Bavandla, Krishna Chandra2025-02-142025-02-142024-06https://hdl.handle.net/11299/269994University of Minnesota Ph.D. dissertation. June 2024. Major: Mechanical Engineering. Advisors: Vinod Srinivasan, Richard Goldstein. 1 computer file (PDF); xiv, 145 pages.Natural convective heat transfer experiments are conducted in a horizontal enclosure filled with a gas-saturated porous medium composed of solid sphere particles. The height-to-pore scale ratio (H/d) is varied from 25 to 150, yielding a low Darcy number (5.68 × 10^−8 ≤ Da ≤ 1.94 × 10^−6), which satisfies the porous medium assumption more rigorously. Solid particles of different sizes, such as 1 mm, 3 mm, and 6 mm, are used in an enclosure of unity aspect ratio (width-to-height ratio, AR = L/H). The 3 mm particles are also used in enclosures of different aspect ratios, 0.75, 0.6, and 0.5, to achieve these different H/d combinations. Different solid particles, such as a stack of glass, steel, and aluminum balls, are used as porous systems. The maximum values attained for the modified Rayleigh numbers (Ra^∗ up to 6150) and fluid Rayleigh numbers (Ra_f up to 2.5 × 10^11) at these low Darcy numbers enable access to both the Darcy and Forchheimer flow regimes. Compressed argon is used as the working fluid to achieve these high fluid Rayleigh numbers. At first, the effect of the Darcy number is studied by conducting experiments with six different H/d combinations varying from 25 to 150 (or 5.87 × 10^−8 ≤ Da ≤ 1.94 × 10^−6 ) using the glass sphere particles, ensuring the same solid-to-fluid thermal conductivity ratio. Before performing the pressurized gas experiments, a vacuum experiment is conducted to find the stagnant thermal conductivity of each porous system by suppressing the advection inside the pressure vessel. Later, the natural convective heat transfer is measured for fluid Rayleigh numbers varied by three orders of magnitude. The stagnant thermal conductivity value is essentially constant over all test cases investigated. Except for H/d = 150, it was possible to conduct experiments starting from the pre-convective regime, passing through the Darcy regime, and ending up in the Forchheimer regime without altering the porous matrix microstructure. These studies found that the heat transfer relationship just beyond the onset of convection is in good accordance with theory and previous literature, varying linearly with the modified Rayleigh number. The data diverge as a function of the Darcy number for higher modified Rayleigh numbers, depending on both the Darcy number and the modified Rayleigh number. Transition points between the Darcy and Forchheimer regimes are estimated. At the highest fluid Rayleigh numbers, the data with the largest pore scales show some evidence of moving towards a regime similar to that of Rayleigh-Bénard convection, where boundary layer and plume length scales are small enough that the details of the porous medium cease to matter. It is argued that even in this regime, the boundary layer length scales are not diminished enough to make the contribution of Brinkman drag significant. Three additional sets of experiments are conducted by employing 1 mm and 3 mm aluminum spheres, and 3 mm steel spheres, all within an enclosure of a unity aspect ratio. These experiments, when combined with the datasets from previous porous systems containing 1 and 3 mm glass sphere particles, yield a total of five porous systems. These five porous systems corresponding to different H/d and thermal conductivities are used to understand the effects of the solid-to-fluid thermal conductivity ratio on natural convective heat transfers. Two different diameters, 1 and 3 mm, are used to establish H/d = 150 and H/d = 50 combinations, respectively. The H/d = 150 combination spans only the Darcy regime, whereas H/d = 50 helps understand the solid thermal conductivity effect in the Forchheimer regime. At low modified Rayleigh numbers (Ra^∗), the Nusselt number (Nu) is independent of the medium conductivity. As Ra^∗ increases, the data diverges, with Nusselt numbers decreasing with increased solid-to-fluid thermal conductivity ratio at a fixed Ra^∗. This non-intuitive result is shown to be the result of the choice of Ra^∗ and Da as the controlling parameters since the heat transfer coefficient appears independent of the conductivity ratio. When the data are expressed by scaling with the modified Pranftl number (Pr_p), it is shown that the data for multiple parameter combinations collapse onto a single curve, which also agrees well with some theoretical predictions. In light of this finding, the data from available literature are assessed, and it is proposed that deviations from theory are likely the result of the strong porous medium condition (low Da) not being satisfied.enDarcy regimeExperimentalForchheimer regimeNatural convectionPorous mediaRayleigh-BénardThesis or Dissertation