Heat transfer and shear-induced migration in dense non-Brownian suspension flows: modelling and simulation

Abstract

Modelling and simulation are developed, generalized and validated for both heat transfer and shear-induced particle migration in dense non-colloidal laminar suspension flows. Past theory and measurements for the effective thermal conductivity in porous materials at zero shear rate are coupled to more recent effective thermal diffusivity measurements of sheared suspensions. The suspension effective heat transfer affected by the local shear rate ($\dot{\unicode[STIX]{x1D6FE}}$), the phenomenon of shear-induced particle migration (SIM), the buoyancy effects ($\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}$) and the thermal Péclet number ($Pe_{d_{p}}=\dot{\unicode[STIX]{x1D6FE}}d_{p}^{2}/\unicode[STIX]{x1D6FC}_{f}$, where $d_{p}$ is the diameter of rigid particles and $\unicode[STIX]{x1D6FC}_{f}$ is the fluid phase thermal diffusivity) at the particle scale are all considered in the present constitutive three-dimensional modelling. Moreover, the influence of the temperature, the shear rate and the particle volume fraction ($\unicode[STIX]{x1D719}$) on the suspension effective viscosity ($\unicode[STIX]{x1D702}_{S}$), the suspension effective thermal properties and the fluid density ($\unicode[STIX]{x1D70C}_{f}$) are taken also into account. The present contribution represents an emerging field of heat transfer applications of complex fluid flows and is very beneficial for many future applications where concentrated suspension laminar flows with conjugate heat transfer may be present (e.g. for designing more innovative and compact heat exchangers).