MWCNTs/SWCNTs Nanofluid Thin Film Flow over a Nonlinear Extending Disc: OHAM Solution
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摘要
The aim of this research is the improvement towards the consumption of energy in the field of engineering and industry. The efforts have been paid to the enhancement of heat transmission and cooling process through a nanofluid coating of a nonlinear stretching disc. The combination of Water(H2 O) and multiple walled carbon nanotubes(MWCNT)/single walled carbon nanotubes(SWCNT) have been used as a nanofluid. The spreading of a thin nano-layer with variable thickness over a nonlinear and radially stretching surface has been considered. The estimated results of the problem have been accomplished using the Optimal Homotopy Analysis Method(OHAM). The residual errors of the OHAM method have been shown physically and numerically. The important physical parameters of skin friction and Nusselt number have been calculated and discussed. The other embedding parameters like generalized magnetic parameter, Prantl number, nanofluid volume fraction and Eckert number have been intended and discussed. The obtained results have been compared with the Numerical(ND-Solve) method for both sorts of CNTs. The closed agreement of both methods has been achieved.
The aim of this research is the improvement towards the consumption of energy in the field of engineering and industry. The efforts have been paid to the enhancement of heat transmission and cooling process through a nanofluid coating of a nonlinear stretching disc. The combination of Water(H2 O) and multiple walled carbon nanotubes(MWCNT)/single walled carbon nanotubes(SWCNT) have been used as a nanofluid. The spreading of a thin nano-layer with variable thickness over a nonlinear and radially stretching surface has been considered. The estimated results of the problem have been accomplished using the Optimal Homotopy Analysis Method(OHAM). The residual errors of the OHAM method have been shown physically and numerically. The important physical parameters of skin friction and Nusselt number have been calculated and discussed. The other embedding parameters like generalized magnetic parameter, Prantl number, nanofluid volume fraction and Eckert number have been intended and discussed. The obtained results have been compared with the Numerical(ND-Solve) method for both sorts of CNTs. The closed agreement of both methods has been achieved.
The aim of this research is the improvement towards the consumption of energy in the field of engineering and industry. The efforts have been paid to the enhancement of heat transmission and cooling process through a nanofluid coating of a nonlinear stretching disc. The combination of Water(H2 O) and multiple walled carbon nanotubes(MWCNT)/single walled carbon nanotubes(SWCNT) have been used as a nanofluid. The spreading of a thin nano-layer with variable thickness over a nonlinear and radially stretching surface has been considered. The estimated results of the problem have been accomplished using the Optimal Homotopy Analysis Method(OHAM). The residual errors of the OHAM method have been shown physically and numerically. The important physical parameters of skin friction and Nusselt number have been calculated and discussed. The other embedding parameters like generalized magnetic parameter, Prantl number, nanofluid volume fraction and Eckert number have been intended and discussed. The obtained results have been compared with the Numerical(ND-Solve) method for both sorts of CNTs. The closed agreement of both methods has been achieved.
引文
[1]Iijima S.,Helical microtubules of graphitic carbon.Nature,1991,354:56?58.
[2]Oberlin A.,Endo M.,Koyama T.,Filamentous growth of carbon through benzene decomposition.Journal of Crystal Growth,1976,32:335?349.
[3]Iijima S.,Ichihashi T.,Single-shell carbon nanotubes of1-nm diameter.Nature,1993,363:603?605.
[4]Bethune D.S.,Kiang C.H.,Devries M.S.,Gorman G.,Savoy R.,Vazquez J.,et al.,Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls.Nature,1993,363:605-607.
[5]Terrones M.,Science and technology of the twenty-first century:synthesis,properties,and applications of carbon nanotubes.Annual Review of Materials Research,2003,33:419?501.
[6]De Volder M.F.L.,Tawfick S.H.,Baughman R.H.,Hart A.J.,Carbon nanotubes:present and future commercial applications.Science,2013,339:535?539.
[7]Negin C.,Ali S.,Xie Q.,Application of nanotechnology for enhancing oil recovery-A review,Petroleum,2016,2:324?333.
[8]Murshed S.M.S.,Nieto de Castro C.A.,Superior thermal features of carbon nanotubes-based nano fluids-Areview,Renewable and Sustainable Energy Reviews,2014,37:155?167.
