Heat Transfer from Gas to Solid (HELP)

[AngelLestat]

Someone knows how to calculate heats transfer from a gas to a solid?

I read many sources, but I still cant have nothing for granted.

A gas can emit radiation? or only solids can do that?

Heat transfer is only by convection, or we need to take into account conduction?

For example, if we have a hot air ballon with a IR refrective layer in the envelope to not allow escape the heat, how we calculate the heat loss from the gas across the envelope.

What of these values are important in this problem?

Gas temperature

Solid temperature

Thermal conductivity

Heat capacity at constant pressure

Heat capacity at constant volume

Gas density

[K^2]

Heat flow in a gas is a very complicated question. First, it does emit/absorb the IR, but not equally well at all frequencies. You need to consider the absorption spectrum. Radiation spectrum will depend on that and the temperature.

Besides radiation, heat also propagates through gases (or fluid) via advection (or convection) and heat flow. You can basically assume that boundary layer of gas (fluid) touching your solid object has the same temperature as object's surface. Through the solid, you only have to worry about heat flow, so you just need to know heat conductivity of the material. Then you can solve for temperature gradient and figure out how heat flows through the solid. In the gas, you'll have heat carried by both the movement of individual molecules, which is going to work like diffusion, meaning it follows the same laws as heat propagation in solids, but also carried by the gas flow.

If you know the flow rate, this is pretty straight forward to figure. Unfortunately, in a lot of cases, the flow depends on how much heat is carried away. Hot air balloon is a good example. As you've pointed out, making skin of the balloon reflective minimizes IR losses. But heat will flow through the skin, heating up surrounding air. As the surrounding air heats up, it will rise, generating a convection current. That will carry away the heat and bring in fresh cold air. That means more heat will escape, and that means a stronger convection current. In order to figure out exactly how much heat you are going to be losing, you need to solve a complicated hydrodynamics problem along with the basic heat transfer problem for the balloon's skin.

So if you are looking for a simple solution from perspective of theory, there is none. It might be possible to come up with an approximate analytical solution for a simple shape of the balloon, but for a general balloon, this would have to be simulated on the computer.

There might be some empirical, very roughly approximate formulas out there. I am not familiar with anything like that, but it seems that for balloon sport, this might have been useful, and somebody would derive approximate formulas based on observation. Try searching the internet, or maybe find an air balloon forum if you need a formula specifically for that. If it's more general, like I said, it's going to be a very complicated computation.

[peadar1987]

Yeah, it's not easy, but you can find rough correlations out there, I'll try and find an open-source one for you.

[AngelLestat]

Thanks K2 and peadar.

So that is the reason why I can not find an intuitive or simple formule. Like you point the gas flow over the surface is also important. I saw in some formules that variable in m/s.

The formules that I find are not easy to understand, I dont know how to calculate each of its variables, and even if I do, I am not sure if can be applied to my cases.

But you are right, find correlations numbers or models to hot air ballons it will be a good start. The problem that eventually I want this knowledge to calculate something a little more complicate.

Well I will post any advance in this matter, it's a shame that most engineering software are not free.