Two Fluid Modeling of Heat Transfer in Flows of Dense Suspensions

Pranay P Nagrani, Purdue University

Abstract

We develop a two-fluid model (TFM) to simulate the particle migration phenomenon in non-Brownian dense suspense flows. The TFM is implemented as solver in the open-source computational framework of OpenFOAM®. We incorporate stress heterogeneity of dense suspension under shear based on the established phenomenological models of viscosity and normal stress. We incorporate thermal transport in the dense suspensions by developing a novel closure relation for inter-phase heat transfer coefficient in the TFM. The closure relation is calibrated successfully against a prior experiment on flow in a concentric Couette cell from the literature. We demonstrate how a thermo-rheological flux term can be deduced from the TFM, in addition to shear-induced flux, to understand the coupling of shear and thermal gradients in the system on particle migration. The interplay between heat transfer and shear migration was studied computationally by imposing shear in the system via rotation of the inner cylinder of Couette cell for two different thermal boundary conditions: ∆T < 0 and ∆T > 0, where ∆T = (Tin − Tout) is the temperature difference across the gap, while Tin and Tout are temperatures at the inner and outer walls of the Couette cell. A novel effect was found for ∆T > 0: that the shear- and thermal-induced migration fluxes act in opposite direction to cancel the net particle migration. Meanwhile, for ∆T < 0, the fluxes act in the same direction to aid the particle migration. Next, in an eccentric Couette cell system. We observed that, for ∆T > 0, the Nusselt number Nu increases with eccentricity owing to secondary flow in the system. Meanwhile, for ∆T < 0, there exists a maximum for Nu, after which it decreases due to enhanced particle migration and large flow re-circulation zones. Finally, we employed the proposed computational TFM framework to analyze electronics cooling by forced convection for microchannel cooling. We used a suspensions of high thermal conductivity (Boron Nitride) particles in a 3M™ Fluorinert™ FC-43 cooling fluid. Threedimensional simulations were run to quantify the temperature distributions under uniform heating (5 W) and under hot-spot heating (2 W/cm2) conditions. A 100 K junction level temperature improvement (enhanced thermal spreading) was seen for hot-spot heating and 15 K was observed for uniform heating, demonstrating the enhanced cooling capabilities of dense particulate suspensions of high-conductivity particles, over a clear FC-43 fluid.

Degree

M.Sc.

Advisors

Christov, Purdue University.

Subject Area

Education|Fluid mechanics|Hydraulic engineering|Mathematics|Mechanics|Petroleum engineering|Physics|Thermodynamics

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