Isn't it great to see a question presented to the forum where the originator has done some engineering to get things started? My thanks.
I may have missed something but I can't see in the analysis by Sorter, et al, where there has been account of heat loss from the system in question. The implied assumption that I draw from their paper is that they've assumed heat losses to be zero. I would expect the heat loss to increase with a reduction in ambient temperature and given that your ambient appears to sit at about 10°C, then this is an issue to be wary of.
Sorter hasn't really explained the methodology used for deriving the collector area equation, which immediately piques my concern. They have also opted for an "active" system, i.e. pumped, and their analysis doesn't appear to account for this energy input and operating cost.
Unless you've chosen the same mechanical design, then you're potentially making an incorrect application of Sorter's design equation. I'm just offering a check question to you here.
I did a quick search and found the following paper by Bolaji:
Bolaji PaperNotable differences between Bolaji and Sorter:
1. Bolaji investigates a natural circulation / thermo-syphon design, i.e. "passive" system
2. Bolaji presents a transparent description of the mass and energy balance equations applied to the problem analysis
3. Sorter considers an indirect heater / Bolaji investigates direct heating
Figure 6 in Bolaji's paper shows the relationship of solar insolation upon collector efficiency. The insolation used in your spreadsheet equates to about 130W/m2, which doesn't show on figure 6 but would result in a number significantly less than 40%.
Based on this I would caution you to confirm that use of a constant 50% efficiency for you application is a valid basis.
Presumably active systems have a flatter insolation/efficiency curve but you would need to find out the detail there. Personally, I doubt whether the curve is perfectly flat.