http://orcid.org/0000-0002-4750-0227
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ABSTRACT
Numerical analysis of natural convection combined with entropy generation in a square open cavity partially filled with a porous medium has been performed for a ferrofluid under the effect of inclined uniform magnetic field. Governing equations with corresponding boundary conditions formulated in dimensionless stream function and vorticity using Brinkman–extended Darcy model for porous layer have been solved numerically using finite difference method. An influence of key parameters on ferrofluid flow and heat transfer has been analyzed. It has been found that an inclusion of spherical ferric oxide nanoparticles can lead to a diminution of entropy generation in the case of similar flow and heat transfer structures.
Nomenclature
| = | magnetic field | |
| B0 | = | magnitude of magnetic field |
| Be | = | local Bejan number |
| Beavg | = | average Bejan number |
| cp | = | specific heat at constant pressure |
| Da | = | Darcy number |
| = | electromagnetic force | |
| g | = | gravitational acceleration vector |
| Ha | = | Hartmann number |
| h | = | height of porous layer |
| H1(ϕ), H2(ϕ), H3(ϕ), H4(ϕ), H5(ϕ,ε), H6(ϕ,ε) | = | special functions |
| = | electric current | |
| K | = | permeability of porous layer |
| L | = | length and height of the cavity |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| = | dimensional pressure | |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| = | dimensional local entropy generation | |
| = | dimensional local entropy generation due to heat transfer | |
| = | dimensional local entropy generation due to fluid friction | |
| = | dimensional local entropy generation due to magnetic field | |
| Sgen | = | dimensionless local entropy generation |
| Sgen,ht | = | dimensionless local entropy generation due to heat transfer |
| Sgen,ff | = | dimensionless local entropy generation due to fluid friction |
| Sgen,mf | = | dimensionless local entropy generation due to magnetic field |
| Sgen,avg | = | dimensionless average entropy generation |
| Sgen,ht,avg | = | dimensionless average entropy generation due to heat transfer |
| Sgen,ff,avg | = | dimensionless average entropy generation due to fluid friction |
| Sgen,mf,avg | = | dimensionless average entropy generation due to magnetic field |
| = | additional parameters | |
| T | = | dimensional temperature |
| t | = | dimensional time |
| Tc | = | upper boundary temperature |
| Th | = | bottom wall temperature |
| u, v | = | dimensionless velocity components |
| = | dimensional velocity components | |
| x, y | = | dimensionless Cartesian coordinates |
| = | dimensional Cartesian coordinates | |
| α | = | inclination angle of magnetic field |
| β | = | thermal expansion coefficient |
| δ | = | dimensionless height of porous layer |
| ε | = | porosity of porous layer |
| η | = | heat capacity ratio |
| θ | = | dimensionless temperature |
| λ | = | thermal conductivity |
| μ | = | dynamic viscosity |
| ρ | = | density |
| = | heat capacitance | |
| ρβ | = | buoyancy coefficient |
| σ | = | electrical conductivity |
| τ | = | dimensionless time |
| ϕ | = | nanoparticles volume fraction |
| χ | = | irreversibility factor |
| ψ | = | dimensionless stream function |
| ω | = | dimensionless vorticity |
| Subscripts | = | |
| avg | = | average |
| c | = | cold |
| f | = | fluid |
| ff | = | fluid friction |
| gen | = | generation |
| h | = | hot |
| ht | = | heat transfer |
| max | = | maximum value |
| mf | = | magnetic field |
| mnf | = | porous medium saturated with a nanofluid |
| nf | = | nanofluid |
| p | = | (nano) particle |
| s | = | solid matrix of porous medium |
Nomenclature
| = | magnetic field | |
| B0 | = | magnitude of magnetic field |
| Be | = | local Bejan number |
| Beavg | = | average Bejan number |
| cp | = | specific heat at constant pressure |
| Da | = | Darcy number |
| = | electromagnetic force | |
| g | = | gravitational acceleration vector |
| Ha | = | Hartmann number |
| h | = | height of porous layer |
| H1(ϕ), H2(ϕ), H3(ϕ), H4(ϕ), H5(ϕ,ε), H6(ϕ,ε) | = | special functions |
| = | electric current | |
| K | = | permeability of porous layer |
| L | = | length and height of the cavity |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| = | dimensional pressure | |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| = | dimensional local entropy generation | |
| = | dimensional local entropy generation due to heat transfer | |
| = | dimensional local entropy generation due to fluid friction | |
| = | dimensional local entropy generation due to magnetic field | |
| Sgen | = | dimensionless local entropy generation |
| Sgen,ht | = | dimensionless local entropy generation due to heat transfer |
| Sgen,ff | = | dimensionless local entropy generation due to fluid friction |
| Sgen,mf | = | dimensionless local entropy generation due to magnetic field |
| Sgen,avg | = | dimensionless average entropy generation |
| Sgen,ht,avg | = | dimensionless average entropy generation due to heat transfer |
| Sgen,ff,avg | = | dimensionless average entropy generation due to fluid friction |
| Sgen,mf,avg | = | dimensionless average entropy generation due to magnetic field |
| = | additional parameters | |
| T | = | dimensional temperature |
| t | = | dimensional time |
| Tc | = | upper boundary temperature |
| Th | = | bottom wall temperature |
| u, v | = | dimensionless velocity components |
| = | dimensional velocity components | |
| x, y | = | dimensionless Cartesian coordinates |
| = | dimensional Cartesian coordinates | |
| α | = | inclination angle of magnetic field |
| β | = | thermal expansion coefficient |
| δ | = | dimensionless height of porous layer |
| ε | = | porosity of porous layer |
| η | = | heat capacity ratio |
| θ | = | dimensionless temperature |
| λ | = | thermal conductivity |
| μ | = | dynamic viscosity |
| ρ | = | density |
| = | heat capacitance | |
| ρβ | = | buoyancy coefficient |
| σ | = | electrical conductivity |
| τ | = | dimensionless time |
| ϕ | = | nanoparticles volume fraction |
| χ | = | irreversibility factor |
| ψ | = | dimensionless stream function |
| ω | = | dimensionless vorticity |
| Subscripts | = | |
| avg | = | average |
| c | = | cold |
| f | = | fluid |
| ff | = | fluid friction |
| gen | = | generation |
| h | = | hot |
| ht | = | heat transfer |
| max | = | maximum value |
| mf | = | magnetic field |
| mnf | = | porous medium saturated with a nanofluid |
| nf | = | nanofluid |
| p | = | (nano) particle |
| s | = | solid matrix of porous medium |