Heat transfer question

Dear clay:

Is the wire and substrate immersed in a fluid? Like air? If so, then convective cooling will have some effect.

Otherwise it is "simple" radiative heat transfer.

David A. Smith

Thank you david,

Yes the medium is air. Is it possible to ignore convection, or will it be significant? The majority of transfer (nearly 80% is infrared)

clay

N:dlzc D:aol T:com (dlzc) wrote:

Dear clay:

Please post in plain text, for those folks that have older readers...

It depends on the temperatures. If your interest is on the surface, and not the wire, then likely the effect of convection will be small. If the wire is close, or there is a "ceiling" close, the column of hot air from the wire can play a significant part, including drawing additional ambient air past the surface. If the surface temperature is close to ambient, and the wire is "far" away, then little heat should be convected away.

David A. Smith

The wire is horizontal & straight, above the flat surface, some distance away. Only interested in the wire/surface temps. If I know the wire resistance, voltage, ambient air temp, and surface material. How do I calculate the wire temp or wattage to get a required surface temp?

ca

Dear clay:

Good, this is the simplest case. It has been a long time since I have done this. I am very sure this will have been done on a web page (or web textbook) somewhere. If you are looking for formulae...

Two control volumes. One around the wire, one around a chunk of surface. I would recommend linear surface "chunks" that run parallel to the wire.

First, the wire. Heat in equals heat out. Heat in equals voltage * voltage / resistance. Heat out equals heat via convection and heat via radiation. You'll need to find a relationship between convective heat transfer in a long horizontal cylinder, given ambient temperature and the unknown cylinder (wire) temperature. You'll need to find a radiative heat transfer relationship between a chunk of surface at an angle and distance from a cylinder. If the wire is "close" to the surface, convective heat transfer will be small.

Second, the surface. Heat in equals heat out. Heat in equals the radiative heat transfer from the wire. If you *assume* the surface chunk does not transmit heat to the strata below it, then heat out is radiative heat transfer to the "room" at ambient temperature, with shape factor = 1.

Result should be two equations in two unknowns. You'll need to integrate over the surface, as there will be a temperature profile from maximum to ambient. If you want a certain maximum surface temperature, you can treat the power of the wire as an unknown, and solve for the relationship between applied voltage and wire resistance.

Good luck!

David A. Smith