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ABSTRACT
The effect of a wavy nanofluid/porous-medium interface on the natural convection of a Cu–water nanofluid in a differentially heated non-Darcy porous cavity was investigated using the ISPH method. Wall boundary conditions were applied by improved scheme using the analytical kernel renormalization function and its gradient based on the quintic kernel function. The effect of the Rayleigh number and the Darcy number on the heat transfer of Cu–water nanofluid with a various solid volume fraction were studied. Results showed that higher amplitude, height, and the undulation number of the sinusoidal interface between the nanofluid and porous medium layer lead to a decrease in the average Nusselt number.
Nomenclature
| a | = | dimensional amplitude of interface |
| A | = | dimensionless amplitude of interface |
| Cp | = | specific heat |
| Da | = | Darcy number |
| dP | = | average particle size |
| F | = | Forchheimer coefficient |
| g | = | gravitational acceleration |
| H | = | dimensionless height of porous medium |
| hs | = | smoothing length |
| h | = | dimensional height of porous medium |
| K | = | permeability |
| k | = | thermal conductivity |
| L | = | length and height of cavity |
| Nu | = | Nusselt number |
| p | = | dimensionless pressure |
| P | = | fluid pressure |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| T | = | Temperature |
| t | = | time |
| u | = | velocity vector |
| u, v | = | dimensional velocity components |
| U, V | = | dimensionless velocity components |
| x, y | = | dimensional coordinates |
| X, Y | = | dimensionless coordinates |
| Greek symbols | = | |
| α | = | thermal diffusivity |
| β | = | thermal expansion coefficient |
| γa | = | kernel renormalization function |
| ε | = | porosity |
| κ | = | undulation number of interface |
| θ | = | dimensionless temperature |
| ϕ | = | solid volume fraction |
| φ | = | phase shift |
| μ | = | dynamic viscosity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| σ | = | capacity ratio |
| τ | = | dimensionless time |
| Ψ | = | stream function |
| Subscripts | = | |
| f | = | fluid |
| nf | = | nanofluid |
| np | = | nanoparticle |
| p | = | porous medium |
Nomenclature
| a | = | dimensional amplitude of interface |
| A | = | dimensionless amplitude of interface |
| Cp | = | specific heat |
| Da | = | Darcy number |
| dP | = | average particle size |
| F | = | Forchheimer coefficient |
| g | = | gravitational acceleration |
| H | = | dimensionless height of porous medium |
| hs | = | smoothing length |
| h | = | dimensional height of porous medium |
| K | = | permeability |
| k | = | thermal conductivity |
| L | = | length and height of cavity |
| Nu | = | Nusselt number |
| p | = | dimensionless pressure |
| P | = | fluid pressure |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| T | = | Temperature |
| t | = | time |
| u | = | velocity vector |
| u, v | = | dimensional velocity components |
| U, V | = | dimensionless velocity components |
| x, y | = | dimensional coordinates |
| X, Y | = | dimensionless coordinates |
| Greek symbols | = | |
| α | = | thermal diffusivity |
| β | = | thermal expansion coefficient |
| γa | = | kernel renormalization function |
| ε | = | porosity |
| κ | = | undulation number of interface |
| θ | = | dimensionless temperature |
| ϕ | = | solid volume fraction |
| φ | = | phase shift |
| μ | = | dynamic viscosity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| σ | = | capacity ratio |
| τ | = | dimensionless time |
| Ψ | = | stream function |
| Subscripts | = | |
| f | = | fluid |
| nf | = | nanofluid |
| np | = | nanoparticle |
| p | = | porous medium |