THERMAL ASPECTS OF A NOVEL VISCOUS PUMP

We have previously introduced a novel method for pumping fluids via a viscous mechanism. The device essentially consists of a cylindrical ro tor eccentrically placed in a channel, and it is suited for hauling hi ghly viscous polymers in macroducts, or more common fluids in microduc ts. Under certain operating conditions, viscous dissipation can be imp ortant and a significant attendant temperature rise can have adverse e ffects on the pump operation. For this reason, we have conducted a num erical experiment to characterize the associated phenomena. The couple d system of the two-dimensional Navier-Stokes equations, with temperat ure-dependent viscosity, and the energy equation with viscous dissipat ion terms retained, are solved using a finite-volume method. Different types of thermal boundary conditions at the rotor-fluid interface are explored in the numerical scheme. An approximate theoretical model is also developed to analyze pow in the region between the rotor and the nearest plate (for small gaps). The results indicate that although th e bulk temperature rise is minimal for typical microscale situations, significantly steep temperature gradients are observed in the legion b etween the rotor and the nearest channel wall where the most intense s hear stress occurs. For certain combinations of Re, Ec, and Pr, temper ature rises along the channel wall of the order of 30 K were calculate d Moreover, for very small values of this gap, large errors in the com puted flowrates and pumping power estimates can arise for large Brinkm an numbers, if the effects of viscous dissipation are ignored. Further more, the existence of an optimum value of rotor position, such that t he bulk velocity is a maximum, is demonstrated These findings are sign ificant as they are indicative of trends associated with the pow of hi ghly viscous polymeric liquids, where much larger temperature rises an d their attendant degradation in performance are likely to occur.