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ABSTRACT
This paper examines forced convection heat transfer and entropy generation of a nanofluid laminar flow through a horizontal channel with wavy walls in the presence of magnetic field, numerically. The Newtonian nanofluid is composed of water as base fluid and Al2O3 as nanoparticle which is exposed to a transverse magnetic field with uniform strength. The inlet nanofluid with higher temperature enters the cool duct and heat is exchanged along the walls of a wavy channel. The effects of the dominant parameters including Reynolds number, solid volume fraction, Hartmann number, and different states of amplitude sine waves are studied on the local and average Nusselt number, skin friction, and total entropy generation. Computations show excellent agreement of the present study with the previous literature. The computations indicate that with the increasing strength of a magnetic field, Nusselt number, skin friction, and total entropy generation are increased. It is found that increasing the solid volume fraction of nanoparticles will increase the Nusselt number and total entropy generation, but its effect on the skin friction is negligible. Also, results imply that increasing amplitude sine waves of the geometry has incremental effect on both Nusselt number and skin friction, but its effect on the total entropy generation is not so tangible.
Nomenclature
| B0 | = | strength of magnetic field |
| Cp | = | specific heat at constant pressure, J/Kg/K |
| dp | = | diameter of the nanoparticles, nm |
| Ha | = | Hartman number |
| k | = | thermal conductivity, W/m/K |
| kf | = | fluid thermal conductivity, W/m/K |
| ks | = | solid thermal conductivity, W/m/K |
| KB | = | Boltzmann constant, J/K |
| L | = | length along the surface of duct, m |
| n | = | normal vector of the surface |
| Nu | = | Nusselt number |
| p | = | Pressure, N/m2 |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| Sθ | = | entropy generation due to heat transfer |
| Sψ | = | entropy generation due to fluid friction |
| T | = | Temperature, K |
| Tin | = | inlet temperature, K |
| Tw | = | wall temperature, K |
| T0 | = | reference temperature |
| x | = | horizontal Cartesian coordinate, m |
| X | = | horizontal dimensionless Cartesian coordinate |
| y | = | vertical Cartesian coordinate, m |
| Y | = | vertical dimensionless Cartesian coordinate |
| u | = | horizontal velocity component, m/s |
| U | = | dimensionless horizontal velocity component |
| v | = | vertical velocity component, m/s |
| V | = | vertical dimensionless velocity component |
| Win | = | inlet width |
| α | = | thermal diffusivity, m2/s |
| σ | = | electrical conductivity (Ω · m)−1 |
| ρ | = | density, Kg/m3 |
| ϕ | = | solid volume fraction of the nanofluid |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity, m2s |
| χ | = | irreversibility distribution ratio |
| Subscript | = | |
| av | = | average |
| f | = | fluid |
| fr | = | freezing point |
| in | = | inlet |
| loc | = | local |
| nf | = | nanofluid |
| s | = | solid nanoparticles |
| w | = | wall |
Nomenclature
| B0 | = | strength of magnetic field |
| Cp | = | specific heat at constant pressure, J/Kg/K |
| dp | = | diameter of the nanoparticles, nm |
| Ha | = | Hartman number |
| k | = | thermal conductivity, W/m/K |
| kf | = | fluid thermal conductivity, W/m/K |
| ks | = | solid thermal conductivity, W/m/K |
| KB | = | Boltzmann constant, J/K |
| L | = | length along the surface of duct, m |
| n | = | normal vector of the surface |
| Nu | = | Nusselt number |
| p | = | Pressure, N/m2 |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| Sθ | = | entropy generation due to heat transfer |
| Sψ | = | entropy generation due to fluid friction |
| T | = | Temperature, K |
| Tin | = | inlet temperature, K |
| Tw | = | wall temperature, K |
| T0 | = | reference temperature |
| x | = | horizontal Cartesian coordinate, m |
| X | = | horizontal dimensionless Cartesian coordinate |
| y | = | vertical Cartesian coordinate, m |
| Y | = | vertical dimensionless Cartesian coordinate |
| u | = | horizontal velocity component, m/s |
| U | = | dimensionless horizontal velocity component |
| v | = | vertical velocity component, m/s |
| V | = | vertical dimensionless velocity component |
| Win | = | inlet width |
| α | = | thermal diffusivity, m2/s |
| σ | = | electrical conductivity (Ω · m)−1 |
| ρ | = | density, Kg/m3 |
| ϕ | = | solid volume fraction of the nanofluid |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity, m2s |
| χ | = | irreversibility distribution ratio |
| Subscript | = | |
| av | = | average |
| f | = | fluid |
| fr | = | freezing point |
| in | = | inlet |
| loc | = | local |
| nf | = | nanofluid |
| s | = | solid nanoparticles |
| w | = | wall |