Abstract
This paper reports on an experimental study of mixed convection flow and heat transfer in a vented, differentially side-heated cubical cavity filled with a porous medium consisting of relatively large solid low-conductivity spheres. Rayleigh numbers and Reynolds numbers are varied over the ranges 6 × 106 < Ra < 7 × 107 and 240 < Re < 4250, respectively, for a fixed Prandtl number of Pr = 6.75, thus covering more than three decades in Richardson numbers Ri = Ra/(Re2 Pr). Heat transfer measurements were combined with measurements of the velocity field (using particle image velocimetry) and the temperature field (using liquid crystal thermography) to better understand the dependence of the Nusselt number, Nu, on the Richardson number. We observed three different flow and heat transfer regimes depending on the Richardson number. For Ri < 10, the flow structure and the Nusselt number scaling are similar to those for the pure forced convection, i.e., the Nusselt number scales as Nu ~ Re0.61 independent of Rayleigh number. For Ri > 40, natural convection dominates the flow in the vicinity of the heating wall. The Nusselt number becomes less sensitive to the Reynolds number and is mainly determined by the Rayleigh number. In the intermediate regime for 10 < Ri < 40, the upward directed natural convection flow at the heating wall competes with the downward directed forced flow leading to a minimum effective Nusselt number. A Nusselt number correlation is derived that is valid in the range 0.1 < Ri < 100 covering all three regimes.
Highlights
Natural convection in closed cavities has been among the most widely studied topics in fluid dynamics due to its simple geometry and relevance to many engineering applications
The Nusselt numbers were measured both in the pure-fluid cavity without porous medium and in the same cavity filled with a porous medium consisting of a Body-Centered Tetragonal (BCT) packing of d/H = 0.2 spheres to identify the effect of the porous medium on the heat transfer
Mixed convection in a vented cavity filled with a porous medium consisting of relatively large (d/L = 0.20) low-conductivity spheres was experimentally studied
Summary
Natural convection in closed cavities has been among the most widely studied topics in fluid dynamics due to its simple geometry and relevance to many engineering applications. Natural convection is characterized by the Rayleigh number, Ra, which measures the strength of the buoyancy forces relative to diffusive forces, and the Prandtl number, Pr, which is the ratio of the kinematic viscosity to the thermal diffusivity of the working fluid. J/kg.K Diameter of spheres, m Gravitational acceleration, m/s2 Height of the inlet/outlet ports, m Inner height of the heating/cooling walls, m Thermal conductivity, W/m.K Inner dimension of the cavity, m Nusselt number Effective Nusselt number Electrical power supplied to the hot wall, W Prandtl Number Rate of heat loss, W Rate of heat carried by the outflow, W Rate of heat supplied to the hot wall, W Rayleigh Number Reynolds Number Richardson Number Time, s Temperature, K Bulk inflow/outflow velocity, V / (h × L), m/s Vertical velocity component, m/s Volumetric flowrate, m3/s Cartesian coordinates, m Greek symbols α.
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