In the present study, we analyse individual and combined effects of conductive horizontal walls and conductive fins on the natural convection of air in side heated cavities (SHC). The flow and heat transfer are studied for Rayleigh numbers in the range of 10⁴−−10⁹: Direct Numerical Simulation (DNS) is conducted for the lower and Large Eddy Simulation (LES) for the higher Rayleigh numbers (>10⁸). Thermally conductive walls destabilize the flow yielding an earlier transition to turbulence and expedite the decay in boundary layer thickness with increase in Rayleigh number. The preheating/precooling along the conductive walls reduces the actual heat transfer at the vertical walls. Above the fin, instabilities are only marginally enhanced for adiabatic horizontal walls, whereas for conductive horizontal walls, plumes erupt from the fin. This localized Rayleigh-Bénard-like effect triggers 3D instabilities in the entire flow field and yields a steeper slope in Nusselt-Rayleigh diagram. The presence of a fin increases the integral heat transfer by 18% for adiabatic and 21% for conductive horizontal walls. We show that 2D and 3D simulations are similar for the smooth cases (i.e., without fin), but differ by 4% and 13% for the adiabatic and conductive fin cases respectively. The local heat transfer characteristics even deviates up to 50%, therefore a 2D simplification should be avoided.

We investigate natural convection driven by a horizontal temperature gradient and a vertical concentration gradient in fluid-filled enclosures with obstructions inside it. Within the domain, nine adiabatic and impermeable cylinders are placed, occupying 30% of the domain volume. The Boussinesq approximation is used to account for density variations within the fluid and the flow is fully resolved. The solutal Rayleigh number has been fixed at Ra_C=10⁶ and the Prandtl number at Pr=5.4. The Lewis number has been varied in the range of 1 ≤ Le ≤ 100 and the buoyancy ratio in the range of 0.1 ≤ |N| ≤ 10. The rate of heat and mass transfer are compared to those found in single-scalar natural convection, i.e solely thermal or concentration driven convection. Besides, the obtained heat and mass transfer rate in the cylinder-packed enclosure have been compared to those found in a fluid-only domain. We observe that the addition of a destabilizing concentration gradient to a side-heated enclosure results in heat transfer enhancement, which decreases with Lewis number and thermal Rayleigh number. Similarly, the temperature gradient increases the mass transfer, especially at high Lewis numbers and lower concentration buoyancy force over its thermal counterpart. Although the presence of the cylindrical obstacles reduced the flow velocity, the mass transfer was enhanced at lower buoyancy ratio.

We numerically investigate natural convection in a bottom-heated top-cooled cavity, fully and partially filled with adiabatic spheres (with diameter-to-cavity-size ratio d/L=0.2) arranged in a Simple Cubic Packing (SCP) configuration. We study the influence of packing height and location of porous media. We carry out the simulations using water as the working fluid with Prandtl number, Pr=5.4 at Rayleigh number Ra=1.16×10⁵, 1.16 × 10⁶ and 2.31 × 10⁷. The applicability and suitability of Darcy-Forchheimer assumption to predict the global heat transfer is analysed by comparing it with the pore-structure resolved simulations. We found that the heat transfer in pore-structure resolved simulations is comparable to that in fluid-only cavities at high Rayleigh numbers, irrespective of the number of layers of packing and its location. Discrepancies in heat transfer between the Darcy-Forchheimer and the fully resolved simulations are observed when the porous medium is close to the isothermal wall and at high Ra, while it vanishes when the porous medium is away from the isothermal bottom wall.

We report numerical simulations of assisting and opposing mixed convection in a side-heated, side-cooled cavity packed with relatively large solid spheres. The mixed convection is generated by imposing a movement on the isothermal vertical walls, either in or opposite to the direction of natural convection flow. For a fluid Prandtl number of 5.4 and fluid Rayleigh numbers of 10⁶ and 10⁷, we varied the modified Richardson number from 0.025 to 500. As in fluids-only mixed convection, we find that the mutual interaction between forced and natural convection, leading to a relative heat transfer enhancement in assisting - and a relative heat transfer suppression in opposing - mixed convection, is most prominent at a Richardson number of approximately one, when the Richardson number is modified with the Darcy number Da and the Forchheimer coefficient C_f = 0.1 as Ri_m = Ri × Da^0.5/C_f. We focus on local flow and heat transfer variations in order to explain differences in local and average heat transfer between a coarse grained and fine grained (Darcy-type) porous medium, at equal porosity and permeability. We found that the ratio between the thermal boundary layer thickness at the isothermal walls and the average pore size plays an important role in the effect that the grain and pore size have on the heat transfer. When this ratio is relatively large, the thermal boundary layer is locally disturbed by the solid objects and these objects cause local velocities and flow recirculation perpendicular to the walls, resulting in significant differences in the wall-averaged heat transfer. The local nature of the interactions between flow and solid objects cannot be captured by a volume averaged approach, such as a Darcy model.

