Heat transfer in duct with different cross section

[googool]

Hello

what is the difference in free convection in a duct with circular cross section and rectangular cross section. is this correct that temperature difference decreases exponentially with distance along the duct (circular cross section )but linearly in ractangular duct?
thx

 

[Maxham1]

I think that in many cases the rectangular duct can be considered circular by using the hydraulic diameter of the duct. Get a hold of a textbook on heat transfer, and you should find an explanation of the hydraulic diameter and its use in equating a rectangular duct to a circular duct.

In regard to exponential versus linear variations with temperature difference, I don't think it has anything to do with the duct cross section. The type of variation in temperature difference along the duct is dependent on the boundary conditions at the external surface of the duct. Two examples are constant temperature or constant heat flux at the duct's outer surface. I forget which is which, but a decent heat transfer book should contain details on the differences.

It's not the complete answer, but I hope it helps you get started.

 

[sailoday28]

First of all, what type of accuracy is needed?
What is the orientation of the duct? vertical, horizontal or what ever?
Hydraulic radius will not necessarily give accurate results. ----unless one has experimental data in terms of dimensionless numbers using the hydraulic radius.

 

[googool]

Thank you for your comments the duct is horizental and i want to know for 2 ducts with same cross section area but with diffrent cross section shape what is the heat transfer behavior in this case ?
thx

 

[sailoday28]

Sorry, but some other information is needed.
Since you state natural convection, I assume there is no net horizontal flow.
For a horizontal circular duct, with for example, a uniform temp on its inside surface, I would expect circulation, but with the bulk inside fluid at the temp of the inside surface.
For the rectangular duct, are the boundary conditions of duct temp the same? If so, the same result as for the circular duct.
Please give more information as to the boundary conditions and if there is to be a net horizontal flow.
Otherwise, the problem is not making too much sence with me.