Buoyant Marangoni convection of nanofluids in square cavity

H. SALEH, I. HASHIM

doi:10.1007/s10483-015-1973-6

Applied Mathematics and Mechanics >

2015 , Vol. 36 >Issue 9: 1169 - 1184

DOI: https://doi.org/10.1007/s10483-015-1973-6

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Buoyant Marangoni convection of nanofluids in square cavity

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1. School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia;
2. Solar Energy Research Institute, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia;
3. Research Institute, Center for Modeling & Computer Simulation(RI/CM & CS), King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia

Received date: 2014-07-08

Revised date: 2015-01-09

Online published: 2015-09-01

Supported by

Project supported by the Fundamental Research Grant Scheme of the Ministry of Education of Malaysia (No. FRGS/1/2014/SG04/UKM/01/1) and the Dana Impak Perdana of Universiti Kebangsaan Malaysia (No.DIP-2014-015)

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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-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.

Key words： nanofluid; finite difference method; Marangoni convection

Cite this article

H. SALEH, I. HASHIM . Buoyant Marangoni convection of nanofluids in square cavity[J]. Applied Mathematics and Mechanics, 2015 , 36(9) : 1169 -1184 . DOI: 10.1007/s10483-015-1973-6

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