Abstract
This investigation explores the natural convection in a water-filled straight inclined fracture in rock subject to a uniform background temperature increasing with depth. The numerical solutions cover aspect ratios from 2 to 50, with Rayleigh numbers of magnitude 1, 10, and 100. The inclination angle ranges from 0° to 90° to the horizontal. The results demonstrate that a straight inclined fracture experiences a gradient-driven convection flow whose strength is strongly dependent on aspect ratio. The flow increases as the fracture angle changes from either purely horizontal or purely vertical, with a maximum at 45°. It is observed that fractures with an aspect ratio as low as 10 exhibit average velocities at the midplane of nearly 90% of the values calculated from the analytical solution for the infinite aspect ratio limit.
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