Two-dimensional analysis of low-pressure flows in an inclined square cavity with two fins attached to the hot wall

The gaseous low-pressure flow of a steady-state two-dimensional laminar natural convection heat transfer in a cavity with an attached two solid fins to the hot wall is numerically investigated. Such flows can be found in many engineering applications such as the “evacuated” solar collectors and in the receivers of the solar Parabolic Trough Collectors (PTCs), nuclear reactor cooling and electronic equipment cooling. Buoyancy effect is modeled using Boussinesq approximation. Effects of Knudsen and Rayleigh numbers, location and length of the fins, conductivity ratio and fins porosity, and the tilt angle on the flow and heat transfer characteristics are investigated. Physical parameters ranges in this study are as follows; 0≤Kn≤0.1, 103≤Ra≤106, LF takes the values of 0.25, 0.5 and 0.75 m, HF takes the values of 0.25_0.5, 0.25_0.75 and 0.5_0.75, 1≤Kr≤8000, 0≤ε≤1 and 0∘≤θ≤90∘. It is shown that Nusselt number depends directly on Rayleigh number and inversely on Knudsen number. In addition, it is found that attaching two solid fins to the hot wall will enhance the heat transfer for such flows. Moreover, it is found that the porous fins are superior to the solid fins as far as the heat transfer is concerned. In addition, it is shown that for the geometry where the lower fin height to cavity length ratio is 0.25 and the upper fin height to cavity length ratio is 0.75, the best heat transfer is achieved. In addition, for the fin lengths considered in the study, it is concluded that by increasing the length of the fin, a better heat transfer is achieved. Also, it is found that by increasing the tilt angle of the cavity, a better heat transfer is achieved up to a certain value which was found to be (30°) where beyond this value, Nusselt number will decrease. In addition, it is found that by increasing the conductivity ratio up to a certain value (103), better heat transfer is gained. Finally, a correlation among Nusselt number and the parameters investigated in this research proposed as Nu=0.02197ε0.00932sin(θ)0.00373Kr0.0273(h2/LF)2.814Ra0.13((h2−h1)/LF)1.373(h1/LF)1.615Kn0.37.