### Abstract

The buoyant Marangoni convection heat transfer in a differentially heated cavity is numerically studied. The cavity is filled with water-Ag, water-Cu, water-Al<inf>2</inf>O<inf>3</inf>, and water-TiO<inf>2</inf> nanofluids. The governing equations are based on the equations involving the stream function, vorticity, and temperature. The dimensionless forms of the governing equations are solved by the finite difference (FD) scheme consisting of the alternating direction implicit (ADI) method and the tri-diagonal matrix algorithm (TDMA). It is found that the increase in the nanoparticle concentration leads to the decrease in the flow rates in the secondary cells when the convective thermocapillary and the buoyancy force have similar strength. A critical Marangoni number exists, below which increasing the Marangoni number decreases the average Nusselt number, and above which increasing the Marangoni number increases the average Nusselt number. The nanoparticles play a crucial role in the critical Marangoni number.

Original language | English |
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Pages (from-to) | 1169-1184 |

Number of pages | 16 |

Journal | Applied Mathematics and Mechanics (English Edition) |

Volume | 36 |

Issue number | 9 |

DOIs | |

Publication status | Published - 22 Jul 2015 |

### Fingerprint

### Keywords

- finite difference method
- Marangoni convection
- nanofluid

### ASJC Scopus subject areas

- Applied Mathematics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

**Buoyant Marangoni convection of nanofluids in square cavity.** / Saleh, H.; Hashim, Ishak.

Research output: Contribution to journal › Article

*Applied Mathematics and Mechanics (English Edition)*, vol. 36, no. 9, pp. 1169-1184. https://doi.org/10.1007/s10483-015-1973-6

}

TY - JOUR

T1 - Buoyant Marangoni convection of nanofluids in square cavity

AU - Saleh, H.

AU - Hashim, Ishak

PY - 2015/7/22

Y1 - 2015/7/22

N2 - The buoyant Marangoni convection heat transfer in a differentially heated cavity is numerically studied. The cavity is filled with water-Ag, water-Cu, water-Al2O3, and water-TiO2 nanofluids. The governing equations are based on the equations involving the stream function, vorticity, and temperature. The dimensionless forms of the governing equations are solved by the finite difference (FD) scheme consisting of the alternating direction implicit (ADI) method and the tri-diagonal matrix algorithm (TDMA). It is found that the increase in the nanoparticle concentration leads to the decrease in the flow rates in the secondary cells when the convective thermocapillary and the buoyancy force have similar strength. A critical Marangoni number exists, below which increasing the Marangoni number decreases the average Nusselt number, and above which increasing the Marangoni number increases the average Nusselt number. The nanoparticles play a crucial role in the critical Marangoni number.

AB - The buoyant Marangoni convection heat transfer in a differentially heated cavity is numerically studied. The cavity is filled with water-Ag, water-Cu, water-Al2O3, and water-TiO2 nanofluids. The governing equations are based on the equations involving the stream function, vorticity, and temperature. The dimensionless forms of the governing equations are solved by the finite difference (FD) scheme consisting of the alternating direction implicit (ADI) method and the tri-diagonal matrix algorithm (TDMA). It is found that the increase in the nanoparticle concentration leads to the decrease in the flow rates in the secondary cells when the convective thermocapillary and the buoyancy force have similar strength. A critical Marangoni number exists, below which increasing the Marangoni number decreases the average Nusselt number, and above which increasing the Marangoni number increases the average Nusselt number. The nanoparticles play a crucial role in the critical Marangoni number.

KW - finite difference method

KW - Marangoni convection

KW - nanofluid

UR - http://www.scopus.com/inward/record.url?scp=84941258823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941258823&partnerID=8YFLogxK

U2 - 10.1007/s10483-015-1973-6

DO - 10.1007/s10483-015-1973-6

M3 - Article

AN - SCOPUS:84941258823

VL - 36

SP - 1169

EP - 1184

JO - Applied Mathematics and Mechanics

JF - Applied Mathematics and Mechanics

SN - 0253-4827

IS - 9

ER -