Before building and validating the model, the feasibility of using a Peltier chip to reach the temperatures required had to be assessed using the heat transfer equations listed
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in the methods section - calculations which also help design the heat sink system. Figure 5.8 shows the TC required to achieve a range of ΔTbrain for different core thicknesses for
a total probe diameter of 2mm. In order to achieve even 4°C cooling at the probe tip, a TC of -10°C is required at the cold side of the Peltier with a 1.5mm or 1.75mm core.
Figure 5.8. Assessment of cold side temperature required to achieve various temperature drops at the probe tip for core diameters of 0.5mm to 1.75mm. A temperature drop of 4°C requires a TC of -10°C for a 1.5 or 1.75mm core.
The Comsol® model also offers total heat flux as an output via surface integration calculations. Therefore, to cool to the brain by even 4°C with a temperature of -10°C at the cold plate, it is necessary to absorb 16.97W of heat at the Peltier surface. The equations detailed in the methods section (5.1, 5.2, 5.3 and 5.4) allow the calculation of the Peltier properties Z, Sm, Rm and Km using the basic manufacturer defined
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model, it is then possible to vary the theoretical current applied to the Peltier and determine the theoretical temperature drop across the Peltier using equations 5.5 and 5.6. As current increases, so does the power of the Peltier chip and therefore the temperature drop across the device increases with a linear relationship (Fig. 5.9). With a TC of -10°C required, a ΔTTEC of approximately 40°C will be required and therefore a
current of approximately 3.5A.
Figure 5.9. Assessment of temperature difference across Peltier with varying current. With a TC of -10 required, a ΔTTEC of approximately 40°C will be required which is
within the capabilities of this Peltier.
Furthermore, it is possible to utilise the final equation to plot the resistance of the heat sink required against the Peltier current (Fig. 5.10). If the Peltier is to function with a current of 3.5A or above, a heat sink with a resistance of 0.3-0.45K/W is required, which
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is within the operating range of a fan cooled heat sink and allows further optimisation using its properties172. For this reason, other cooling systems for the hotside of the
Peltier were not investigated. Aside from thermal performance, aesthetic and functional features may necessitate the consideration of other cooling methods for clinical applications.
Figure 5.10. Assessment of heat sink resistance with varying current. A heat sink with 0.35-0.45K/W resistance is sufficient if operating at a current of 4A or above.
5.3.4 Experimental Validation
In order to reduce the number of variables and potential for error, experimental validation was carried out using an uncoated probe (Fig. 5.11). The top 3cm of the plant foam brain model was not submerged in the water to prevent splashing on the Peltier element but saturation of the foam and initial temperature of 37°C was checked for each trial.
137 Figure 5.11. Experimental Set up.
Firstly, the calculated cooling potential of the Peltier was plotted against the experimental results and exhibited similar trendlines with the model having a slope of 11.7 vs 10.2 for the observed results. It should be noted that the difference between modelled and measured ΔTTEC increases with increasing current. At 3.5A the difference
is 12.5% (Fig. 5.12).
Although the mechanical stiffness of the foam ensured that the cooling probe and the temperature probes were held in place, its dense nature made it difficult to ensure the temperature probes were in direct contact with the cooling probe. For this reason, the temperature probe was finally inserted at the top, beside the cooling probe to different depths, ensuring a consistent gap of 2mm from the cooling probe at all times. In order to compare similar outputs, the Comsol® model was also configured to draw a temperature profile for heat at this distance away from the cooling probe. Figure 5.13 shows how the move away from the probe affects the temperature profile, with up to
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10°C temperature drop as the temperature sensor moves away from the surface. This was carried out at 3 different TC to ensure the validity of the model over a range.
Figure 5.12. Peltier Current vs ΔTTEC predicted vs real results showing good prediction
of temperatures with some divergence of values at currents of 4A and higher.
By varying the current through the Peltier chip, the cold side of the Peltier was kept at temperatures comparable to those used in our model. The difference between the model and the experimental results was not significant at a TC of -10°C (Fig 5.14A). For
the models at 10°C and 0°C the temperature deviated from the model by a few degrees at most in the initial length of the probe, with identical temperature profiles for all temperatures after 3cm of probe length (Fig. 5.14B and C).
139 Figure 5.13. Comsol® model of temperature at core vs 2mm away from the surface of probe for initial temperatures of -10°C to 10°C shows a loss of up to 10°C radially at the base of the probe.
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Figure 5.14. Comsol® Model vs experimental results for temperatures 2mm from probe showing similar temperatures profiles.
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In order to incorporate the heat sink specifications into the overall probe design, a study was carried out relating the required heat sink resistance to the voltage applied to it. By increasing the voltage applied to the fan cooled heat sink, the heat removed from the hot side of the Peltier was increased, resulting in a lower Th. This results in a lower heat
sink resistance as the heat sink is working more effectively at a higher voltage and the resistance of this heat sink is between 0.34 and 0.42K/W (Fig. 5.15).
Figure 5.15. Heat sink resistance as a function of voltage. Resistance decreases as voltage increases and heat sink operates at 0.34-0.42K/W. Error bars represent the standard deviation of the average of 5 trials.