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Buoyant Marangoni convection of nanofluids in square cavity

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia

    H. Saleh & I. Hashim

  2. Solar Energy Research Institute, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia

    I. Hashim

  3. Research Institute, Center for Modeling & Computer Simulation (RI/CM&CS), King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

    I. Hashim

Authors
  1. H. Saleh
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  2. I. Hashim
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Corresponding author

Correspondence to H. Saleh.

Additional information

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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Saleh, H., Hashim, I. Buoyant Marangoni convection of nanofluids in square cavity. Appl. Math. Mech.-Engl. Ed. 36, 1169–1184 (2015). https://doi.org/10.1007/s10483-015-1973-6

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

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