Analog Solution of Laminar Heat Transfer in Noncircular Ducts by Moire´ Method and Point-Matching

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Abstract
The problem of fully developed laminar flow heat transfer in polygonal ducts with axially uniform wall heat flux is considered. The well-known analogy between laminar heat transfer in ducts and simply supported thin flat plates of the same shape under uniform lateral loading is used to obtain heat transfer characteristics. It is shown that both the fully developed laminar flow characteristics in noncircular ducts and the steady temperature distribution in infinitely long prismatical bars with uniform internal heat generation can also be obtained by the plate analogy based on the Dirichlet problem. The plate problem may be solved by the Moire´ method and point-matching technique, and it is pointed out that the former can be applied to ducts of any shape. For a square duct, the results from these two approximate methods are given, and comparisons are made which show good agreement with the exact solution.

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