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ABSTRACT
A numerical investigation has been carried out to study the natural convection and entropy generation within the three-dimensional enclosure with fillets. There are two immiscible fluids of Multi-Walled Carbon Nano-Tubes (MWCNTs)-water and air in the enclosure, which is simulated as two discrete phases. There are two heaters with constant heat flux at the sides, and the top and bottom walls are kept at cold constant temperature. The finite volume approach is applied to solve the governing equations. Moreover, a numerical method is developed based on the three-dimensional solution of Navier–Stokes equations. The fluid flow, heat transfer, and total volumetric entropy generation due to natural convection are studied carefully in a three-dimensional enclosure. The effects of the corner radius of fillets (r = 0, 0.15, 0.2, and 0.25), Rayleigh number (103 < Ra < 106), and solid volume fraction (φ = 0.002 and 0.01) of the nanofluid have been investigated on both natural convection characteristic and volumetric entropy generation.* The results show that the curved corner can be an effective method to control fluid flow and energy consumption, and three dimensional solutions render more accurate results.
Nomenclature
| R | = | radius of the corner |
| r | = | dimensionless radius of the corner (r = R/L) |
| h | = | length of the heater, m |
| b | = | distance of the heater from the bottom wall, m |
| g | = | gravitation acceleration, ms−2 |
| H | = | height of the cavity, m |
| D | = | depth of the cavity, m |
| L | = | width of the cavity, m |
| CP | = | specific heat, j Kg−1 K−1 |
| K | = | thermal conductivity, Wm−1 K−1 |
| Nus | = | local Nusselt number along the heater |
| Pr | = | Prandtl number, (νf,0/αf,0) |
| q″ | = | heat generation per area, (W/m2) |
| Ra | = | Rayleigh number, Ra = gβf,0((TH − TC))L3// νf,0αf,0 |
| Be | = | Bejan number |
| Stotal | = | total entropy generation |
| T | = | temperature, KTC cold temperature |
| = | dimensionless velocity components | |
| x′, y′, z′ | = | Cartesian coordinates, m |
| X, Y, Z | = | dimensionless coordinates (x′/L, y′/H, z′/D) |
| α | = | thermal diffusivity, m2 s−1(k/(ρCp)) |
| β | = | thermal expansion coefficient, k−1 |
| φ | = | solid volume fraction |
| θ | = | dimensionless temperature (T-TC/ΔT) |
| μ | = | dynamic viscosity, Nsm−2 |
| ν | = | kinematic viscosity, m2 s−1 (μ/ρ) |
| ρ | = | density, kgm−3 |
| Subscripts | = | |
| C | = | cold wall |
| H | = | hot wall |
| f,0 | = | pure fluid |
Nomenclature
| R | = | radius of the corner |
| r | = | dimensionless radius of the corner (r = R/L) |
| h | = | length of the heater, m |
| b | = | distance of the heater from the bottom wall, m |
| g | = | gravitation acceleration, ms−2 |
| H | = | height of the cavity, m |
| D | = | depth of the cavity, m |
| L | = | width of the cavity, m |
| CP | = | specific heat, j Kg−1 K−1 |
| K | = | thermal conductivity, Wm−1 K−1 |
| Nus | = | local Nusselt number along the heater |
| Pr | = | Prandtl number, (νf,0/αf,0) |
| q″ | = | heat generation per area, (W/m2) |
| Ra | = | Rayleigh number, Ra = gβf,0((TH − TC))L3// νf,0αf,0 |
| Be | = | Bejan number |
| Stotal | = | total entropy generation |
| T | = | temperature, KTC cold temperature |
| = | dimensionless velocity components | |
| x′, y′, z′ | = | Cartesian coordinates, m |
| X, Y, Z | = | dimensionless coordinates (x′/L, y′/H, z′/D) |
| α | = | thermal diffusivity, m2 s−1(k/(ρCp)) |
| β | = | thermal expansion coefficient, k−1 |
| φ | = | solid volume fraction |
| θ | = | dimensionless temperature (T-TC/ΔT) |
| μ | = | dynamic viscosity, Nsm−2 |
| ν | = | kinematic viscosity, m2 s−1 (μ/ρ) |
| ρ | = | density, kgm−3 |
| Subscripts | = | |
| C | = | cold wall |
| H | = | hot wall |
| f,0 | = | pure fluid |