# Radiation heat transfer between air or wall

1. Nov 25, 2009

### zenite

Lets say a hot object is at 500K and placed in a chamber with wall temperature of 300K. The surrounding air in the chamber is 320K.

So what is the mode of heat transfer for the hot objection? There is convection and radiation. so the heat transfer rate, q = q(conv) + q(rad), right?

Convection is between object and surrounding air. But what about radiation? Is it between the object and the chamber walls or is it between the object and the surrounding air? Depending on which is chosen, the q(rad) will varies since q(rad) depends on the temperature difference of the 2 body.

Can anyone help me out? I am confused on using 500K and 300K to calculate q(rad) or 500K and 320K.

2. Nov 25, 2009

### zenite

Ok, I think I got it. Please correct me if I am wrong.

Rate of energy radiation of an object (T is given by
qo = A$$\sigma$$$$\epsilon$$T4

If the object is in a chamber with wall temperature of Tw and surrounding air of Ta, then the object receives heat radiation from both wall and air.
qwall to object = A$$\sigma$$$$\epsilon$$Tw4

qair to object = A$$\sigma$$$$\epsilon$$Ta4

Hence, the net q for object to air and wall is:
qnet = A$$\sigma$$$$\epsilon$$(T4-Ta4-Tw4)

ps: the sigma and epsilon isn't suppose to be superscript, not sure why it turns out this way

3. Nov 25, 2009

### Mapes

Hi zenite, welcome to PF. The air isn't going to participate to any significant effect in the heat transfer between the object and the wall. (Another way of looking at this is that a few meters of air won't block radiative heat transfer, just as a few meters of air doesn't attenuate visible light to any noticeable degree). The air properties are only going to affect the convection term.

4. Nov 25, 2009

### zenite

Ok, so radiation takes place between the object and the walls only? Is there no radiation taking place between the air and the object or is it insignificant as compared to the other modes of heat transfer?

And yes, I realised that the formula that I put up earlier on is incorrect, since taking T4 - Ta4 - Tw4 can give a negative value, which is illogical if T>Ta>Tw.

5. Nov 25, 2009

### Mapes

It exists but is insignificant.

6. Nov 25, 2009

### zenite

Oh thanks for clearing my doubts. I have another question on convection.

If an air gap exists between 2 walls, say, wall A and wall B. the convective heat transfer coefficient of the air is h. Assuming no radiation and conduction in the air gap, what is the heat transfer rate between the 2 walls?

Let Ta be temperature of wall A, Tb of wall B and Tair of the air.

q = hA (Ta - Tair) + hA (Tair - Tb) = hA (Ta - Tb)
or is it...
q = 0.5hA (Ta - Tb)

Since convection takes place 'twice', between wall A and air, and between wall B and air, should the h be multiply by 0.5?

Last edited: Nov 25, 2009
7. Nov 25, 2009

### Mapes

I don't think this approach is going to prove fruitful. Convection removes heat energy by fluid motion tangential to a surface. The convective flow isn't going to automatically divert to the other wall and deposit heat energy there. And I don't see the sense in adding the heat flux values together. Assuming that convection does dominate in this problem (which isn't clear), it's the same flux of energy; adding the values is nonsensical.

The general approach is to calculate the values of heat flux by each mechanism (conduction, convection, radiation) and determine if one or more can be assumed negligible.