Turbulent boundary layer heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary

The turbulent boundary layer (TBL) heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary are investigated. Five different shapes of nanoparticles are taken into account. Prandtl mixing length theory is adopted to divide the TBL into two parts, laminar su...

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Published inZeitschrift für Naturforschung. A, A journal of physical sciences Vol. 77; no. 4; pp. 369 - 377
Main Authors Zhang, Jiaojiao, Liu, Shengna, Zheng, Liancun
Format Journal Article
LanguageEnglish
Published De Gruyter 26.04.2022
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ISSN0932-0784
1865-7109
DOI10.1515/zna-2021-0268

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Abstract The turbulent boundary layer (TBL) heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary are investigated. Five different shapes of nanoparticles are taken into account. Prandtl mixing length theory is adopted to divide the TBL into two parts, laminar sub-layer and turbulent region. The numerical solutions are obtained by bvp4c and accuracy is verified with previous results. It is found that the transfer of momentum and heat in the TBL is more obvious in laminar sub-layer than in turbulent region. The rise of velocity ratio parameter increases the velocity and temperature while decreases the local friction coefficient. The heat transfer increases significantly with the increase of velocity ratio parameter, Biot number, and nanoparticles volume fraction. For nanoparticles of different shapes, the heat transfer characteristics are Nu (sphere) < Nu (hexahedron) < Nu (tetrahedron) < Nu (column) < Nu (lamina).
AbstractList The turbulent boundary layer (TBL) heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary are investigated. Five different shapes of nanoparticles are taken into account. Prandtl mixing length theory is adopted to divide the TBL into two parts, laminar sub-layer and turbulent region. The numerical solutions are obtained by bvp4c and accuracy is verified with previous results. It is found that the transfer of momentum and heat in the TBL is more obvious in laminar sub-layer than in turbulent region. The rise of velocity ratio parameter increases the velocity and temperature while decreases the local friction coefficient. The heat transfer increases significantly with the increase of velocity ratio parameter, Biot number, and nanoparticles volume fraction. For nanoparticles of different shapes, the heat transfer characteristics are Nu (sphere) < Nu (hexahedron) < Nu (tetrahedron) < Nu (column) < Nu (lamina).
The turbulent boundary layer (TBL) heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary are investigated. Five different shapes of nanoparticles are taken into account. Prandtl mixing length theory is adopted to divide the TBL into two parts, laminar sub-layer and turbulent region. The numerical solutions are obtained by bvp4c and accuracy is verified with previous results. It is found that the transfer of momentum and heat in the TBL is more obvious in laminar sub-layer than in turbulent region. The rise of velocity ratio parameter increases the velocity and temperature while decreases the local friction coefficient. The heat transfer increases significantly with the increase of velocity ratio parameter, Biot number, and nanoparticles volume fraction. For nanoparticles of different shapes, the heat transfer characteristics are Nu x (sphere) < Nu x (hexahedron) < Nu x (tetrahedron) < Nu x (column) < Nu x (lamina).
Author Zhang, Jiaojiao
Zheng, Liancun
Liu, Shengna
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  email: liancunzheng@ustb.edu.cn
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Cites_doi 10.1016/j.ijnonlinmec.2015.08.006
10.1016/j.jnnfm.2013.05.003
10.1115/1.1571080
10.1016/j.ijheatmasstransfer.2009.02.006
