# Trapping sun heat the most - greenhouse

Greenhouse have recently caught my attention lately, which yesterday I posted in Why greenhouse's inside temperature never been infinitely hot?

From what I understand recently, greenhouse gases traps the sun heat (infrared radiation) on earth, by making it harder to dissipate back into space, reflecting most of them again. The exact same process happen in hydroponic greenhouse. If that's the case - why then, hydroponic greenhouse inner temperature don't keep increasing infinitely? I mean, if we assume the greenhouse is perfectly insulated transparent container (either by several layer glazing or gas-filled), where sun heat strike daily, and less of that amount dissipate back, Shouldn't it be increasing infinitely? (income > outcome). Because in mine, the temperature tend to be stable. It did always warmer than outer air in certain degree though. Now I assume other than inside reflection, there might also be outer reflection. So not only it retaining existing heat to go out, its also blocking the new one. That's why insulated glass commercially marketed to keep the room inside cool. But if that was the case, then why we should be worry with this greenhouse effect after all? The nature seems always be in equilibrium state no matter what; lots of greenhouse gases = less incoming heat but retain the outcome, little amount of them = more outcoming heat but always up for more incoming one. Or do I missed something?

I still wonder though, if, hypothetically, I have tasked to setup new greenhouse (or generally any container) with main objective to traps sun heat the most inside, how is the best way to do it? (means within same area of space, create hottest possible greenhouses - regardless of the shape, cost, and ambient temperature of surrounding region)

Will insulation (with glazing/gas-filling) do the job? Or instead of transparent glass, will use black-surfaced metal do it?

I have no physics background whatsoever, so pardon for my shallow understanding of the topic. Any input is really appreciated

• The quoted portion regarding "perfectly insulated container" is unrealistic. The level of insulation and heat retention is related to how much money one wishes to throw at a project. Aerogel walls (transparent and high insulating) would be astronomically priced, just as an example. Black surface metal means no light passes. How would the plants feel about that aspect? If sunlight is not part of the program, it's not a green house. – fred_dot_u Nov 12 '20 at 0:48
• @fred_dot_u Sorry if mistakenly understood, I would emphasize the objective to trap sun heat the most (which i assume how to maintain existing heat from getting lost while keeping heat from the sun constantly striking - as in greenhouse), not specifically for plant uses though – gijoe Nov 12 '20 at 1:07
• Then you will need a thermal sink like water to capture and store the heat. Energy moves from higher to lower. Sun heats up greenhouse, but glass has a high thermal transmission, so heat will escape from the glass if there is a temperature differential. – StainlessSteelRat Nov 12 '20 at 2:06
• Even if you had a perfectly insulating greenhouse (physics now, not engineering), eventually the temperature will get hot enough that the things in the greenhouse will emit the same radiation as the sun, which will go out through the greenhouse because the greenhouse doesn't block those frequencies. – user253751 Nov 12 '20 at 15:21

Greenhouses generally work by trapping radiation (infrared to be more specific). More specifically what they do is allow most of the sun radiation to come through and then trap the infrared radiation which is re-emitted from the objects within the greenhouse.

## types of heat transfer

For the greenhouse equilibrium you need to consider all 3 types of heat transfer :

2. conductive: between two solid bodies
3. convective between a solid body and a fluid (see air).

Quick word about conductive heat transfer, it is very important with metals. However in this case, the only surface that usually concerns heat conductivity is the floor of the greenhouse, and the thermal conductance coefficient is quite low for soil. Although, this is usually negligible, the equation is the following

$$\dot{Q}_{cond} = U\; A_{cond} \Delta T_{cond}$$

Now, regarding convective heat transfer, this probably has the maximum effect, and is what usually brings an equilibrium to the system. It is depended on:

• the surface area (which is all exposed sides of the greenhouse),
• the temperature difference between solid (i.e. greenhouse walls and roof) and fluid (usually air). So you can understand as the temperature rises the outward heat transfer increases proportionally.
• the heat transfer coefficient which in turn depends mainly on the fluid properties and its velocity. The higher the velocity, the higher the transfer rate for the same temperature different.

The equation if your are interested has the following form: $$\dot{Q}_{conv} = h\; A_{conv} \Delta T$$

## energy equilibrium

So in the end you have a fixed power coming from the sun radiation. Lets say about I= 1000 - 1500$$W\over m^2$$. So $$\dot{Q}_{radiation}= I A_{windows}$$ (A denotes area). Therefore you can approximate the energy equilibrium by the following equation:

$$\dot{Q}_{IN} = \dot{Q}_{OUT}$$ $$\dot{Q}_{radiation} = \dot{Q}_{conv}-\dot{Q}_{cond}$$

If you have the dimensions of greenhouse you can derive the temperature difference (for calculation simplicity here I am assuming $$\dot{Q}_{cond}=0$$):

$$\Delta T=\frac{\dot{Q}_{radiation}}{ h\; A_{conv} }\Rightarrow T_{\text{greenhouse walls} } = \frac{\dot{Q}_{radiation}}{ h\; A_{conv} } + T_{air}$$

## How you can increase the temperature in the green house more

(Notice that I am NOT saying 'optimize the heat trapped')

The best way IMHO is you use double glazing windows that allow most of the sun radiation to pass through. The double glazing, will create two different temperature (one on the inside wall and on the outside wall). However for the convection with the outside air what will be important is the temperature of the outside window.

## BONUS: Do you want to increase the temperature more

I live in an island in the Mediterranean that has some areas packed with greenhouses.

They only work from October to April because, in the summer they are unlivable. The temperatures in the winter can go up to $$50^oC$$ easily if its a sunny day (unless ventilation windows are opened), while in the summer they can get over 70 or $$80^oC$$. That is without using double glazing.

• Why would someone want a greenhouse to hit 50 C in the winter? – Eric S Dec 12 '20 at 13:23
• It is to help with the cultivation of cucumbers and other vegetables which are exported to other parts of the world. The 50C is if you keep all ventilation windows closed. Normally the temperature is kept between 30 το 35oC, when the outside temperature is about 10 to 15C (during the day). If you are interested I can find more specific information. – NMech Dec 12 '20 at 13:28
• 30 C makes sense. Your answer made me think that the greenhouses were actually used at 50 C. I like your answer. – Eric S Dec 12 '20 at 13:57
• Since is English is not my native language, if you feel the offending portion can be rewritten in a manner which might not be misleading, I would welcome edit suggestions. – NMech Dec 12 '20 at 14:03
• Your English is excellent. If you want to edit for clarity then perhaps change “50 C” to “50 C unless ventilation windows are opened”. – Eric S Dec 12 '20 at 17:01