### Abstract

The problem of darcian natural convection in inclined square cavity partially filled between the centralsquare hole filled with fluid and inside a square porous cavity filled with nanofluid is numericallystudied using the finite element m ethod. The left vertical wall is maintained at a constant hot temperatureT_{h} and the right vertical wall is maintained at a constant cold temperature T_{c}, while the horizontalwalls are adiabatic. The governing equations are obtained by applying the Darcy model andBoussinesq approximation. COMSOL's finite element method is used to solve the non-dimensionalgoverning equations together with the specified boundary c onditions. The governing parameters ofthis study are the Rayleigh number (10^{3}≤Ra≤10^{7}), the Darcy number (10^{-5}≤Da≤10^{-3}), thefluid layer thickness (0.4≤S≤0.8) and the inclination angle of the cavity (0°≤ω≤6 0°). Theresults for the values of the governing parameters in terms of the streamlines, isotherms and averageNusselt number will be presented. The convection is shown to be inhibited by the presence of thehole insert. The thermal property of the insert and the size have opposite influence on the convection.The results have possible applications in heat-removal and heat-storage fluid-saturated poroussystems.

Original language | English |
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Pages (from-to) | 1763-1775 |

Number of pages | 13 |

Journal | Journal of Applied Fluid Mechanics |

Volume | 9 |

Issue number | 4 |

Publication status | Published - 2016 |

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### Keywords

- Darcy model
- Interface
- Nanofluid
- Natural convection
- Square cavity

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

*Journal of Applied Fluid Mechanics*,

*9*(4), 1763-1775.

**Darcian natural convection in inclined square cavity partially filled between the central square hole filledwith a fluid and inside a square porous cavity filledwith nanofluid.** / Alsabery, A. I.; Saleh, H.; Hashim, Ishak; Hussain, S. H.

Research output: Contribution to journal › Article

*Journal of Applied Fluid Mechanics*, vol. 9, no. 4, pp. 1763-1775.

}

TY - JOUR

T1 - Darcian natural convection in inclined square cavity partially filled between the central square hole filledwith a fluid and inside a square porous cavity filledwith nanofluid

AU - Alsabery, A. I.

AU - Saleh, H.

AU - Hashim, Ishak

AU - Hussain, S. H.

PY - 2016

Y1 - 2016

N2 - The problem of darcian natural convection in inclined square cavity partially filled between the centralsquare hole filled with fluid and inside a square porous cavity filled with nanofluid is numericallystudied using the finite element m ethod. The left vertical wall is maintained at a constant hot temperatureTh and the right vertical wall is maintained at a constant cold temperature Tc, while the horizontalwalls are adiabatic. The governing equations are obtained by applying the Darcy model andBoussinesq approximation. COMSOL's finite element method is used to solve the non-dimensionalgoverning equations together with the specified boundary c onditions. The governing parameters ofthis study are the Rayleigh number (103≤Ra≤107), the Darcy number (10-5≤Da≤10-3), thefluid layer thickness (0.4≤S≤0.8) and the inclination angle of the cavity (0°≤ω≤6 0°). Theresults for the values of the governing parameters in terms of the streamlines, isotherms and averageNusselt number will be presented. The convection is shown to be inhibited by the presence of thehole insert. The thermal property of the insert and the size have opposite influence on the convection.The results have possible applications in heat-removal and heat-storage fluid-saturated poroussystems.

AB - The problem of darcian natural convection in inclined square cavity partially filled between the centralsquare hole filled with fluid and inside a square porous cavity filled with nanofluid is numericallystudied using the finite element m ethod. The left vertical wall is maintained at a constant hot temperatureTh and the right vertical wall is maintained at a constant cold temperature Tc, while the horizontalwalls are adiabatic. The governing equations are obtained by applying the Darcy model andBoussinesq approximation. COMSOL's finite element method is used to solve the non-dimensionalgoverning equations together with the specified boundary c onditions. The governing parameters ofthis study are the Rayleigh number (103≤Ra≤107), the Darcy number (10-5≤Da≤10-3), thefluid layer thickness (0.4≤S≤0.8) and the inclination angle of the cavity (0°≤ω≤6 0°). Theresults for the values of the governing parameters in terms of the streamlines, isotherms and averageNusselt number will be presented. The convection is shown to be inhibited by the presence of thehole insert. The thermal property of the insert and the size have opposite influence on the convection.The results have possible applications in heat-removal and heat-storage fluid-saturated poroussystems.

KW - Darcy model

KW - Interface

KW - Nanofluid

KW - Natural convection

KW - Square cavity

UR - http://www.scopus.com/inward/record.url?scp=84975686273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975686273&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 1763

EP - 1775

JO - Journal of Applied Fluid Mechanics

JF - Journal of Applied Fluid Mechanics

SN - 1735-3572

IS - 4

ER -