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Onset of thermal convection in non-colloidal suspensions

Published online by Cambridge University Press:  06 April 2021

Changwoo Kang Open the ORCID record for Changwoo Kang [Opens in a new window] ,
Harunori N. Yoshikawa Open the ORCID record for Harunori N. Yoshikawa [Opens in a new window]  and
Parisa Mirbod Open the ORCID record for Parisa Mirbod [Opens in a new window]
Changwoo Kang
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor Street, Chicago, IL60607, USA Department of Mechanical Engineering, Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do54896, Republic of Korea
Harunori N. Yoshikawa
Affiliation:
Institut de Physique de Nice, Université Côte d'Azur, CNRS UMR 7010, 06100Nice, France
Parisa Mirbod*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor Street, Chicago, IL60607, USA
*
†Email address for correspondence: pmirbod@uic.edu
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Abstract

This study explores thermal convection in suspensions of neutrally buoyant, non-colloidal suspensions confined between horizontal plates. A constitutive diffusion equation is used to model the dynamics of the particles suspended in a viscous fluid and it is coupled with the flow equations. We employ a simple model that was proposed by Metzger, Rahli & Yin (J. Fluid Mech., vol. 724, 2013, pp. 527–552) for the effective thermal diffusivity of suspensions. This model considers the effect of shear-induced diffusion and gives the thermal diffusivity increasing linearly with the thermal Péclet number (Pe) and the particle volume fraction (ϕ). Both linear stability analysis and numerical simulation based on the mathematical models are performed for various bulk particle volume fractions $({\phi _b})$ ranging from 0 to 0.3. The critical Rayleigh number $(R{a_c})$ grows gradually by increasing ${\phi _b}$ from the critical value $(R{a_c} = 1708)$ for a pure Newtonian fluid, while the critical wavenumber $({k_c})$ remains constant at 3.12. The transition from the conduction state of suspensions is subcritical, whereas it is supercritical for the convection in a pure Newtonian fluid $({\phi _b} = 0)$. The heat transfer in moderately dense suspensions $({\phi _b} = 0.2\text{--}0.3)$ is significantly enhanced by convection rolls for small Rayleigh number (Ra) close to $R{a_c}$. We also found a power-law increase of the Nusselt number (Nu) with Ra, namely, $Nu\sim R{a^b}$ for relatively large values of Ra where the scaling exponent b decreases with ${\phi _b}$. Finally, it turns out that the shear-induced migration of particles can modify the heat transfer.

JFM classification

Instability: Nonlinear instability Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A128
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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