Developing convective heat transfer in helical pipes with finite pitch

Simultaneous development of laminar Newtonian flow and heat transfer in helical pipes is numerically studied. The governing equations are fully parabolized in the axial direction and are written in an orthogonal helical coordinate system. For the special case of a torus, the numerical results for Nusselt number agree well with published data. The Nusselt number in the developing region is found to be oscillatory. The asymptotic Nusselt number and the thermal entrance length are correlated with the fluid Prandtl number and the flow Dean number, Dn = Re λ ^{1 2}. Here Re is the flow Reynolds number and λ is the dimensionless curvature ratio. When torsion is dominant, the asymptotic Nusselt number decreases while the thermal developing length increases with γ, where γ(=ηλ ^{-1 2}Dn ^{-1 2}) is the flow-pattern transition parameter for high Dean number flows. Here η is the dimensionless torsion. When γ is large, the asymptotic Nusselt number tends to the limits corresponding to a Poiseuille flow.