Pseudoplastic fluid flows for different Prandtl numbers: Steady and time-dependent solutions

Abstract

In this work, a variational multiscale (VMS) nite element formulation is used to approximate numerically the natural convection in square cavity with dierentially heated from sidewalls problem for Newtonian and power-law uids. The problem is characterized for going through a Hopf bifurcation when reaching high enough Reyleigh numbers, which initiates the transition between steady and time dependent behavior, however, results found in the literature are only for air Prandtl number. The presented VMS formulation is validated using existing results, and is used to study highly convective cases, to determine the ow conditions at which it becomes time dependent, and to establish new benchmark solutions for non-Newtonian uid ows for dierent Pr and power-law indexes n. The range of solutions were found in the range 0.6 < n < 1 and 0.01 < Pr < 1, 000, and the critical Rayleigh number (Ra c ) where Hopf bifurcations appear were identied for all cases. Obtained results have good agreement with those previously reported in the specic literature, and new data related to the heat transfer capabilities of pseudoplastic uids and its oscillatory behavior was identied. This non-Newtonian inuence of the uid is later checked in a 3D model of a simplied heat exchanger, where the capability of pseudoplastic uids for energy transport proved to be enhanced when compared to the Newtonian case.