Air Temperature Adjacent to Heat Source

[ballen]

I'm trying to find a relatively simple way to estimate air temperature at a given distance from a heat source. For example, assume a large room with average temp. of 90 deg F. Within the room is a large (48" o.d.) steel chimney with a constant exterior surface temperature of 500 deg. F. How would you calculate the surrounding air temperature at, say, 24" away from the surface of the chimney?
I know this depends on alot of factors, especially if forced convection is considered (for this example assume it is not). I've done some research and this problem is quite a bit more complicated than I though it would be. At this point I'm just looking for an equation for a rough estimate.

Thanks.

 

[Noexpert]

at 24 inches i would imagine you're well outside the boundary layer which would develop along the chimney (unless it's really tall) meaning the temperature could simply be assumed equal to the bulk room temp.

there would tend to be a stratification effect due to buoyancy so any temp measurement in the room would also be a function of elevation as well as distance from the chimney.

assuming the room isn't heating up due to the presence of the chimney ie. the heat put in is being dissipated elsewhere the temp at 24 inches would roughly average out to 90 deg F for various heights.

if the room is heating up, you've got a more complicated transient problem.

you can estimate the heat into the room for this nat convection case as q ~ 1 btu/hr/ft^2/deg f * (500 - 90 ) * Surface Area

why are you looking for this number?

if you're thinking about putting an object close to the chimney you may want to consider radiation from the chimney as a potential heat source.

 

[poetix99]

If what you really wanted was to know what radiated temperature would be "seen" by a "gray body" at a given distance from your hot chimney wall, this is relatively simple view factor geometry. At 500F, radiation would not be negligible, so this might be a start...

Otherwise, there is no equation for a rough estimate of the air temperature in the model that you've described.

If there is a LOT of forced convection and the air in the room is well circulated, the air temperature in the room may be approximated to be uniform, and is calculable for some equilibrium condition. This is as simple as your problem will become and it still depends upon the steady state heat transfer to/from all of the surfaces of the room, not just the chimney.

If there is no forced convection, there will be plenty of natural convective currents established in the room. Because the hot surface is vertical (rather than the bottom surface), I doubt that a stable stratified temp. gradient will be established. The convective influence of other surfaces of the room might also need to be accounted for. You will never be able to predict the temperature at a particular location with any accuracy.

If the room is not otherwise quiescent, (i.e. if there are engineers walking around, trying to measure air temperatures) the problem is a combination of insufficiently-forced-to-be-considered-uniform and not-quite-undisturbed-enough-to-have-fully-developed-natural-currents.

It is possible (this is just a guess) that ASHRAE handbooks might provide some insights into simplified approaches to your problem, because this is similar to having a very tall (very hot) "radiator" in a room. (So-called "radiators" are much more significantly convectors.)