Coupling between heat and momentum transfer mechanisms for drag-reducing polymer and surfactant solutions

Drug-reducing solutions exhibit simultaneous friction and heat transfer red uctions, yet it ha been widely believed that there is no direct coupling be tween the two. In this work, we have conducted a stud to re-examine this is sue using measurements of friction and heat transfer over a wide range of f low conditions from onset to asymptotic various pipe diameters, and several polymer and surfactant solutions. Contrary to some earlier suggestions, ou r tests show that no decoupling of the momentum and heat transfer mechanism was seen at the onset of drag reduction, nor upon departure from the asymp totes, but rather that the friction and heat transfer reductions change sim ultaneously in those regions for asymptotic surfactant and polymer solution s, the ratio of heat transfer and drag reductions was seen to be constant o ver a large range of Reynolds numbers, if modified definitions of the reduc tion parameters are used. In the nonasymptotic region, however, the ratio o f heat transfer to drag reductions is higher and is a function of the reduc tion level, but is approximately the same for polymer and surfactant soluti ons. This variation is consistent with the concept of a direct coupling thr ough a nonunity constant Pr-i, as also suggested by our local measurements of temperature and velocity profiles. We also saw that our diameter scaling technique for friction applies equally well to heat transfer. These findin gs allow us to predict directly the heat transfer from friction measurement s or vice versa for these drag-reducing fluids,and also suggest that a stro ng coupling exists between the heat and momentum transfer mechanisms.