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ABSTRACT
In this work, a 2-D numerical investigation and a sensitivity analysis have been done on the natural convection heat transfer in a wavy surface cavity filled with a nanofluid. For this purpose, the effects of three parameters, the Rayleigh number (103 ≤Ra ≤ 105), nanoparticles volume fraction (0.00 ≤ϕ ≤ 0.04), and the shape of the nanoparticles (spherical, blade, and cylindrical), are studied. Discretization of the governing equations is performed using a finite volume method (FVM) and solved with the SIMPLE algorithm. The effective parameters analysis is processed utilizing the Response Surface Methodology (RSM). Comparison with previously published work is performed and the results are found to be in good agreement. The results showed that increasing the Rayleigh number and ϕ increases the mean Nusselt number and the total entropy generation. Also, the nanofluids with spherical- and cylindrical-shaped nanoparticles have the highest and lowest Nusselt numbers and entropy generations, respectively. The sensitivity of the mean Nusselt number and entropy generation ratio to Ra and ϕ is found to be positive, whereas it is predicted to be negative to nanoparticles shape.
Nomenclature
| Cp | = | specific heat (J kg−1 K−1) |
| Ec | = | Eckert number, |
| g | = | gravitational acceleration (m s−2) |
| H | = | height of the cavity (m) |
| k | = | thermal conductivity (Wm−1K−1) |
| Nu | = | Nusselt number |
| p | = | pressure (N m−2) |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| q″0 | = | heat flux (W m−2) |
| Ra | = | Rayleigh number, |
| S | = | entropy generation (W m−3 K−1) |
| T | = | temperature (K) |
| TL | = | low temperature (K) |
| u*, v* | = | velocity components in transformed coordinate system |
| U, V | = | dimensionless of velocity component |
| W | = | width of cavity (m) |
| x, y | = | x- and y-axis coordinates, respectively |
| X, Y | = | dimensionless Cartesian coordinates |
| α | = | thermal diffusivity, |
| β | = | thermal expansion coefficient, (K−1) |
| ϕ | = | nanoparticle volume fraction (%) |
| µ | = | dynamic viscosity (Pa s) |
| θ | = | dimensionless temperature |
| ρ | = | density (kg m−3) |
| ξ | = | transformed coordinate system |
| υ | = | kinematics viscosity(m2 s−1) |
| = | Subscripts | |
| bf | = | base fluid |
| p | = | particle |
| nf | = | nanofluid |
Nomenclature
| Cp | = | specific heat (J kg−1 K−1) |
| Ec | = | Eckert number, |
| g | = | gravitational acceleration (m s−2) |
| H | = | height of the cavity (m) |
| k | = | thermal conductivity (Wm−1K−1) |
| Nu | = | Nusselt number |
| p | = | pressure (N m−2) |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| q″0 | = | heat flux (W m−2) |
| Ra | = | Rayleigh number, |
| S | = | entropy generation (W m−3 K−1) |
| T | = | temperature (K) |
| TL | = | low temperature (K) |
| u*, v* | = | velocity components in transformed coordinate system |
| U, V | = | dimensionless of velocity component |
| W | = | width of cavity (m) |
| x, y | = | x- and y-axis coordinates, respectively |
| X, Y | = | dimensionless Cartesian coordinates |
| α | = | thermal diffusivity, |
| β | = | thermal expansion coefficient, (K−1) |
| ϕ | = | nanoparticle volume fraction (%) |
| µ | = | dynamic viscosity (Pa s) |
| θ | = | dimensionless temperature |
| ρ | = | density (kg m−3) |
| ξ | = | transformed coordinate system |
| υ | = | kinematics viscosity(m2 s−1) |
| = | Subscripts | |
| bf | = | base fluid |
| p | = | particle |
| nf | = | nanofluid |
Notes
1semi-implicit method for pressure-linked equations consistent.