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International Heat Transfer Conference 10

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)


Shijie Liu
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada T6G 2G6

Jacob H. Masliyah
Department of Chemical Engineering, University of Alberta, Edmonton, Canada T6G 2G6

DOI: 10.1615/IHTC10.2320
pages 61-66


Fluid flow and convective heat transfer in circular helical pipes having a finite pitch are numerically studied for Newtonian fluids of constant physical properties. It is found that the flow and heat transfer properties are better characterized using the generic coordinate system than using the orthogonal coordinate system.
The controlling parameters for the fluid flow are the Reynolds number Re, curvature ratio, λ = αRc'[Rc'2+(H'/2π)2], and torsion, η = α(H'/2π)[Rc'2+(H'/2π)2]. Here, α is the pipe radius, Re' is the radius and H' is the pitch of the coil. The Prandtl number Pr is an additional controlling parameter for heat transfer. When the loose coiling limit is invoked, the controlling parameters for fluid flow become: the flow Dean number, Dn = Re λ½, and the flow pattern transition parameter, γ = η / (λDn)½.
When torsion is small or the flow is torus-like, the flow and heat transfer properties in a helical pipe rely strongly on Dn and Pr. At small Dn, the flow and heat transfer characteristics are very similar to those due to a straight pipe. When Dn is large, the centrifugal force effects become significant. The local heat transfer coefficient and wall shear rate are higher near the outer wall and lower near the inner wall. The asymptotic Nusselt number and the friction factor increase with increasing Dn. When Pr is large, the isotherms form a depression zone along the vortex dividing line. The asymptotic Nusselt number increases with Pr.
When torsion is dominant, the flow becomes swirl-like or a Poiseuille flow with a superimposed swirling secondary flow (one-vortex). All the flow and heat transfer properties including the flow resistance and heat transfer coefficient tend to their corresponding limits governed by the Poiseuille flow even though the centrifugal forces can be strong (i.e., Dn is not very small). An increase in torsion gives a smaller heat transfer coefficient and lower flow resistance. The local heat transfer coefficient and wall shear rate are relatively uniform over the pipe circumference.

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