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Inertial effects on the transfer of heat or mass from neutrally buoyant spheres in a steady linear velocity field

### Abstract

Microscale inertia is found to break the degenerate closed-streamline configuration that occurs in a shearing flow past a neutrally buoyant torque-free spherical particle in the inertialess limit. The broken symmetry at small but finite allows heat or mass to be convected away in an efficient manner in sharp contrast to the inertialess diffusion-limited scenario. Inertial forces scale with the particle Reynolds number, defined as , where is the radius of the particle, is the characteristic magnitude of the velocity gradient, and is the kinematic viscosity of the suspending fluid. The dimensionless heat or mass transfer rate is then given by when and , the constant being a function of the flow in the vicinity of the particle. Here, is the Nusselt number defined as , where is the dimensional heat/mass flux, the appropriate transport coefficient, and the driving force viz. the temperature or concentration difference between the particle and the ambient fluid; for pure diffusion, . The Peclét number is a dimensionless measure of the relative dominance of the convective and diffusive transfer mechanisms. It is shown that equals for a two-dimensional linear flow, where measures the relative magnitudes of extension and vorticity. For simple shear , knowledge of the inertial velocity field to enables one to determine the next term in the asymptotic expansion for ; one finds in the limit . It is argued that the convective enhancement at finite via symmetry-breaking streamline bifurcations will occur in generic shearing flows with nonlinear velocity profiles; the degenerate Stokes streamline pattern around a neutrally buoyant torque-free particle in a quadratic flow serves to reinforce this assertion. The above mechanism represents a possible means for heat or mass transfer enhancement from the dispersed phase in multiphase systems. Implications for particles in turbulent flows are also discussed.

© 2006 American Institute of Physics

Received 29 September 2005
Accepted 24 May 2006
Published online 14 July 2006

Acknowledgments:
This work was supported by Department of Energy Grant No. DE-FG02-03-ER46073.

Article outline:

I. INTRODUCTION
II. STREAMLINE CONFIGURATION: THE INERTIALESS AND FINITE SCENARIOS
A. A torque-free cylinder in a planar linear flow
B. A torque-free sphere in a simple shear flow
C. A torque-free sphere in a planar linear flow
III. BOUNDARY LAYER ANALYSIS FOR SMALL BUT FINITE
IV. EFFECT OF FLUID INERTIA ON HEAT TRANSFER FROM PARTICLES IN NONLINEAR FLOWS
V. DISCUSSION AND CONCLUSIONS

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2006-07-14

2016-02-05

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