Trapping sun heat the most - greenhouse

Question

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

Answer 1

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 :

1. radiation (Already covered)
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.