Abstract
We model hydrothermal convection using a partial differential equation formed by Darcy velocity and temperature—the velocity formulation. Using the Elder problem as a benchmark, we found that the velocity formulation is a valid model of hydrothermal convection. By performing simulations with Rayleigh numbers in the non-oscillatory regime, we show that multiple quasi-steady-state solutions can be one of the reasons that caused the Nusselt–Rayleigh discrepancy found in previous experiments. The results reveal more understandings about the nature of uncertainty of convection modes in porous media.
Highlights
Natural convection in porous media occurs in various geological and industrial settings, such as groundwater, geothermal reservoirs, heat sinks and thermal energy storage
We present the conservation laws that model natural convection in porous media under the following assumptions mentioned by Horne (1979):
We found out that the separation angle of the box [21∕4, 21∕4] between modes (0, 1) and (1, 1) using the basin stability analysis
Summary
Natural convection in porous media occurs in various geological and industrial settings, such as groundwater, geothermal reservoirs, heat sinks and thermal energy storage. We use the Rayleigh number (Ra) to characterize the material properties of porous media, such as permeability, fluid density and the temperature difference between the top and bottom boundaries. We measure the quality of convective heat transfer using the Nusselt number (Nu). It is beneficial to correlate the Rayleigh number and the Nusselt number. Cheng (1979) compiled the experimental, analytical and numerical results of the Nusselt number and the Rayleigh number for convection heat transfer in a porous layer heated from below. The compilation showed widespread Nusselt numbers for a particular
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