[9]Qiu L.,Scheider K.,Radwan S.A.,Larkin L.S.,Saltonstall C.B.,Feng Y.,Zhang X.,Norris P.M.,Thermal transport barrier in carbon nanotube array nano-thermal interface materials,Carbon,2017,120:128?136.
[10]Qiu L.,Wang X.,Tang D.,Zheng X.,Norris P.M.,Wen D.,Zhao J.,Zhang X.,Li Q.,Functionalization and densification of inter-bundle interfaces for improvement in electrical and thermal transport of carbon nanotube fibers,Carbon,2016,105:248?259.
[11]Qiu L.,Zhu N.,Zou H.,Feng Y.,Zhang X.,Tang D.,Advances in thermal transport properties at nanoscale in China,International Journal of Heat and Mass Transfer,2018,125:413?433.
[12]Zaidi Z.,Mohyud-din S.T.,Mohsen B.B.,Convective heat transfer and MHD analysis of wall jet flow of nanofluids containing carbon nanotubes,Engineering Computations,2017,34:1?9.
[13]Sreedevi P.,Reddy P.S.,Chamkha A.J.,Magnetohydrodynamics heat and mass transfer analysis of single and multi-wall carbon nanotubes over vertical cone with convective boundary condition,International Journal of Mechanical Science,2018,135:646?655.
[14]Haq R.U.,Shahzad F.,Al-Mdallal Q.M.,MHD pulsatile flow of engine oil based carbon nanotubes between two concentric cylinders.Results in Physics,2017,7:57?68.
[15]Xue Q.,Model for thermal conductivity of carbon nanotube-based composites.Physica B:Condensed Matter,2005,368:302?307.
[16]Garbadeen I.D.,Sharifpur M.,Slabber J.M.,Meyer J.P.,Experimental study on natural convection of MWCNT-water nanofluids in a square enclosure.International Communications in Heat and Mass Transfer,2017,88:1-8.
[17]Khan U.,Ahmed N.,Mohyud-Din S.T.,Sikander W.,Flow of carbon nanotubes suspended nanofluid in stretchable non-parallel walls,Neural Computing Applications,2017:DOI:https://doi.org/10.1007/s00521-017-2891-1.
[18]Sheikholeslami M.,Seyednezhad M.,Nanofluid heat transfer in a permeable enclosure in presence of variable magnetic field by means of CVFEM.International Journal of Heat and Mass Transfer,2017,114:1169?1180.
[19]Khan N.S.,Gul T.,Islam S.,Khan I.,Aisha M.A.,Ali S.A.,Magnetohydrodynamic nanoliquid thin film sprayed on a stretching cylinder with heat transfer.Applied Sciences,2017,7,271.
[20]Ali S.A.,Gul T.,The convective study of the Al2O3-H2Oand Cu-H2O nano-liquid film sprayed over a stretching cylinder with viscous dissipation.The European Physical Journal Plus,2017,132:495.
[21]Sparrow E.M.,Gregg J.L.,A theory of rotating condensation.Journal of Heat Transfer,1959,81:113-120.
[22]Wang C.Y.,Liquid film on an unsteady stretching surface.Quarterly of Applied Mathematics,1990,48(4):601-610.
[23]Rehman A.U.,Mehmood R.,Nadeem S.,Akbar N.S.,Motsa S.S.,Effects of single and multi-walled carbon nano tubes on water and engine oil based rotating fluids with internal heating,Advanced Powder Technology,2017,28(9):1991?2002.
[24]Ellahi R.,Hassan M.,Zeeshan A.,Study of natural convection MHD nanofluid by means of single and multiwalled carbon nanotubes suspended in a salt water solution.IEEE Transactions on Nanotechnology,2015,14(4):1?10.
[25]Sajid M.,Hayat T.,Asghar S.,Non-similar solution for the axisymmetric flow of a third-grade fluid over a radially stretching sheet.Acta Mechanica,2007,189:193-205.
[26]Gul T.,Scattering of a thin layer over a nonlinear radially extending surface with Magneto hydrodynamic and thermal dissipation.Surface Review and Letters,2018,1850123:1-7.DOI:10.1142/S0218625X18501238.
