Thermal Aspects of a Novel Viscous Pump

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Abstract
We have previously introduced a novel method for pumping fluids via a viscous mechanism. The device essentially consists of a cylindrical rotor eccentrically placed in a channel, and it is suited for hauling highly viscous polymers in macroducts, or more common fluids in microducts. Under certain operating conditions, viscous dissipation can be important, and a significant attendant temperature rise can have adverse effects on the pump operation. For this reason, we have conducted a numerical experiment to characterize the associated phenomena. The coupled system of the two-dimensional Navier-Stokes equations, with temperature-dependent viscosity, and the energy equation, with viscous dissipation 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 flow in the region between the rotor and the nearest plate (for small gaps). The results indicate that although the bulk temperature rise is minimal for typical microscale situations, significantly steep temperature gradients are observed in the region between the rotor and the nearest channel wall where the most intense shear stress occurs. For certain combinations of Re, Ec, and Pr, temperature rises along the channel wall of the order of 30 K were calculated. Moreover, for very small values of this gap, large errors in the computed flowrates and pumping power estimates can arise for large Brinkman numbers, if the effects of viscous dissipation are ignored. Furthermore, the existence of an optimum value of rotor position, such that the bulk velocity is a maximum, is demonstrated. These findings are significant, as they are indicative of trends associated with the flow of highly viscous polymeric liquids, where much larger temperature rises and their attendant degradation in performance are likely to occur.