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ABSTRACT
The problem of natural convection in an eccentric annulus between two horizontal cylinders filled with Cu–Al2O3/water hybrid nanofluids is investigated numerically in this paper. The inner cylinder wall is heated at a uniform temperature whereas the outer wall is kept isothermally cooled. The basic equations that govern the problem are formulated in the bipolar coordinates and written in terms of the vorticity-stream function equations using the dimensionless form for the bidimensional, laminar, and incompressible flow under steady-state conditions. The dimensionless equations are discretized using the finite-volume method and solved by a FORTRAN program. A numerical parametric study is performed for an annulus filled with regular water, Al2O3/water nanofluid, and Cu–Al2O3/water hybrid nanofluid for various volume fractions of nanoparticles and hybrid nanoparticles (0 ≤ ϕ ≤0.12) and Rayleigh numbers (103 ≤ Ra ≤ 106). It is found that employing a Cu–Al2O3/water hybrid nanofluid provides a better thermal and dynamic performance compared with the similar Al2O3/water nanofluid.
Nomenclature
| Cp | = | specific heat at constant pressure (J kg−1 K−1) |
| D | = | hydraulic diameter (m) |
| g | = | gravitational acceleration (m. s−2) |
| h | = | scale factor (m) |
| H | = | dimensionless of h |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number |
| R | = | radius ratio |
| Ra | = | Rayleigh number |
| Ri, Ro | = | inner and outer radii of annulus, respectively (m) |
| T | = | dimension temperature (K) |
| u, v | = | axial and radial velocities (m.s−1) |
| Vξ, Vθ | = | velocity components in the ξ, θ directions. (m.s−1) |
| x, y | = | Cartesian coordinates (m) |
| Greek symbols | = | |
| α | = | thermal diffusivity (m2. s−1) |
| β | = | thermal expansion coefficient (K−1). |
| γ | = | orientation angle of the annulus (°) |
| λ | = | thermal conductivity (Wm−1 K−1) |
| μ | = | dynamic viscosity (kgm−1 s−1) |
| υ | = | kinematic viscosity (m2 s−1) |
| ρ | = | density (kg m−3) |
| ϕ | = | volume fraction of the nanoparticles |
| θ | = | second bipolar coordinate |
| ξ | = | first bipolar coordinate |
| ψ | = | stream function (m2. s−1) |
| ω | = | vorticity (s−1) |
| ε | = | absolute eccentricity (m) |
| σ | = | dimensionless eccentricity |
| Subscripts | = | |
| c | = | cold |
| h | = | hot |
| nf | = | nanofluid |
| hnf | = | hybrid nanofluid |
| f | = | fluid |
| p | = | solid particles |
| i | = | inner cylinder |
| o | = | outer cylinder |
| Superscript | = | |
| * | = | dimensionless parameters |
Nomenclature
| Cp | = | specific heat at constant pressure (J kg−1 K−1) |
| D | = | hydraulic diameter (m) |
| g | = | gravitational acceleration (m. s−2) |
| h | = | scale factor (m) |
| H | = | dimensionless of h |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number |
| R | = | radius ratio |
| Ra | = | Rayleigh number |
| Ri, Ro | = | inner and outer radii of annulus, respectively (m) |
| T | = | dimension temperature (K) |
| u, v | = | axial and radial velocities (m.s−1) |
| Vξ, Vθ | = | velocity components in the ξ, θ directions. (m.s−1) |
| x, y | = | Cartesian coordinates (m) |
| Greek symbols | = | |
| α | = | thermal diffusivity (m2. s−1) |
| β | = | thermal expansion coefficient (K−1). |
| γ | = | orientation angle of the annulus (°) |
| λ | = | thermal conductivity (Wm−1 K−1) |
| μ | = | dynamic viscosity (kgm−1 s−1) |
| υ | = | kinematic viscosity (m2 s−1) |
| ρ | = | density (kg m−3) |
| ϕ | = | volume fraction of the nanoparticles |
| θ | = | second bipolar coordinate |
| ξ | = | first bipolar coordinate |
| ψ | = | stream function (m2. s−1) |
| ω | = | vorticity (s−1) |
| ε | = | absolute eccentricity (m) |
| σ | = | dimensionless eccentricity |
| Subscripts | = | |
| c | = | cold |
| h | = | hot |
| nf | = | nanofluid |
| hnf | = | hybrid nanofluid |
| f | = | fluid |
| p | = | solid particles |
| i | = | inner cylinder |
| o | = | outer cylinder |
| Superscript | = | |
| * | = | dimensionless parameters |