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ABSTRACT
In this study, numerical simulations by single- and two-phase models of nanofluids turbulent forced convection in a three-dimensional arc rib-grooved channel with constant wall temperature are investigated. The elliptical, coupled, steady-state, three-dimensional governing partial differential equations for turbulent forced convection of nanofluids are solved numerically using the finite volume approach. The average Nusselt number of arc rib-grooved channels is found to improve more with smaller rib-grooved height ratios, and some ratios of arc rib-grooved pitch. In addition, the optimization of this problem is also presented by using the response surface methodology (RSM) and the genetic algorithm (GA) method. It is found that the objective function E is better at Re = 10,000, and the arc rib-groove has a 42.1% enhancement.
Nomenclature
| A | = | acceleration, m/s2 |
| A | = | bottom area of the heating zone, mm2 |
| = | closure coefficients | |
| Cp | = | specific heat of constant pressure, J/kg · K |
| dp | = | particles diameter, mm |
| Dh | = | hydraulic diameter, mm |
| E | = | performance factor |
| fdrag | = | drag function |
| G | = | acceleration of gravity, m/s2 |
| G | = | generation of turbulent kinetic energy, kg/m · s3 |
| H | = | channel height, mm |
| H | = | convection heat transfer coefficient, W/m · K |
| K | = | conduction heat transfer coefficient, W/m · K |
| K | = | turbulent kinetic energy, m2/s2 |
| L1 | = | inlet length, mm |
| L2 | = | length of the heating zone, mm |
| L | = | total length, mm |
| = | average Nusselt number | |
| P | = | rib-grooved pitch, mm |
| Δp | = | pressure drop, Pa |
| q″ | = | heat flux, W/m2 |
| r1 | = | rib-grooved height, mm |
| r2 | = | rib-grooved half-width, mm |
| Re | = | Reynolds number |
| T | = | temperature, K |
| Vdr | = | drift velocity, m/s |
| Vpf | = | relative velocity, m/s |
| u, v, w | = | velocity component, m/s |
| V | = | velocity, m/s |
| x, y, z | = | Cartesian x, y, z-coordinate, mm |
| ρ | = | density of the fluid, kg/m3 |
| μ | = | dynamic viscosity, kg/m · s |
| ϵ | = | turbulent kinetic dissipation, m2/s3 |
| τ | = | stress tensor, N/m2 |
| φ | = | nanoparticle volume concentration |
| Subscripts | = | |
| 0 | = | smooth channel |
| bf | = | base fluid |
| eff | = | effective |
| f | = | fluid |
| in | = | inlet |
| m | = | mean |
| nf | = | nanofluid |
| out | = | outlet |
| p | = | particle |
| w | = | wall |
Nomenclature
| A | = | acceleration, m/s2 |
| A | = | bottom area of the heating zone, mm2 |
| = | closure coefficients | |
| Cp | = | specific heat of constant pressure, J/kg · K |
| dp | = | particles diameter, mm |
| Dh | = | hydraulic diameter, mm |
| E | = | performance factor |
| fdrag | = | drag function |
| G | = | acceleration of gravity, m/s2 |
| G | = | generation of turbulent kinetic energy, kg/m · s3 |
| H | = | channel height, mm |
| H | = | convection heat transfer coefficient, W/m · K |
| K | = | conduction heat transfer coefficient, W/m · K |
| K | = | turbulent kinetic energy, m2/s2 |
| L1 | = | inlet length, mm |
| L2 | = | length of the heating zone, mm |
| L | = | total length, mm |
| = | average Nusselt number | |
| P | = | rib-grooved pitch, mm |
| Δp | = | pressure drop, Pa |
| q″ | = | heat flux, W/m2 |
| r1 | = | rib-grooved height, mm |
| r2 | = | rib-grooved half-width, mm |
| Re | = | Reynolds number |
| T | = | temperature, K |
| Vdr | = | drift velocity, m/s |
| Vpf | = | relative velocity, m/s |
| u, v, w | = | velocity component, m/s |
| V | = | velocity, m/s |
| x, y, z | = | Cartesian x, y, z-coordinate, mm |
| ρ | = | density of the fluid, kg/m3 |
| μ | = | dynamic viscosity, kg/m · s |
| ϵ | = | turbulent kinetic dissipation, m2/s3 |
| τ | = | stress tensor, N/m2 |
| φ | = | nanoparticle volume concentration |
| Subscripts | = | |
| 0 | = | smooth channel |
| bf | = | base fluid |
| eff | = | effective |
| f | = | fluid |
| in | = | inlet |
| m | = | mean |
| nf | = | nanofluid |
| out | = | outlet |
| p | = | particle |
| w | = | wall |