3.1. Heat generation within a single cell

The thermal characteristics of a Li-ion battery cell are first investigated using Eqs. (1)–(19), which form thermal-electrochemical coupled model. The cell used in these calculations has an electrolyte consisting of zinc and lithium salts dissolved in water. When the battery is fully charged, the anode consists of nonporous zinc and the cathode of porous Mn2O4. It is important to note that some of the electrochemical calculations are strongly dependent on coefficients, which are in turn strongly dependent of experimental results. For example, for the electrolyte just described, the specific conductivity Eq. (11) of the electrolyte is a function of temperature and the concentration of the electrolyte in the liquid phase, and so the ionic conductivity, κ<sup>i</sup> had to be determined by experiment, the results of which are summarised in Figure 4.

Figure 4. Ionic conductivity of electrolyte consisting of a ZnCl2 and LiCl aqueous solution.

The effect of using different current rates during discharge of the battery cell is illustrated in Figure 5. Here temperature on the cell surface is calculated against the depth of discharge (DOD), which indicates the state of discharge of the battery cell starting at 100% fully charged. In these calculations, DOD was calculated as time ∗ <sup>C</sup> rate <sup>3600</sup> and the heat transfer coefficient h was set at 1.0 Wm�<sup>2</sup> K�<sup>1</sup> . As would be expected, the cell surface gets hotter as the discharge current rate increases. There is a 'kink' in the curve at lower current rates, which is thought to be due to an interaction between the ohmic and reversible heat in the energy balance equation.

Also calculated were the profiles of cell surface temperatures over a long time of discharge. Two limiting cases, that is, adiabatic and isothermal were used as the boundaries for this study with different heat transfer coefficients used for the intervening calculations, as shown in Figure 6. It can be seen that the heat transfer coefficient 1.0 W�<sup>2</sup> K�<sup>1</sup> gives a reasonable result and keeps the battery cell well within the desired operating range, while the 0.1 W�<sup>2</sup> K�<sup>1</sup> setting allows the battery cell wall temperature to reach the upper region of the desired range.

#### 3.2. Cooling the battery module

In this part of the study, the temperature history of the battery module was modelled with ambient conditions (T∞Þ set at 293.15 K, and each of the cells sets initially at Tinit¼313:15 K and then at Tinit¼349:15 K. This part of the calculations is important to the design process in that, in addition to testing, if the chosen geometry parameters are suitable, it also gives an indication concerning the selection of a suitable pump and heater/refrigeration unit. Typical velocity contours for the liquid coolant are shown in Figure 7. The important part here is that heat can be removed from the coolant in the plenum chamber efficiently. From Figure 7, it can be seen that there is slow moving water adjacent to the heating/refrigeration unit, and hence there is sufficient time for dissipation of heat.

Figure 6. Cell surface temperature for different cooling conditions.

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Figure 7. Velocity contours, uin ¼ 0:01 m/s, Tin ¼ 293:15 K, rinner ¼ 10 mm, T<sup>∞</sup> ¼ 293:15 K.

Figure 5. Cell surface temperature during discharge at different current rates.

Figure 6. Cell surface temperature for different cooling conditions.

The effect of using different current rates during discharge of the battery cell is illustrated in Figure 5. Here temperature on the cell surface is calculated against the depth of discharge (DOD), which indicates the state of discharge of the battery cell starting at 100% fully charged.

rate increases. There is a 'kink' in the curve at lower current rates, which is thought to be due to

Also calculated were the profiles of cell surface temperatures over a long time of discharge. Two limiting cases, that is, adiabatic and isothermal were used as the boundaries for this study with different heat transfer coefficients used for the intervening calculations, as shown in Figure 6. It can be seen that the heat transfer coefficient 1.0 W�<sup>2</sup> K�<sup>1</sup> gives a reasonable result and keeps the battery cell well within the desired operating range, while the 0.1 W�<sup>2</sup> K�<sup>1</sup> setting allows the battery cell wall temperature to reach the upper region of the desired range.

In this part of the study, the temperature history of the battery module was modelled with ambient conditions (T∞Þ set at 293.15 K, and each of the cells sets initially at Tinit¼313:15 K and then at Tinit¼349:15 K. This part of the calculations is important to the design process in that, in addition to testing, if the chosen geometry parameters are suitable, it also gives an indication concerning the selection of a suitable pump and heater/refrigeration unit. Typical velocity contours for the liquid coolant are shown in Figure 7. The important part here is that heat can be removed from the coolant in the plenum chamber efficiently. From Figure 7, it can be seen that there is slow moving water adjacent to the heating/refrigeration unit, and hence there is

an interaction between the ohmic and reversible heat in the energy balance equation.

138 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

. As would be expected, the cell surface gets hotter as the discharge current

<sup>3600</sup> and the heat transfer coefficient h was

In these calculations, DOD was calculated as time ∗ <sup>C</sup> rate

set at 1.0 Wm�<sup>2</sup> K�<sup>1</sup>

3.2. Cooling the battery module

sufficient time for dissipation of heat.