10.1557/PROC-457-3
10.1016/j.powtec.2015.01.039
10.1002/aic.690070211
10.1016/j.cja.2013.10.008
10.1016/j.molliq.2016.04.108
10.1016/j.amc.2016.11.024
10.1016/j.ijheatmasstransfer.2017.06.082
10.1007/s40430-019-1966-6
10.1063/1.1700493
10.1016/j.ijmecsci.2017.08.043
10.18488/journal.24/2015.4.1/24.1.27.41
10.1007/s13204-015-0430-x
10.1016/j.ijthermalsci.2008.03.009
10.1186/1687-2770-2014-163
10.1016/j.apm.2014.05.023
10.1016/j.ijheatmasstransfer.2011.10.047
10.1017/S0022112075001474
10.1016/S0252-9602(17)30727-0
10.1002/ceat.200900634
10.1063/5.0011292
10.1016/0020-7225(92)90115-W
10.1016/j.powtec.2016.06.029
10.1016/j.molliq.2017.01.009
10.1007/s10494-013-9479-3
10.1017/jfm.2021.577
10.1016/j.amc.2010.06.026
10.1016/j.applthermaleng.2018.11.035
10.2478/ijame-2013-0025
10.1016/j.cnsns.2008.05.003
10.2298/TSCI191014144A
10.1016/j.ijheatfluidflow.2013.03.002
10.1007/s11771-008-0143-3
10.1016/j.ijthermalsci.2016.02.006
10.1142/S0217979220501301
10.17515/resm2020.174na0114
10.1017/jmech.2018.40
10.1016/j.ijmultiphaseflow.2016.03.009
10.1088/1402-4896/abe82d
10.1615/JPorMedia.2020028850
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References 2023040103485441082_j_zna-2021-0268_ref_019
2023040103485441082_j_zna-2021-0268_ref_030
2023040103485441082_j_zna-2021-0268_ref_010
2023040103485441082_j_zna-2021-0268_ref_032
2023040103485441082_j_zna-2021-0268_ref_031
2023040103485441082_j_zna-2021-0268_ref_016
2023040103485441082_j_zna-2021-0268_ref_038
2023040103485441082_j_zna-2021-0268_ref_015
2023040103485441082_j_zna-2021-0268_ref_037
2023040103485441082_j_zna-2021-0268_ref_018
2023040103485441082_j_zna-2021-0268_ref_017
2023040103485441082_j_zna-2021-0268_ref_039
2023040103485441082_j_zna-2021-0268_ref_012
2023040103485441082_j_zna-2021-0268_ref_034
2023040103485441082_j_zna-2021-0268_ref_011
2023040103485441082_j_zna-2021-0268_ref_033
2023040103485441082_j_zna-2021-0268_ref_014
2023040103485441082_j_zna-2021-0268_ref_036
2023040103485441082_j_zna-2021-0268_ref_013
2023040103485441082_j_zna-2021-0268_ref_035
2023040103485441082_j_zna-2021-0268_ref_009
2023040103485441082_j_zna-2021-0268_ref_008
2023040103485441082_j_zna-2021-0268_ref_041
2023040103485441082_j_zna-2021-0268_ref_040
2023040103485441082_j_zna-2021-0268_ref_021
2023040103485441082_j_zna-2021-0268_ref_043
2023040103485441082_j_zna-2021-0268_ref_020
2023040103485441082_j_zna-2021-0268_ref_042
2023040103485441082_j_zna-2021-0268_ref_005
2023040103485441082_j_zna-2021-0268_ref_027
2023040103485441082_j_zna-2021-0268_ref_004
2023040103485441082_j_zna-2021-0268_ref_026
2023040103485441082_j_zna-2021-0268_ref_048
2023040103485441082_j_zna-2021-0268_ref_007
2023040103485441082_j_zna-2021-0268_ref_029
2023040103485441082_j_zna-2021-0268_ref_006
2023040103485441082_j_zna-2021-0268_ref_028
2023040103485441082_j_zna-2021-0268_ref_001
2023040103485441082_j_zna-2021-0268_ref_023
2023040103485441082_j_zna-2021-0268_ref_045
2023040103485441082_j_zna-2021-0268_ref_022
2023040103485441082_j_zna-2021-0268_ref_044
2023040103485441082_j_zna-2021-0268_ref_003
2023040103485441082_j_zna-2021-0268_ref_025
2023040103485441082_j_zna-2021-0268_ref_047
2023040103485441082_j_zna-2021-0268_ref_002
2023040103485441082_j_zna-2021-0268_ref_024
2023040103485441082_j_zna-2021-0268_ref_046
References_xml – ident: 2023040103485441082_j_zna-2021-0268_ref_015
  doi: 10.1016/j.ijnonlinmec.2015.08.006
– ident: 2023040103485441082_j_zna-2021-0268_ref_011
  doi: 10.1016/j.jnnfm.2013.05.003
– ident: 2023040103485441082_j_zna-2021-0268_ref_020
  doi: 10.1115/1.1571080
– ident: 2023040103485441082_j_zna-2021-0268_ref_022
  doi: 10.1016/j.ijheatmasstransfer.2009.02.006
– ident: 2023040103485441082_j_zna-2021-0268_ref_019
  doi: 10.1557/PROC-457-3
– ident: 2023040103485441082_j_zna-2021-0268_ref_044
  doi: 10.1016/j.powtec.2015.01.039
– ident: 2023040103485441082_j_zna-2021-0268_ref_003
– ident: 2023040103485441082_j_zna-2021-0268_ref_031
