Thermodynamics of an Arctic greenhouse?

[Jefffff]

For a business project, I'm looking into the viability of a greenhouse situated in Canada's far northern town of Iqaluit. The problem is how to mathematically simulate the internal air temperature of the greenhouse. What I already have are detailed 3D renderings of the greenhouse as well as all materials with their corresponding thermodynamic values such as K-values etc. I also have climate data that shows the approximate intensity of solar radiation in Iqaluit, angles of sunlight throughout the day and hourly temperature data. I also have data for the required environment for certain crops to thrive, such as humidity, required sunlight, temperature fluctuations, pH, etc.

What make this greenhouse investigation unique is that the greenhouse is a much smaller affordable design that is meant to grow a small supplementary source of fresh produce for low-income families which often suffer from food insecurity in northern towns such as Iqaluit due to prohibitively high costs for fresh produce. We would also like to strive for simplistic, mechanical systems that are easier to maintain and less prone to failure. A major concern of the group as of now is by how much could the internal air temperature plummet by at night? The goal in mind is to use the information we have so far to determine:

1) Is it possible to grow vegetables such as leafy greens within the current design WITHOUT an external power source other than purely sunlight? (A greenhouse that does not require electric heating is a major goal) How does the internal air temperature vary with the current design?

2) In the case that the current design is not sufficient for healthy crop growth, what modifications are necessary? (Many potential solutions have been considered)

i) Have a solar powered heater that charges through the day and intermittently provides heat through the night.

ii) Greatly increase thermal insulation surrounding the greenhouse through the use of a thick air-inflated wrap that surrounds the entire structure in addition to thicker poly-carbonate panels for construction.

iii) Use a setup of concave reflective panels surrounding the greenhouse to increase the amount of heat collected during the day.

I have already done some calculations but my numbers ended up far off. Equations I have worked with so far are Q = mcΔT, Q/t = (A) (ΔT) / (Thermal Heat Transfer Coefficient).

I think the problem demands looking at every single material and also examining the characteristics of the air inside as an ideal gas, as well as the poly-carbonate and it's emissivity/albedo (black body) characteristics. Any steps or hints in the right direction with equations or methods of calculation would be greatly appreciated!

 

[Bystander]

detailed 3D renderings

 

[sophiecentaur]

I think that cost-benefit analysis is what's required here. It is possible to use the available solar heat and 'store' it for some length of time. But the cost would be proportionally high when the temperature differences in winter are an order of magnitude greater than in temperate regions and the sunless times would dominate.
Back of a fag packet calculation is more useful at this stage than detailed renderings.
u values are available for most construction materials and so are the transmission characteristics of the various forms of glazing. It would not be hard to work out how much energy would be admitted over the year and to work out how much heat would be lost per day when the outside temperature is at, say -50°C (or whatever you choose). A 'business project' needs to earn you money so you need 'detailed performance' figures before deciding what it's going to look like'. What temperature do you need inside and for how long. Which months do you want it to operate for? At this stage, your question is a bit 'how long is a piece of string'.

 

[anorlunda]

I don't think there is much unique about your task. My son worked selling greenhouse supplies in Fairbanks Alaska, which in latitude and climate probably approximates your task. My point is that there is a wealth of real life experience on your subject.

I suggest that you arrange a visit to University of Alaska at Fairbanks as a starting point rather than starting cold. (Pun intended)

Edit: Also check out greenhouses in Kiruna Sweden, 68.7 degrees north.