Figure 5. Cell surface temperature during discharge at different current rates.

Figure 7. Velocity contours, uin ¼ 0:01 m/s, Tin ¼ 293:15 K, rinner ¼ 10 mm, T<sup>∞</sup> ¼ 293:15 K.

Several tests were conducted, where the battery module was cooled to find appropriate values for the parameters, uin and the optimum number of helix coil turns. Figure 8 shows temperature values obtained at the centre of a cell versus time during cooling. The figure shows results for two initial cell temperatures, that is, 313.15 and 349.15 K, and the temperature profiles were obtained for different inlet velocities to the helix tube ranging from 0.005 to 0.1 m/s. It was found that when using an inlet velocity of 0.005 m/s, the cell temperature did not reach an acceptable temperature over what was regarded as a reasonable time. When the inlet velocity was increased to 0.01 m/s, acceptable temperatures were calculated after 80 and 20 s for the higher and lower initial temperatures, respectively. With the much higher inlet velocity of coolant to the helix pipe, that is, 0.1 m/s, there was a definite faster reduction in temperature. However, this faster velocity has design implications in that more powerful pumps together with a greater danger of coolant leakage make use of this inlet velocity value less attractive. Therefore, it was decided to continue the study with uin ¼ 0:01 m/s. It is also noticeable from Figure 8 that as the initial temperature of the cells was reduced, increasing the velocity of the coolant through the pipe had much less effect on the cooling rate. This could mean that, although the coolant at higher velocity had more capacity to carry heat energy away from the battery pack, the temperature gradient between solid helix pipe and water was no longer sufficient to drive heat energy from solid to liquid effectively. This could possibly be due to the complex nature of the flow within the helix tube. Inside the tube, the flow is stretched from the inner wall, where most of the heat energy enters the liquid towards the outer wall due to centrifugal forces. Secondary flow also results due to the centrifugal forces. This aspect of the design needs further research.

stage and also the integrity of the structure may suffer. If the number of coils is too small, then cooling of the battery to its ideal operating temperature range may become unacceptable. As can be seen from Figure 9, there is a big advantage to the cooling system when increasing the number of turns for 5 to say 15, but after that, the cooling effect of increasing the number of turns is greatly diminished. Increasing the number of turns is equal to lengthening the heat transfer path. According to Figure 9, as the number of turns increases, the amount of the heat transfer coefficient decreases significantly and after, say, 15 turns, it remains almost constant. The Prandtl number for water is larger than the one which would make the thermal entrance greater than the hydraulic entrance length. This means that after about 15 turns the thermal entrance length has been passed. An optimum number of turns appear to be around 10. The rest of this study continues with the number of helix turns in the aluminium block to be 10.

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It is important for the lengthening of battery cell life and the enhancement of charging and discharging performance that uniformity of temperature is achieved throughout each cell, in addition to uniformity of cell temperatures across the cells within the battery module. To confirm that uniformity of temperature could be achieved across a single cell lodged within the battery module, temperature profiles were calculated in the radial direction through the battery module. As can be seen from Figure 10, where the radius at 0 is the battery module centre and radius at 130 mm is the outer wall of the module, the temperature profiles gradually move from an initial profile distorted by the hot cell to an acceptable final uniform distribution

Another series of tests were conducted on the battery module which had, in addition to initial temperatures of 313.15 and 349.15 K, an internal heat source for each cell of either 0.25, 0.5 or 1 W. Results for the module with each of the cells having internal heat sources of 1 W are

Figure 9. Temperature values at the centre of a cell for different number of helix coil turn after 50 s. Here, Tinit ¼ 313:15 K,

uin ¼ 0:01 m/s, rinner ¼ 10 mm, T<sup>∞</sup> ¼ 293:15 K, Tin ¼ 293:15 K.

after about 15 s.

It is important to know the optimum number of turns the helix coil makes for a number of reasons. One is that if too many coils are used, then more expense occurs in the manufacturing

Figure 8. Temperature cooling profiles versus time at the centre of a cell for different initial cell temperatures and fluid velocities in the helix tube. Here rinner ¼ 10 mm, T<sup>∞</sup> ¼ 293:15 K and Tin ¼ 293:15 K.

stage and also the integrity of the structure may suffer. If the number of coils is too small, then cooling of the battery to its ideal operating temperature range may become unacceptable. As can be seen from Figure 9, there is a big advantage to the cooling system when increasing the number of turns for 5 to say 15, but after that, the cooling effect of increasing the number of turns is greatly diminished. Increasing the number of turns is equal to lengthening the heat transfer path. According to Figure 9, as the number of turns increases, the amount of the heat transfer coefficient decreases significantly and after, say, 15 turns, it remains almost constant. The Prandtl number for water is larger than the one which would make the thermal entrance greater than the hydraulic entrance length. This means that after about 15 turns the thermal entrance length has been passed. An optimum number of turns appear to be around 10. The rest of this study continues with the number of helix turns in the aluminium block to be 10.

