# Water Jacket Systems for Temperature Control of Petri Dish Cell Culture Chambers
## 3 Results and Discussion
### Analyzing the Effect of Petri Dish Parameters  
Next, we investigate the thermal performance of the water jacket system with respect to the diameter of the Petri dish, volume of the sample stored inside the Petri dish, material of the Petri dish, and incorporation of an integrated heater as discussed below.  
_Petri dish diameter:_ Figure 4a shows the temperature profile across the radial axis of the Petri dish when varying the diameter of the Petri dish (\(D_{Petri\,dish}\)) from 15 to 45 mm. The temperature contours across the middle cross-section of the Petri dish at various Petri dish diameters are presented in Figure S6. The amount of heat transferred into the Petri dish is proportional to the surface area of the side walls, and therefore proportional to \(D_{Petri\,dish}\). However, the amount of heat lost through the bottom and top surfaces of the Petri dish is proportional to the surface area of these surfaces and, therefore, proportional to \(D_{Petri\,dish}^{2}\). Hence, decrease of \(D_{Petri\,dish}\) reduced the ratio of heat loss to heat gain, leading to a more uniform temperature profile across the Petri dish.  
_Sample volume:_ Figure 4b presents the temperature profile when varying the volume of sample inside the Petri dish (\(V_{sample}\)) from 25% to 100%. The temperature contours at various sample volumes are presented in Figure S7. Decrease of \(V_{sample}\) reduced the height of the sample, and consequently enhanced the conductive loss through the sample. This in turn increased the temperature gradient along the radial axis of the Petri dish.  
Figure 3: Numerical characterization of the temperature profile along the bottom surface of the Petri dish with respect to various operating conditions, including (**a**) the flow rate of water recirculated through the water jacket (\(Q_{autor}\)) varied from 15 to 120 mL/min. (**b**) The temperature of the water entering the water jacket (\(T_{autor@initel}\)) varied from 15 to 45 \({}^{\circ}\)C. (**c**) The temperature of the surrounding air (\(T_{air}\)) varied from 16 to 24 \({}^{\circ}\)C. (**d**) The convective heat transfer coefficient of ambient air (\(h_{air}\)) varied from 5 to 20 W/m\({}^{2}\)K. The detailed temperature contours across the middle cross-section of the Petri dish obtained at the above conditions are presented in Figures S2-S5.  
Petri dish material:Figure 4c shows the temperature profile against the material of the Petri dish with the associated temperature contours presented in Figure S8. The higher thermal conductivity of glass compared to that of polystyrene (0.3 _vs._ 0.15 W/ mk) facilitated the conductive heat transfer across the bottom surface of the Petri dish, and consequently reduced the temperature gradient along the radial axis of the Petri dish. It should be noted that changing the material of the water jacket from aluminum to stainless steel did not change the temperature profile of the sample inside the Petri dish.  
Heater integration:Figure 4d presents the temperature profile following the integration of a heater underneath the Petri dish. The heater consisted of a 100 \(\upmu\)m thick glass substrate coated with ITO (indium tin oxide) that released 187 mW of thermal power uniformly across the bottom surface of the Petri dish with the associated temperature contour presented in Figure S9. The heater compensated the convective heat loss at the free surfaces of the Petri dish, and decreased the temperature gradient along the radial axis of the Petri dish to \(\sim\)0.4 \({}^{\circ}\)C.