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ABSTRACT
The effect of porous rib arrays on the heat transfer and entropy generation of laminar nanofluid flow inside annuli is studied numerically, using a two-phase mixture model for nanofluid flow simulation. Porous media, nanoparticles, and vortex formation are simultaneously affecting the characteristics of the system. Results showed that the permeability and height of porous ribs have significant effects on the thermal performance of system. Vortex zones also affect the trend of variation of entropy and performance numbers, and local optimums exist for these two parameters. The role of nanofluid in heat transfer enhancement in recirculating zones is more significant for higher volume fractions.
Nomenclature
| A | = | heat transfer surface (m2) |
| A | = | acceleration (m/s) |
| Be | = | Bejan number |
| Cd | = | drag coefficient |
| Da | = | Darcy number |
| Do | = | external diameter of the annulus (m) |
| dp | = | nanoparticles diameter (m) |
| Dh | = | hydraulic diameter (m); (Dh = 4A/P) |
| fdrag | = | drag function |
| FFI | = | fluid friction irreversibility |
| g | = | acceleration due to gravity (m/s2) |
| h | = | heat transfer coefficient (W/m2/K) |
| HTI | = | heat transfer irreversibility |
| K | = | permeability of porous medium (m2) |
| Ns | = | entropy generation number |
| Nu | = | Nusselt number |
| P | = | pressure (Pa) |
| Δp | = | pressure drop per unit length (Pa/m) |
| q″ | = | uniform wall heat flux (W/m2) |
| r | = | radial coordinate (m) |
| Re | = | Reynolds number |
| Rh | = | hydraulic radius (m) |
| ri | = | internal radius of annulus (m) |
| ro | = | external radius of annulus (m) |
| rp | = | porous medium radius (m) |
| Sgen | = | entropy generation rate (W/m3/K) |
| Sgen,T | = | thermal entropy gen. rate (W/m3/K) |
| Sgen,f | = | friction entropy gen. rate (W/m3/K) |
| T | = | temperature (K) |
| Tin | = | inlet temperature (K) |
| Tw | = | wall temperature (K) |
| Tb | = | bulk temperature (K) |
| Uin | = | inlet velocity (ms) |
| V | = | volume (m3) |
| = | velocity vector (ms) | |
| vx,vr | = | velocity components in x, r directions (ms) |
| W1 | = | porous rib width (m) |
| W2 | = | porous rib height (m) |
| W3 | = | porous block spacing (m) |
| x,r | = | cylindrical coordinates (m) |
| Greek symbols | = | |
| ε | = | porosity |
| μ | = | viscosity (kg/m/s) |
| ρ | = | density (kg/m3) |
| λ | = | thermal conductivity (W/m/K) |
| ϕ | = | volume fraction |
| Subscripts | = | |
| bf | = | base fluid |
| c | = | clear fluid |
| p | = | porous region |
| in | = | inlet |
| m | = | mixture |
| eff | = | effective |
| np | = | nanoparticle |
| s | = | solid |
| w | = | wall |
| dr | = | drift |
| k | = | of water or nanoparticle |
Nomenclature
| A | = | heat transfer surface (m2) |
| A | = | acceleration (m/s) |
| Be | = | Bejan number |
| Cd | = | drag coefficient |
| Da | = | Darcy number |
| Do | = | external diameter of the annulus (m) |
| dp | = | nanoparticles diameter (m) |
| Dh | = | hydraulic diameter (m); (Dh = 4A/P) |
| fdrag | = | drag function |
| FFI | = | fluid friction irreversibility |
| g | = | acceleration due to gravity (m/s2) |
| h | = | heat transfer coefficient (W/m2/K) |
| HTI | = | heat transfer irreversibility |
| K | = | permeability of porous medium (m2) |
| Ns | = | entropy generation number |
| Nu | = | Nusselt number |
| P | = | pressure (Pa) |
| Δp | = | pressure drop per unit length (Pa/m) |
| q″ | = | uniform wall heat flux (W/m2) |
| r | = | radial coordinate (m) |
| Re | = | Reynolds number |
| Rh | = | hydraulic radius (m) |
| ri | = | internal radius of annulus (m) |
| ro | = | external radius of annulus (m) |
| rp | = | porous medium radius (m) |
| Sgen | = | entropy generation rate (W/m3/K) |
| Sgen,T | = | thermal entropy gen. rate (W/m3/K) |
| Sgen,f | = | friction entropy gen. rate (W/m3/K) |
| T | = | temperature (K) |
| Tin | = | inlet temperature (K) |
| Tw | = | wall temperature (K) |
| Tb | = | bulk temperature (K) |
| Uin | = | inlet velocity (ms) |
| V | = | volume (m3) |
| = | velocity vector (ms) | |
| vx,vr | = | velocity components in x, r directions (ms) |
| W1 | = | porous rib width (m) |
| W2 | = | porous rib height (m) |
| W3 | = | porous block spacing (m) |
| x,r | = | cylindrical coordinates (m) |
| Greek symbols | = | |
| ε | = | porosity |
| μ | = | viscosity (kg/m/s) |
| ρ | = | density (kg/m3) |
| λ | = | thermal conductivity (W/m/K) |
| ϕ | = | volume fraction |
| Subscripts | = | |
| bf | = | base fluid |
| c | = | clear fluid |
| p | = | porous region |
| in | = | inlet |
| m | = | mixture |
| eff | = | effective |
| np | = | nanoparticle |
| s | = | solid |
| w | = | wall |
| dr | = | drift |
| k | = | of water or nanoparticle |