Solution of the heat transfer of laminar forced-convection in non-circular pipes

Summary

The heat transfer problems of forced-convection in non-circular pipes have many engineering applications. In this a paper a formal solution is given when the mapping function z=w(ζ)=$\sum\limits_{n = 0}^\infty {}$ a, which maps conformally the cross-section of the channel onto the unit circle γ in the ζ-plane is known. The expression for the average velocity, average temperature, mixed mean temperature, heat transfer rate and the Nusselt number have been expressed in terms of the constants a _n .