# Water Jacket Systems for Temperature Control of Petri Dish Cell Culture Chambers
## 3 Results and Discussion
### Thermal Analysis of the Water Jacket under Transient Conditions  
We also investigated the thermal performance of the water jacket system under transient conditions. The inlet water temperature was increased from 39 to 48.5 \({}^{\circ}\)C to raise the sample temperature at the side walls from 37 to 45 \({}^{\circ}\)C.  
An infrared thermal imaging camera was utilized to monitor the temperature distribution at the top surface of the water jacket system over a period of 30 min. Supplementary Movie 1 presents the transient temperatures over the first 15 min of the process. Figure 7a presents the experimental  
Figure 6: Comparison of temperature gradients along the bottom surface of the Petri dish under different conditions, obtained by numerical simulations. The reference conditions presented in Figure 2 are shown with * symbol. (**a**) Flow rate of water recirculating through the water jacket (\(Q_{water}\)). (**b**) Temperature of water entering the water jacket (\(T_{water}\)). (**c**) Ambient temperature (\(T_{air}\)). (**d**) Convective coefficient of ambient air (\(h_{air}\)). (**e**) Diameter of Petri dish (\(D_{Petri\,dish}\)). (**f**) Sample volume stored in Petri dish (\(V_{sample}\)). (**g**) Thermal conductivity of Petri dish by replacing polystyrene with glass. (**h**) Placing a heater element underneath the Petri dish. (**i**) Placing the water jacket system on a microscope stage. (**j**) Thermal conductivity of the gap between the water jacket and the Petri dish by inserting a rubber washer. (**k**) Covering the Petri dish with a polystyrene lid. (**l**) Changing the geometry of the water jacket from circular to a square or semi-circular configuration. temperature contours at four snapshots, corresponding to 0.5, 2, 4 and 15 min. Our measurements revealed the rapid temperature change of the sample in the first few minutes of the process, which can be clearly seen by comparing the size of the cold region at the middle of the Petri dish that is colored in purple. The system reached its steady-state conditions within \(\sim\)25 min. Figure 7b shows the temperature contours of the system 0.5, 5, 15, and 25 min after the inlet water temperature was increased. Simulations revealed that the temperature of the water recirculating through the water jacket reaches steady-state conditions in less than 1 min due to the dominance of forced convection. In contrast, the temperature of the sample inside the Petri dish reached steady-state conditions in \(>\)25 min due to dominance of conduction. The detailed temperature contours from 0 to 35 min are presented in Figure S15. Figure 7c compares the dynamic temperature profiles along the radial axis of the Petri dish at different time steps ranging from 0 to 35 min before the entire system reached steady-state conditions. The simulations revealed that the rate of temperature change reduces toward the end of the process, which is in line with our experiments. For example, while the middle region of the Petri dish experienced a temperature rise of \(\sim\)5.5 \({}^{\circ}\)C from 0 to 15 min, it only experienced a temperature rise of \(\sim\)1 \({}^{\circ}\)C from 15 to 35 min. Figure 7d further investigates the temporal temperature changes at the three representative locations of the Petri dish, including the middle, quarter, and sidewall axes, as shown in Figure 7c. The sidewall region, influenced by convection heat exchange through the sidewalls of the Petri dish, experienced a relatively quick temperature rise. Alternatively, the middle region, influenced by conductive heat exchange, experienced a relatively slow temperature rise. The quarter region, although symmetrically located between the sidewall and middle regions, was more influenced by the conduction mechanism.