Two fluid modeling of heat transfer in dense suspension flows in Couette cells

We propose a two fluid model (TFM) to capture thermal transport coupled to particle migration in shear flows of suspensions in the non-Brownian regime. Specifically, we introduce a closure relation for the inter-phase heat transfer coefficient as $K_h(\dot\gamma,\phi) = K_{h,0}[1 + \beta\phi(\|\dot{\boldsymbol{\gamma}}_p\|d_p^2/\alpha_p)^m]$, where $\phi$, $d_p$, $\dot{\boldsymbol{\gamma}}_p$ and $\alpha_p$ are the particle volume fraction, diameter, rate-of-shear-strain tensor and thermal diffusivity, respectively. Importantly, we capture shear-induced effects by using the full tensor $\dot{\boldsymbol{\gamma}}_p$, which is made possible by use of a TFM. We successfully calibrate $\beta$ and $m$ (and, thus, the TFM) by comparing to experiments in a Couette cell. Next, we perform a parametric study to understand how radial shear-induced migration influences the thermal transport performance in this system for different shear rates set by the rotation of the inner cylinder $\Omega_{in}$, $d_p$ and bulk volume fraction $\phi|_{t=0}$. Compared to a clear fluid, suspensions enhance thermal transport, and our computational model identifies the combinations of $d_p/(R_{out}-R_{in})$, $Pe_p = \Omega_{in} d_p^2/\alpha_p$, and $\phi|_{t=0}$ that maximize transport and/or efficiency.