New application of MOL-PACT for simulating buoyancy convection of a copper-water nanofluid in a square enclosure containing an insulated obstacle

Fahad Alsharari; Mohamed M. Mousa; Fahad Alsharari; Mohamed M. Mousa

doi:10.3934/math.20221111

AIMS Mathematics

2022, Volume 7, Issue 11: 20292-20312. doi: 10.3934/math.20221111

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New application of MOL-PACT for simulating buoyancy convection of a copper-water nanofluid in a square enclosure containing an insulated obstacle

Fahad Alsharari ^{1
,
,},
Mohamed M. Mousa ^{2,3
,
,}

1.
Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, 77455, Saudi Arabia
2.
Department of Finance, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi Arabia
3.
Department of Basic Engineering Sciences, Faculty of Engineering at Benha, Benha University, Benha 13512, Egypt

Received: 02 August 2022 Revised: 28 August 2022 Accepted: 04 September 2022 Published: 16 September 2022
MSC : 65M06, 76R10

In this study, we have simulated transient and steady state free convection flow and heat transfer inside a square enclosure filled with a copper-water nanofluid of spherical shape nanoparticles following Tiwari-Das model. The cavity containing an insulated rectangular obstacle of height ranging from 0% to 50% of the cavity side-length. The vertical sides of the enclosure are kept at different temperatures, while the flat sides are assumed to be adiabatic as the obstacle. The combined method of lines/penalty-artificial compressibility technique (MOL-PACT) has been applied to solve the dimensional time dependent mathematical model after converting it into a non-dimensional structure. The combined method of lines/penalty-artificial compressibility technique is recently successfully applied to simulate free convection of MHD fluid in square enclosure with a localized heating. The extension of this promising technique for studying heat transfer of nanofluids is one of the objectives of this paper. Another objective of the study is to inspect the impact of several model parameters such as, the obstacle height, nanoparticles volume-fraction, nanoparticles radius and Rayleigh number on streamlines, temperature distribution and Nusselt number as an expression of heat transfer inside the enclosure. The results have been discussed and shown graphically. Comparisons with former results for related cases in the literature are made and reasonably good agreements are observed.
- nanofluid,
- buoyancy convection,
- heat transfer,
- method of lines,
- artificial compressibility technique
Citation: Fahad Alsharari, Mohamed M. Mousa. New application of MOL-PACT for simulating buoyancy convection of a copper-water nanofluid in a square enclosure containing an insulated obstacle[J]. AIMS Mathematics, 2022, 7(11): 20292-20312. doi: 10.3934/math.20221111

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Abstract

In this study, we have simulated transient and steady state free convection flow and heat transfer inside a square enclosure filled with a copper-water nanofluid of spherical shape nanoparticles following Tiwari-Das model. The cavity containing an insulated rectangular obstacle of height ranging from 0% to 50% of the cavity side-length. The vertical sides of the enclosure are kept at different temperatures, while the flat sides are assumed to be adiabatic as the obstacle. The combined method of lines/penalty-artificial compressibility technique (MOL-PACT) has been applied to solve the dimensional time dependent mathematical model after converting it into a non-dimensional structure. The combined method of lines/penalty-artificial compressibility technique is recently successfully applied to simulate free convection of MHD fluid in square enclosure with a localized heating. The extension of this promising technique for studying heat transfer of nanofluids is one of the objectives of this paper. Another objective of the study is to inspect the impact of several model parameters such as, the obstacle height, nanoparticles volume-fraction, nanoparticles radius and Rayleigh number on streamlines, temperature distribution and Nusselt number as an expression of heat transfer inside the enclosure. The results have been discussed and shown graphically. Comparisons with former results for related cases in the literature are made and reasonably good agreements are observed.

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