  doi: 10.1002/aic.690070211
– ident: 2023040103485441082_j_zna-2021-0268_ref_001
– ident: 2023040103485441082_j_zna-2021-0268_ref_042
  doi: 10.1016/j.cja.2013.10.008
– ident: 2023040103485441082_j_zna-2021-0268_ref_045
  doi: 10.1016/j.molliq.2016.04.108
– ident: 2023040103485441082_j_zna-2021-0268_ref_007
  doi: 10.1016/j.amc.2016.11.024
– ident: 2023040103485441082_j_zna-2021-0268_ref_035
  doi: 10.1016/j.ijheatmasstransfer.2017.06.082
– ident: 2023040103485441082_j_zna-2021-0268_ref_023
  doi: 10.1007/s40430-019-1966-6
– ident: 2023040103485441082_j_zna-2021-0268_ref_046
  doi: 10.1063/1.1700493
– ident: 2023040103485441082_j_zna-2021-0268_ref_012
  doi: 10.1016/j.ijmecsci.2017.08.043
– ident: 2023040103485441082_j_zna-2021-0268_ref_037
  doi: 10.18488/journal.24/2015.4.1/24.1.27.41
– ident: 2023040103485441082_j_zna-2021-0268_ref_047
  doi: 10.1007/s13204-015-0430-x
– ident: 2023040103485441082_j_zna-2021-0268_ref_021
  doi: 10.1016/j.ijthermalsci.2008.03.009
– ident: 2023040103485441082_j_zna-2021-0268_ref_040
  doi: 10.1186/1687-2770-2014-163
– ident: 2023040103485441082_j_zna-2021-0268_ref_026
  doi: 10.1016/j.apm.2014.05.023
– ident: 2023040103485441082_j_zna-2021-0268_ref_036
  doi: 10.1016/j.ijheatmasstransfer.2011.10.047
– ident: 2023040103485441082_j_zna-2021-0268_ref_048
  doi: 10.1017/S0022112075001474
– ident: 2023040103485441082_j_zna-2021-0268_ref_032
  doi: 10.1016/S0252-9602(17)30727-0
– ident: 2023040103485441082_j_zna-2021-0268_ref_009
  doi: 10.1002/ceat.200900634
– ident: 2023040103485441082_j_zna-2021-0268_ref_017
  doi: 10.1063/5.0011292
– ident: 2023040103485441082_j_zna-2021-0268_ref_033
  doi: 10.1016/0020-7225(92)90115-W
– ident: 2023040103485441082_j_zna-2021-0268_ref_027
  doi: 10.1016/j.powtec.2016.06.029
– ident: 2023040103485441082_j_zna-2021-0268_ref_004
– ident: 2023040103485441082_j_zna-2021-0268_ref_016
  doi: 10.1016/j.molliq.2017.01.009
– ident: 2023040103485441082_j_zna-2021-0268_ref_006
  doi: 10.1007/s10494-013-9479-3
– ident: 2023040103485441082_j_zna-2021-0268_ref_002
– ident: 2023040103485441082_j_zna-2021-0268_ref_005
  doi: 10.1017/jfm.2021.577
– ident: 2023040103485441082_j_zna-2021-0268_ref_041
  doi: 10.1016/j.amc.2010.06.026
– ident: 2023040103485441082_j_zna-2021-0268_ref_013
  doi: 10.1016/j.applthermaleng.2018.11.035
– ident: 2023040103485441082_j_zna-2021-0268_ref_034
  doi: 10.2478/ijame-2013-0025
– ident: 2023040103485441082_j_zna-2021-0268_ref_039
  doi: 10.1016/j.cnsns.2008.05.003
– ident: 2023040103485441082_j_zna-2021-0268_ref_030
  doi: 10.2298/TSCI191014144A
– ident: 2023040103485441082_j_zna-2021-0268_ref_010
  doi: 10.1016/j.ijheatfluidflow.2013.03.002
– ident: 2023040103485441082_j_zna-2021-0268_ref_014
  doi: 10.1007/s11771-008-0143-3
– ident: 2023040103485441082_j_zna-2021-0268_ref_025
  doi: 10.1016/j.ijthermalsci.2016.02.006
– ident: 2023040103485441082_j_zna-2021-0268_ref_018
– ident: 2023040103485441082_j_zna-2021-0268_ref_028
  doi: 10.1142/S0217979220501301
– ident: 2023040103485441082_j_zna-2021-0268_ref_038
  doi: 10.17515/resm2020.174na0114
– ident: 2023040103485441082_j_zna-2021-0268_ref_024
  doi: 10.1017/jmech.2018.40
– ident: 2023040103485441082_j_zna-2021-0268_ref_008
  doi: 10.1016/j.ijmultiphaseflow.2016.03.009
– ident: 2023040103485441082_j_zna-2021-0268_ref_029
  doi: 10.1088/1402-4896/abe82d
– ident: 2023040103485441082_j_zna-2021-0268_ref_043
  doi: 10.1615/JPorMedia.2020028850
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Snippet The turbulent boundary layer (TBL) heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary are investigated. Five...
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SubjectTerms continuously moving plate
convective boundary condition
nanofluids
turbulent boundary layer
Title Turbulent boundary layer heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary
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