[27]Beata G.,Jacek K.,Modeling of thermal properties of thermal insulation layered with transparent,opaque and reflective film.Journal of Thermal Science,2018,27(5):463?469.
[28]Pawe?M.,Paulina K.,Magdalena H.,Edyta K.,Mariusz J.,Comprehensive approach for porous materials analysis using a dedicated preprocessing tool for mass and heat transfer modeling.Journal of Thermal Science,2018,27(.5):479?486.
[29]Ran T.,Xiaoye D.,Dabiao W.,Lin S.,Study on Al2O3extraction from activated coal gangue under different calcination atmospheres.Journal of Thermal Science,2017,26(6):570?576.
[30]Grunt K.,?uraw A.,Pietrowicz S.,Analysis of Nusselt number distribution in case of a strongly heated,horizontal rod.Journal of Thermal Science,2016,25(6):542?548.
[31]Gul T.,Firdous K.,The experimental study to examine the stable dispersion of the graphene nanoparticles and to look at the GO-H2O nanofluid flow between two rotating disks.Applied Nanoscience,2018:1?17.DOI:https://doi.org/10.1007/s13204-018-0851-4.
[32]Liao S.J.,An optimal homotopy-analysis approach for strongly nonlinear differential equations,Communications in Nonlinear Science and Numerical Simulation,2010,15:2003?2016.
[33]Hayat T.,Muhammad T.,Shehzad S.A.,Alsaedi A.,An analytical solution for magnetohydrodynamic Oldroyd-Bnanofluid flow induced by a stretching sheet with heat generation/absorption,International Journal of Thermal Science,2017,111:274?288.
[2]Oberlin A.,Endo M.,Koyama T.,Filamentous growth of carbon through benzene decomposition.Journal of Crystal Growth,1976,32:335?349.
[3]Iijima S.,Ichihashi T.,Single-shell carbon nanotubes of1-nm diameter.Nature,1993,363:603?605.
[4]Bethune D.S.,Kiang C.H.,Devries M.S.,Gorman G.,Savoy R.,Vazquez J.,et al.,Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls.Nature,1993,363:605-607.
[5]Terrones M.,Science and technology of the twenty-first century:synthesis,properties,and applications of carbon nanotubes.Annual Review of Materials Research,2003,33:419?501.
[6]De Volder M.F.L.,Tawfick S.H.,Baughman R.H.,Hart A.J.,Carbon nanotubes:present and future commercial applications.Science,2013,339:535?539.
[7]Negin C.,Ali S.,Xie Q.,Application of nanotechnology for enhancing oil recovery-A review,Petroleum,2016,2:324?333.
[8]Murshed S.M.S.,Nieto de Castro C.A.,Superior thermal features of carbon nanotubes-based nano fluids-Areview,Renewable and Sustainable Energy Reviews,2014,37:155?167.
[9]Qiu L.,Scheider K.,Radwan S.A.,Larkin L.S.,Saltonstall C.B.,Feng Y.,Zhang X.,Norris P.M.,Thermal transport barrier in carbon nanotube array nano-thermal interface materials,Carbon,2017,120:128?136.
[10]Qiu L.,Wang X.,Tang D.,Zheng X.,Norris P.M.,Wen D.,Zhao J.,Zhang X.,Li Q.,Functionalization and densification of inter-bundle interfaces for improvement in electrical and thermal transport of carbon nanotube fibers,Carbon,2016,105:248?259.
[11]Qiu L.,Zhu N.,Zou H.,Feng Y.,Zhang X.,Tang D.,Advances in thermal transport properties at nanoscale in China,International Journal of Heat and Mass Transfer,2018,125:413?433.
[12]Zaidi Z.,Mohyud-din S.T.,Mohsen B.B.,Convective heat transfer and MHD analysis of wall jet flow of nanofluids containing carbon nanotubes,Engineering Computations,2017,34:1?9.
[13]Sreedevi P.,Reddy P.S.,Chamkha A.J.,Magnetohydrodynamics heat and mass transfer analysis of single and multi-wall carbon nanotubes over vertical cone with convective boundary condition,International Journal of Mechanical Science,2018,135:646?655.
[14]Haq R.U.,Shahzad F.,Al-Mdallal Q.M.,MHD pulsatile flow of engine oil based carbon nanotubes between two concentric cylinders.Results in Physics,2017,7:57?68.
