Heating a small greenhouse - heat loss

[Appiani]

I have to build a small green house and to calculate if one heating wire is enough (or even too much...)
Just for my curiosity I would like to understand the physics implied in this.
The starting point is the desired dimensions: two modules of greenhouse with the following dimensions:
60 cm height
50 cm width
50 cm depth
I bought a heated wire and thermostat
https://www.amazon.it/gp/product/B00JFSPIS2/

How do you calculate exactly how big the greenhouse should , how powerful the wire should be, how much is the heat loss?
Thank you

 

[russ_watters]

You can describe your greenhouse's windows to google and ask for an insulation value (U or R: U=1/R). Then use the simple equation Q=UAΔT

 

[stockzahn]

It's not easy to give a general answer to your question. But basically you have to provide as much (heating) power to your green house to compensate the heat losses to the ambiance.

$$P_{el} = \dot{Q}_{loss}$$

The electrical power $P_{el}$ consumed by the wire corresponds to heating power (resistive heating) - that's easy. However, to calculate the heat losses $\dot{Q}_{loss}$ you need to define/know several parameters, e.g. temperature difference to ambiance, area and material of the green house walls, position of the green house (to account for wind, sun and rain) etc. Of course the ambient condition change (warm days with lots of energy from the sun, clear nights with high heat losses due to radiation, strong winds, ...).

Probably you should start by deciding where to put the green house. If you've already chosen a place, you have to make assumptions regarding the extreme ambient conditions, calculate the heat losses depending on the required temperature level in the green house to find the needed electrical power. If you've several locations you could put the green house, then try to choose one, where the difference of these extreme ambient conditions are small - then you can decrease the electrical power.

Of course you also need a first idea of the size and the materials the green house will be made of.

 

[sophiecentaur]

You can describe your greenhouse's windows to google and ask for an insulation value (U or R: U=1/R). Then use the simple equation Q=UAΔT

I tried doing it that way when estimating the heating requirements for a house, several years ago. I then discovered that the air exchange can easily dominate the heating load. I guess a hermetically sealed greenhouse may be a bit easier to achieve but airflow will be relevant in practice.
Actually, if the greenhouse actually exists, it would be fairly easy to do some measurements and get a good ball park figure. Take a relatively powerful heater (say 2kW) and heat the greenhouse to, say 20°C or more above ambient temperature. Measure the temperature as it cools, every so often (say 1minute intervals). Choose a couple of temperatures and see what proportion of time the heater needs to be on for in order to maintain those particular temperatures. A bit of jiggery pokery will tell you what continuous heater power is needed to sustain those chosen temperatures and, using the cooling curve, you could extrapolate (sketch the curve by eye or plot on log/lin paper) to estimate the power input for a larger temperature difference than your experiment allows. Check the outside temperature doesn't change too much and you may need to do a bit of correction. You need not actually stand inside the greenhouse for this as onlookers may wonder what you are doing in their, stripped to the waist.
Make your permanent heater power somewhere near the maximum value you get from the experiment. It will upset you, I expect and you will probably reconsider what internal temperature you actually want to maintain. Exotic plants are expensive to grow in some parts of the world. I believe people often use soil heaters and they can get away with less heat input that way; the leaves are not so fussy as the roots.
PS Buy a bigger heater than you think. A thermostat will limit the actual Energy consumption to what's actually needed and a big heater will help establish the desired temperature after opening the door etc.

 

[Appiani]

Thank you, interesting answers

 

[russ_watters]

I tried doing it that way when estimating the heating requirements for a house, several years ago. I then discovered that the air exchange can easily dominate the heating load. I guess a hermetically sealed greenhouse may be a bit easier to achieve but airflow will be relevant in practice.

Yeah, that's a good point. New houses are pretty good, but for an old house it is difficult to estimate and can vary from about 0.4-1.4 air changes per hour.

A quick calc tells me that if my house has an infiltration rate of about 0.5 ach, That's 7,000 btu/hr or about 20-30% of the heating load.

 

[sophiecentaur]

Yeah, that's a good point. New houses are pretty good, but for an old house it is difficult to estimate and can vary from about 0.4-1.4 air changes per hour.

A quick calc tells me that if my house has an infiltration rate of about 0.5 ach, That's 7,000 btu/hr or about 20-30% of the heating load.

And many families have doors open almost continually. Kids in and out of the garden, chasing each other and taking hot air with them every time.