We report numerical simulations of natural convection and conjugate heat transfer in a differentially heated cubical cavity packed with relatively large hydrogel beads (d/L=0.2) in a Simple Cubic Packing configuration. We study the influence of a spatially non-uniform, sinusoidally varying, wall temperature on the local flow and heat transfer, for a solid-to-fluid conductivity ratio of 1, a fluid Prandtl number of 5.4, and fluid Rayleigh numbers between 10⁵ and 10⁷. We present local and overall flow and heat transfer results for both sphere packed and water-only filled cavities, when subjected to variations of the wall temperature at various combinations of the amplitude and characteristic phase angle of the imposed wall temperature variations. It is found that imposing a sinusoidal spatial variation in the wall temperature may significantly alter the local flow and heat transfer, and consequently the overall heat transfer. At identical average temperature difference, applying a spatial variation in wall temperature at well-chosen phase angle can lead to significant heat transfer enhancement when compared to applying uniform wall temperatures. However, this is achieved at the cost of increased entropy generation.

This paper reports on an experimental study of natural convection in an enclosure that is heated at the bottom and cooled at the top, filled with a packed bed of relatively large solid spheres. Nusselt numbers were measured for various sphere conductivities, spheres sizes and sphere packings for Rayleigh numbers varying between 10⁷ and 10⁹. The Nusselt number measurements showed that at lower Rayleigh numbers, the heat transfer is lower than that for pure Rayleigh-Bénard convection, with the difference depending on packing type, size, and conductivity of the spheres. However, at high Rayleigh numbers, there exists an asymptotic regime where the convective contribution of the total heat transfer for all sphere conductivities, sizes, and packing types collapse on a single curve which is very close to the curve for pure Rayleigh-Bénard convection. Refractive index-matching of the fluid and the solid spheres enabled the use of particle image velocimetry and liquid crystal thermography to obtain highly resolved velocity and temperature fields. The comparison of the velocity and temperature fields for the two heat transfer regimes showed that the velocity magnitudes inside the pores in the core region are much higher in the asymptotic regime than those in the low Rayleigh number regime, which lead to a deeper penetration of cold and hot fluid elements and higher heat transfer.

We report numerical simulations of fluid natural convection with conjugate heat transfer in a bottom-heated, top-cooled cubical cavity packed with relatively large (d/L=0.2) solid spheres in a Body Centred Tetragonal (BCT) configuration. We study largely varying solid-to-fluid thermal conductivity ratios between 0.3 and 198, for a fluid Prandtl number of 5.4 and fluid Rayleigh numbers between 1.16 × 10 ⁶ and 1.16 × 10 ⁸ and compare global heat transfer results from our present simulations to our previously published experimental results. The interplay between convection suppression due to the solid packing, and conductive heat transfer in the packing leads to three different regimes, each with a distinct impact of the solid packing on the flow and heat transfer. At low Rayleigh numbers ≈ 10 ⁶ , all packings suppress convective flow. Compared to fluid only Rayleigh–Bénard convection, heat transfer is therefore reduced in low conductivity packings, whereas for high conductivity packings it is increased due to significant conductive heat transfer. At intermediate Rayleigh numbers ≈ 10 ⁷ , low conductivity packings no longer suppress convection, whereas flow is still suppressed in high conductivity packings due to the thermal stratification imposed on the fluid by the solid. Consequently, heat transfer is lower compared to fluid only Rayleigh–Bénard convection, even in high conductivity packings. With a further increase of Rayleigh number ≳ 10 ⁸ , convection starts to be the dominant heat transfer mechanism in all packings, and convective heat transfer is close to that for fluid only Rayleigh–Bénard convection. The contribution of solid conduction in high conductivity packings causes the overall heat transfer to be above that for Rayleigh–Bénard convectin.