Buoyant Marangoni convection of nanofluids in square cavity

doi:10.1007/s10483-015-1973-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (9): 1169-1184.doi: https://doi.org/10.1007/s10483-015-1973-6

Buoyant Marangoni convection of nanofluids in square cavity

H. SALEH¹, I. HASHIM^1,2,3

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

收稿日期:2014-07-08 修回日期:2015-01-09 出版日期:2015-09-01 发布日期:2015-09-01
通讯作者: H. SALEH E-mail:Dr.habibissaleh@gmail.com
基金资助:
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)

Buoyant Marangoni convection of nanofluids in square cavity

H. SALEH¹, I. HASHIM^1,2,3

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:2014-07-08 Revised:2015-01-09 Online:2015-09-01 Published:2015-09-01
Contact: H. SALEH E-mail:Dr.habibissaleh@gmail.com
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)

摘要/Abstract

摘要： 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.

关键词: Marangoni convection, nanofluid, finite difference method

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

中图分类号:

O353.4

H. SALEH, I. HASHIM. Buoyant Marangoni convection of nanofluids in square cavity[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(9): 1169-1184.

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Buoyant Marangoni convection of nanofluids in square cavity

Buoyant Marangoni convection of nanofluids in square cavity

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