It's a big assumption. Is it entirely consistent with the observed trend of inlet water temperature?
Yes, indeed, very big. And IMO is entirely consistent with the experimental evidences and the outcomes of the above model.
I called it "assumption", but I should have used "deduction", considering the clear evidences in favor of a water stopping. Not only because of the typical heating trend of Tin, which clearly indicates an asymptotic progressive warming toward Tamb, but also because it starts just when Tout begins to rise again.
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For example, what could have caused it to decline at an apparently accelerating pace before the water flow got interrupted?
I don't think that the decline phase can compromise the significance of the rising one. But your question is intriguing, so I tried to imagine a possible explanation. Here is my best guess.
In the calorimetric report, we can read: "Before igniting the reactor the water flux was set and measured by collecting, and then weighting, an amount of water in a container in a given time. The measured flux was of 168 +/- 2 g in 45 +/- 0.1 s."
The phrase "the water flux was set" suggests that there was a precise level of water flux to be set. In my opinion, this level was the flow that should have given a power out of 10 kW, assuming dry steam at the outlet. Considering a delta T of 85°C, as indicated in the report, and the evaporation entalpy of 2272 J/g, each g/s of water flux would have been equivalent to: 85 x 4,185 + 2272 = 2628 W/(g/s). Therefore a power of 10 kW would have required a water flux of 3,805 g/s. So, it was first necessary to open the water tap as much as necessary to get that flux, at the specific pressure of the water system at that time.
Consequently, after the data acquisition system was turned on, the water tap was slightly opened and held in this position for a few minutes, until the water has started to escape from the end of the outlet tube. At that point, the water flux was measured by weighting the water poured into a container over a given period of time. If the weight was significantly lower than the target value, the handle of the water tap was rotated by a fixed angle, the container empted, and all the operations repeated.
This way of working would also explain the reason why the time base used to fill the container was set to the strange and unusual value of 45 s. I suspect that a normal watch was used to measure time, and that a time base of 45 s would have allowed to complete a measuring step – filling, weighting, pouring and rotating - in a complete turn of the second's hand, facilitating in this way the control of the timing.
Thus, it was established that the target value for the water mass was 3.805 x 45 = 171 g in 45 s. When the fairly close weigh of 168 g was measured, it was decided to switch on the heaters. It happened at t=7s of your graphs. Thereafter, the curve of Tin has two more downward steps with about the same length followed by a much longer lowest level, which is the expected trend for a cooling down at a constant flow.
So, this setup procedure would explain both the accelerating pace of the downwards steps up to t=7s, and the subsequent decelerating pace.
Is it reasonable for you? Any other objection?
Going a little further. After switching on, it was expected that temperatures would rise on the PC screen, but it didn't happen, probably because of the wrong setting of the acquisition timestep. After a while, the time step was set at 10 s, and the first real point was plotted on the T graph.
If you have time and possibility, it would be useful to have a graph with the experimental data (power in and temperatures) plotted in function of the real local time, and starting from the presumed time when the data acquisition system was switched on, with these actions marked on it.