Several tests were conducted, where the battery module was cooled to find appropriate values for the parameters, uin and the optimum number of helix coil turns. Figure 8 shows temperature values obtained at the centre of a cell versus time during cooling. The figure shows results for two initial cell temperatures, that is, 313.15 and 349.15 K, and the temperature profiles were obtained for different inlet velocities to the helix tube ranging from 0.005 to 0.1 m/s. It was found that when using an inlet velocity of 0.005 m/s, the cell temperature did not reach an acceptable temperature over what was regarded as a reasonable time. When the inlet velocity was increased to 0.01 m/s, acceptable temperatures were calculated after 80 and 20 s for the higher and lower initial temperatures, respectively. With the much higher inlet velocity of coolant to the helix pipe, that is, 0.1 m/s, there was a definite faster reduction in temperature. However, this faster velocity has design implications in that more powerful pumps together with a greater danger of coolant leakage make use of this inlet velocity value less attractive. Therefore, it was decided to continue the study with uin ¼ 0:01 m/s. It is also noticeable from Figure 8 that as the initial temperature of the cells was reduced, increasing the velocity of the coolant through the pipe had much less effect on the cooling rate. This could mean that, although the coolant at higher velocity had more capacity to carry heat energy away from the battery pack, the temperature gradient between solid helix pipe and water was no longer sufficient to drive heat energy from solid to liquid effectively. This could possibly be due to the complex nature of the flow within the helix tube. Inside the tube, the flow is stretched from the inner wall, where most of the heat energy enters the liquid towards the outer wall due to centrifugal forces. Secondary flow also results due to the centrifugal forces. This aspect of the

140 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

It is important to know the optimum number of turns the helix coil makes for a number of reasons. One is that if too many coils are used, then more expense occurs in the manufacturing

Figure 8. Temperature cooling profiles versus time at the centre of a cell for different initial cell temperatures and fluid

velocities in the helix tube. Here rinner ¼ 10 mm, T<sup>∞</sup> ¼ 293:15 K and Tin ¼ 293:15 K.

design needs further research.

It is important for the lengthening of battery cell life and the enhancement of charging and discharging performance that uniformity of temperature is achieved throughout each cell, in addition to uniformity of cell temperatures across the cells within the battery module. To confirm that uniformity of temperature could be achieved across a single cell lodged within the battery module, temperature profiles were calculated in the radial direction through the battery module. As can be seen from Figure 10, where the radius at 0 is the battery module centre and radius at 130 mm is the outer wall of the module, the temperature profiles gradually move from an initial profile distorted by the hot cell to an acceptable final uniform distribution after about 15 s.

Another series of tests were conducted on the battery module which had, in addition to initial temperatures of 313.15 and 349.15 K, an internal heat source for each cell of either 0.25, 0.5 or 1 W. Results for the module with each of the cells having internal heat sources of 1 W are

Figure 9. Temperature values at the centre of a cell for different number of helix coil turn after 50 s. Here, Tinit ¼ 313:15 K, uin ¼ 0:01 m/s, rinner ¼ 10 mm, T<sup>∞</sup> ¼ 293:15 K, Tin ¼ 293:15 K.

shown in Figures 11 and 12. As with the previous tests, what was important was the control of temperature between acceptable limits and a good uniformity of temperature across each cell.

It can be seen from Figures 11 and 12 that in the early stages of cooling, non-uniformity was found, but after, say, 1 min, uniformity was acceptable throughout each cell, and after 2 min, each cell was within the desired operating temperature limits (Note: each sub-figure has its

Figure 10. Temperature profiles in the radial direction for Tinit ¼ 313:15 K, uin ¼ 0:01 m/s, rinner ¼ 10 mm, T<sup>∞</sup> ¼ 293:15 K, Tin ¼ 293:15 K.

own temperature scale). At times greater than 2 min, the heat loss to the atmosphere was slightly higher than heat production within the cells, even at 1 W, so reducing the need for further cooling. In the propose prototype, the temperature would be monitored using a ther-

Figure 12. Plan view of temperature profiles for Tinit =313.15 K, uin ¼ 0:01m=s, rinner ¼ 10 mm, Tin ¼ 293:15 K, and heat

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Preliminary results useful to the final design of a prototype battery module have been produced. The values found for the important parameters help in confirming the chosen geometry, and give indications of necessary pump and heating/refrigeration specifications needed when assembling

mostat, and further cooling would ensue intermittently as necessary.

4. Conclusion(s)

source within each cell of 1 W:

Figure 11. Front view of temperature profiles for Tinit =313.15 K, uin ¼ 0:01m=s, rinner ¼ 10 mm, Tin ¼ 293:15 K, and heat source within each cell of 1 W:

Figure 12. Plan view of temperature profiles for Tinit =313.15 K, uin ¼ 0:01m=s, rinner ¼ 10 mm, Tin ¼ 293:15 K, and heat source within each cell of 1 W:

own temperature scale). At times greater than 2 min, the heat loss to the atmosphere was slightly higher than heat production within the cells, even at 1 W, so reducing the need for further cooling. In the propose prototype, the temperature would be monitored using a thermostat, and further cooling would ensue intermittently as necessary.
