Influence of high shear on the effective thermal conduction of spherical micro- and nanoparticle suspensions in view of particle rotation

In the past three decades, different physical models to describe the thermal conductivity enhancements of suspensions with micro- and nanoparticles with respect to particle sizes, shape, volume fraction etc. were established. However, none of these models considered the effect of shear, although an influence has been observed experimentally in a few studies for very high shear rates. Possible underlying mechanisms for shear induced thermal conductivity enhancement have not been explained in detail yet. In this article, the finite element method is used to evaluate how shear induced particle rotation and the velocity field around the rotating particle drives thermal conductivity enhancement. For nanoparticles it is found that particle rotation does not enhance the heat transfer inside the particle. However, within the Péclet number (Pe=γ˙d2/a) range of 0−300, particle rotation linearly enforces the heat transport up to 5−30%, mainly due to advective motion (eddies) around the particle. For high shear rates (Pe>500), the enhancement approaches a constant value, at which the particle material becomes irrelevant for the effective conductivity enhancement. In this case, asymmetric advective motion around the particle dominates the heat transfer. Note that the Péclet number range for which an advective motion plays a significant role is relevant for suspensions with micrometer-size particles but not for nanoparticle suspensions. In a final step, the influence of the shear-affected thermal conductivity is evaluated for a forced-convection laminar pipe flow with a parabolic velocity profile. Utilizing a thermal conductivity model which accounts for the local shear, the overall heat transfer enhancement in the channel flow is determined. It is found that a 65% cross-section saturation with shear-induced enhancement is hard to be reached within the laminar flow region. Thus, the shear enforcements mainly take effect close to the pipe wall.