The study of thermal convection in porous media is of both fundamental and practical interest. Typically, numerical studies have relied on the volumeaveraged Darcy–Oberbeck–Boussinesq (DOB) equations, where convection dynamics are assumed to be controlled solely by the Rayleigh number ( Ra ). Nusselt numbers ( Nu ) from these models predict Nu – Ra scaling exponents of 0.9–0.95. However, experiments and direct numerical simulations (DNS) have suggested scaling exponents as low as 0.319. Recent findings for solutal convection between DNS and DOB models have demonstrated that the ‘porescale parameters’ not captured by the DOB equations greatly influence convection. Thermal convection also has the additional complication of different thermal transport properties (e.g. solidtofluid thermal conductivity ratio k s / k f and heat capacity ratio σ ) in different phases. Thus, in this work we compare results for thermal convection from the DNS and DOB equations. On the effects of pore size, DNS results show that Nu increases as pore size decreases. Megaplumes are also found to be more frequent and smaller for reduced pore sizes. On the effects of conjugate heat transfer, two groups of cases (Group 1 with varying k s / k f at σ = 1 and Group 2 with varying σ at k s / k f = 1) are examined to compare the Nu – Ra relations at different porosity ( ϕ ) and k s / k f and σ values. Furthermore, we report that the boundary layer thickness is determined by the pore size in DNS results, while by both the Rayleigh number and the effective heat capacity ratio, $\bar{\phi } = \phi + (1  \phi )\sigma$ , in the DOB model.
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Onset of thermal convection in noncolloidal suspensions
This study explores thermal convection in suspensions of neutrally buoyant, noncolloidal 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 shearinduced 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 powerlaw 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 shearinduced migration of particles can modify the heat transfer.
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 Award ID(s):
 1854376
 NSFPAR ID:
 10278348
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 915
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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