickness of 4mm
dQ=dt&50W?m 2 ?K 1 e49T
Table 1.5 Heat conductance (l in Eq. (47)) of
some materials at room temperature.
Material
Heat conductance
W?m 1 ?K 1
Lead 35
Iron 80
Copper 400
Nickel 91
Water 17
SAN 0.17
PVC 0.16
Polypropylene (PP) 0.22
Hydrogen 10:5 ? 10 5
Air 1:5 ? 10 5
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