Heating of the Battery and Heat Capacity

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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