[15]Xue Q.,Model for thermal conductivity of carbon nanotube-based composites.Physica B:Condensed Matter,2005,368:302?307.
[16]Garbadeen I.D.,Sharifpur M.,Slabber J.M.,Meyer J.P.,Experimental study on natural convection of MWCNT-water nanofluids in a square enclosure.International Communications in Heat and Mass Transfer,2017,88:1-8.
[17]Khan U.,Ahmed N.,Mohyud-Din S.T.,Sikander W.,Flow of carbon nanotubes suspended nanofluid in stretchable non-parallel walls,Neural Computing Applications,2017:DOI:https://doi.org/10.1007/s00521-017-2891-1.
[18]Sheikholeslami M.,Seyednezhad M.,Nanofluid heat transfer in a permeable enclosure in presence of variable magnetic field by means of CVFEM.International Journal of Heat and Mass Transfer,2017,114:1169?1180.
[19]Khan N.S.,Gul T.,Islam S.,Khan I.,Aisha M.A.,Ali S.A.,Magnetohydrodynamic nanoliquid thin film sprayed on a stretching cylinder with heat transfer.Applied Sciences,2017,7,271.
[20]Ali S.A.,Gul T.,The convective study of the Al2O3-H2Oand Cu-H2O nano-liquid film sprayed over a stretching cylinder with viscous dissipation.The European Physical Journal Plus,2017,132:495.
[21]Sparrow E.M.,Gregg J.L.,A theory of rotating condensation.Journal of Heat Transfer,1959,81:113-120.
[22]Wang C.Y.,Liquid film on an unsteady stretching surface.Quarterly of Applied Mathematics,1990,48(4):601-610.
[23]Rehman A.U.,Mehmood R.,Nadeem S.,Akbar N.S.,Motsa S.S.,Effects of single and multi-walled carbon nano tubes on water and engine oil based rotating fluids with internal heating,Advanced Powder Technology,2017,28(9):1991?2002.
[24]Ellahi R.,Hassan M.,Zeeshan A.,Study of natural convection MHD nanofluid by means of single and multiwalled carbon nanotubes suspended in a salt water solution.IEEE Transactions on Nanotechnology,2015,14(4):1?10.
[25]Sajid M.,Hayat T.,Asghar S.,Non-similar solution for the axisymmetric flow of a third-grade fluid over a radially stretching sheet.Acta Mechanica,2007,189:193-205.
[26]Gul T.,Scattering of a thin layer over a nonlinear radially extending surface with Magneto hydrodynamic and thermal dissipation.Surface Review and Letters,2018,1850123:1-7.DOI:10.1142/S0218625X18501238.
[27]Beata G.,Jacek K.,Modeling of thermal properties of thermal insulation layered with transparent,opaque and reflective film.Journal of Thermal Science,2018,27(5):463?469.
[28]Pawe?M.,Paulina K.,Magdalena H.,Edyta K.,Mariusz J.,Comprehensive approach for porous materials analysis using a dedicated preprocessing tool for mass and heat transfer modeling.Journal of Thermal Science,2018,27(.5):479?486.
[29]Ran T.,Xiaoye D.,Dabiao W.,Lin S.,Study on Al2O3extraction from activated coal gangue under different calcination atmospheres.Journal of Thermal Science,2017,26(6):570?576.
[30]Grunt K.,?uraw A.,Pietrowicz S.,Analysis of Nusselt number distribution in case of a strongly heated,horizontal rod.Journal of Thermal Science,2016,25(6):542?548.
[31]Gul T.,Firdous K.,The experimental study to examine the stable dispersion of the graphene nanoparticles and to look at the GO-H2O nanofluid flow between two rotating disks.Applied Nanoscience,2018:1?17.DOI:https://doi.org/10.1007/s13204-018-0851-4.
[32]Liao S.J.,An optimal homotopy-analysis approach for strongly nonlinear differential equations,Communications in Nonlinear Science and Numerical Simulation,2010,15:2003?2016.
[33]Hayat T.,Muhammad T.,Shehzad S.A.,Alsaedi A.,An analytical solution for magnetohydrodynamic Oldroyd-Bnanofluid flow induced by a stretching sheet with heat generation/absorption,International Journal of Thermal Science,2017,111:274?288.