Heat transfer from air to plate (transient)

[borgwiser]

I was recently working on a project for a customer and after a few S.W.A.G.s I got the results I wanted. In the process, however, I found out that I really didn't know quite as much as I thought about heat transfer.

Every transfer book I've used and seen does a marvelous job at situations like "air moving over a hot plate at a constant temperature: what's the heat loss?" Fine. But, in many applications I encounter, not good enough. I have a question like:
"Hot air is passed over a long plate/board. The board is initially at a uniform temperature T. What is the temperature distribution with respect to length and time of the board and air if all properties of the air are known (initial temp, composition, direction, flowrate, etc.)"
I've tried some iterations using the Nusselt number and using the q value from a really small section to find the T of the next section of the board (using q = mCp(dT) ) and the new temp of the air (a little unsure on this part). Anyone have any input on this matter or a place to where I can go to find out more about transient states in heat transfer? I'm tired of seeing texts reduce and simplify everything to such trivial problems (arghh!!).

many, many thanks.

Ryan

 

[corus]

Thh air temperture is generally to be assumed to be some unchanging bulk temperature away from the board and is thus unaffected by the temperature of the board as it changes. The long board measns that the problem is one dimensional away from the ends and is thus basically a trivial problem not worth screaming about.

corus

 

[borgwiser]

I'm looking at the most complicated situation (again, out of curiosity, not so much for application). But, if I generalize it to the extent that the bulk mass does not change in temperature then......Ahhh!....it all came clear as I was writing this. I'm wanting to make a model to describe the temperature at every point along the plate with respect to time and I've been approaching it the wrong way. Okay...got it.
Many thanks.

RH