Radiation heat transfer between air or wall

[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.

 

[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
q_o = A\sigma\epsilonT⁴

If the object is in a chamber with wall temperature of T_w and surrounding air of T_a, then the object receives heat radiation from both wall and air.
q_{wall to object} = A\sigma\epsilonT_w⁴

q_{air to object} = A\sigma\epsilonT_a⁴

Hence, the net q for object to air and wall is:
q_net = A\sigma\epsilon(T⁴-T_a⁴-T_w⁴)

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

 

[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.

 

[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 realized 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.

 

[Mapes]

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?

It exists but is insignificant.

 

[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 T_a be temperature of wall A, T_b of wall B and T_air 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?

 

[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.