Micromechanical origin of heat transfer to granular flow

Heat transfer across a granular flow is comprised of two resistances in series : near the wall and within the bulk particle bed, neither of which is well understood due to the lack of experimental probes to separate their respective contribution. Here, we use a frequency modulated photothermal technique to separately quantify the thermal resistances in the near-wall and the bulk bed regions of particles in flowing states. Compared to the stationary state, the flowing leads to a higher near-wall resistance and a lower thermal conductivity of bulk beds. Coupled with discrete element method simulation, we show that the near-wall resistance can be explained by particle diffusion in granular flows.

Figure 1

Overview of MPR measurement on a flowing particle bed. (a) MPR signal collecting system. (b) Flowing particle bed in a vertical channel. (c) Schematic of laser heat penetration into the particle bed. (d) HSP 40/70 experimental data and fitting at $300{}^{\circ }\mathrm{C}$; error bars are standard deviations of replicate measurements. Insets: thermal penetration depth at different frequencies.

Figure 2

Model fitting results of flowing beds as a function of velocity. $k_{\mathrm{eff}}$ of (a) CP 40/100 and (b) HSP 40/70. $D_{\mathrm{air}}$ of (c) CP 40/100 and (d) HSP 40/70. Insets show the averaged $D_{\mathrm{air}}$ over three temperatures with error bars representing the standard deviation.

Figure 3

DEM simulation results of packing structure's impact on $k_{\mathrm{eff}}$. (a) A snapshot of DEM simulation and particle bed samples extracted from the bulk and the near-wall region. (b) Modeling of $k_{\mathrm{eff}}$ in comsol. (c) Comparison between MPR results, THW results and simulated $k_{\mathrm{eff}}$ at different locations in the HSP 40/70 bed at 300 °C. (d) Wall-to-wall packing density distribution from DEM simulation. Inset: a schematic of THW measurement. (e) Average coordination number of granular media. The inset shows particle A having a coordination number of 3; letters $C$ and $N$ represent particles in contact and not in contact with particle A, respectively.

Figure 4

DEM simulation results of particle diffusive behavior. $v_y^{\prime }$ and $D_{yy}$ of flowing (a) CP 40/100 and (b) HSP 40/70. (c) $D_{yy}$ of the first layer of wall-adjacent particles. (d) Comparison of the $L_D$ and the measured increment in $D_{\mathrm{air}}$ between stationary and flowing particle beds.

Figure 5

$P_{\mathrm{center}}$ of flowing (a) CP 40/100 and (b) HSP 40/70.