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ABSTRACT
In this work, the effect of a variable spatial magnetic field on ferro-nanofluid flow and heat transfer in a double-sided lid-driven enclosure with a sinusoidal hot wall is investigated. The working fluid is a mixture of iron oxide (Fe3O4) nanoparticles and water and is referred to as a ferro-nanofluid. The control volume-based finite element method (CVFEM) is used to solve the governing equations in the stream function–vorticity formulation. In deriving the governing equations for this investigation, the effect of both ferro-hydrodynamics and magneto-hydrodynamics is taken into account. The numerical calculations are performed for different governing parameters namely; the Reynolds number, nanoparticle volume fraction, magnetic number (arising from Ferrohydrodynamics (FHD) consideration), and the Hartmann number (arising from Magnetohydrodynamics (MHD) consideration). The results show that an enhancement in heat transfer has a direct relationship with the Reynolds number and the Hartmann number, but it has an inverse relationship with the magnetic number. Also, it can be concluded that the Nusselt number increases with the increase of the nanoparticle volume fraction, magnetic number, and the Reynolds number while the opposite trend is observed for the Hartmann number.
Nomenclature
| a | = | dimensionless amplitude of the sinusoidal wall |
| B | = | magnetic induction (= μ0H) |
| Cp | = | specific heat at constant pressure |
| Ec | = | Eckert number |
| En | = | heat transfer enhancement |
| Hx, Hy | = | components of the magnetic field intensity |
| H | = | the magnetic field strength |
| Ha | = | Hartmann number |
| k | = | thermal conductivity |
| K′ | = | constant parameter |
| L | = | gap between inner and outer boundaries of the enclosure L = rout − rin |
| MnF | = | magnetic number arising from FHD |
| M | = | magnetization |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number (= υf/αf) |
| Re | = | Reynolds number (= ρfL ULid/μf) |
| T | = | fluid temperature |
| = | Curie temperature | |
| u, v | = | velocity components in the x-direction and y-direction |
| U, V | = | dimensionless velocity components in the x-direction and y-direction |
| x, y | = | space coordinates |
| X, Y | = | dimensionless space coordinates |
| α | = | thermal diffusivity |
| ϕ | = | volume fraction |
| γ | = | magnetic field strength at the source |
| ϵ1 | = | temperature number (= T1/ΔT) |
| ϵ2 | = | Curie temperature number |
| σ | = | electrical conductivity |
| μ | = | dynamic viscosity |
| μ0 | = | magnetic permeability of vacuum |
| υ | = | kinematic viscosity |
| = | stream function and dimensionless stream function | |
| Θ | = | dimensionless temperature |
| ρ | = | fluid density |
| ω, Ω | = | vorticity and dimensionless vorticity |
| Subscripts | = | |
| c | = | cold |
| h | = | hot |
| ave | = | average |
| loc | = | local |
| nf | = | nanofluid |
| f | = | base fluid |
| s | = | solid particles |
| in | = | inner |
| out | = | outer |
Nomenclature
| a | = | dimensionless amplitude of the sinusoidal wall |
| B | = | magnetic induction (= μ0H) |
| Cp | = | specific heat at constant pressure |
| Ec | = | Eckert number |
| En | = | heat transfer enhancement |
| Hx, Hy | = | components of the magnetic field intensity |
| H | = | the magnetic field strength |
| Ha | = | Hartmann number |
| k | = | thermal conductivity |
| K′ | = | constant parameter |
| L | = | gap between inner and outer boundaries of the enclosure L = rout − rin |
| MnF | = | magnetic number arising from FHD |
| M | = | magnetization |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number (= υf/αf) |
| Re | = | Reynolds number (= ρfL ULid/μf) |
| T | = | fluid temperature |
| = | Curie temperature | |
| u, v | = | velocity components in the x-direction and y-direction |
| U, V | = | dimensionless velocity components in the x-direction and y-direction |
| x, y | = | space coordinates |
| X, Y | = | dimensionless space coordinates |
| α | = | thermal diffusivity |
| ϕ | = | volume fraction |
| γ | = | magnetic field strength at the source |
| ϵ1 | = | temperature number (= T1/ΔT) |
| ϵ2 | = | Curie temperature number |
| σ | = | electrical conductivity |
| μ | = | dynamic viscosity |
| μ0 | = | magnetic permeability of vacuum |
| υ | = | kinematic viscosity |
| = | stream function and dimensionless stream function | |
| Θ | = | dimensionless temperature |
| ρ | = | fluid density |
| ω, Ω | = | vorticity and dimensionless vorticity |
| Subscripts | = | |
| c | = | cold |
| h | = | hot |
| ave | = | average |
| loc | = | local |
| nf | = | nanofluid |
| f | = | base fluid |
| s | = | solid particles |
| in | = | inner |
| out | = | outer |