Prof. Michael Louge
College of Engineering, Cornell University
Agitated grains are frequently used to augment convective heat transfer at the walls of the vessels that hold them. To elucidate the origin of this augmentation, we predict it for dense homogeneous suspensions of agitated solids in conductive fluids by coupling the fluid and solid phases through a source term modeling the heat exchange rate between the two phases. The enhancement is governed by a Damkohler number demarcating two asymptotic limits, namely an "exchange limit" arbitrated by the source term, and a "diffusion limit" set by the ability of agitated particles to self-diffuse. We point out effects of particle ordering on mixture conductivity and heat exchange rate, carry out thermal simulations to justify the form of these terms, and model further enhancements from gas velocity fluctuations induced by solids of high agitation.
We tested the theory in the exchange limit by vibrating acrylic and aluminum spheres in a box consisting of two flat, vertical isothermal walls, two bumpy, horizontal, insulated walls, and two flat vertical insulated surfaces. The steady heat flux through the thermally-guarded hot wall was recorded at different temperatures of the opposite wall cooled by thermoelectric modules, and enhancements of suspension conductivity were calculated using a lumped-parameter model of the box. To compare results and theory, we also predicted vertical profiles of agitation and solid volume fraction in the box using granular dynamics.
This work was published in the International J. Heat and Mass Transfer, see http://grainflowresearch.mae.cornell.edu/heat_transfer/heat_transfer.html