Forced convection in a helical pipe filled with a saturated porous medium

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An analysis is made of laminar forced convection in a helical pipe of circular cross-section and filled by a porous medium saturated with a fluid, for the case when the curvature and torsion of the pipe are both small. The Darcy model is employed, and boundaries with either uniform flux or uniform temperature are considered. It is found that curvature induces a secondary flow at first order in the parameter ε = κa, where κ is the curvature and a is the radius of the pipe. On the other hand, the Nusselt number is unchanged to first order in ε but is increased at second order, for either set of thermal boundary conditions. The effect of torsion on the velocity appears at second order, but torsion does not affect the Nusselt number at second order.