碳纳米流体的Darcy-Forchheimer流体特征在化学物质框架中的数值意义（英文）
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摘要
本文对碳纳米管中发生的Darcy-Forchheimer流体化学反应进行了研究。当碳纳米管被认为是纳米材料时,使用水作基液,由于指数拉伸弯曲表面流动的产生而出现热源。采用纳米液体的薛氏关系式研究了碳纳米管(单壁、多壁碳纳米管)的特性。利用变换技术得到非线性常微分方程,对控制系统进行数值求解。用图示说明所涉及的参数在增加表面摩擦系数的情况下,对流动、温度、浓度、热传递速率(Nusselt数)的影响。速度随着Forchheimer数和孔隙度的增大而减慢,但温度则呈相反的趋势。与单壁碳纳米管相比,多壁碳纳米管的作用更显著。
Present work reports chemically reacting Darcy-Forchheimer flow of nanotubes. Water is utilized as base liquid while carbon nanotubes are considered nanomaterial. An exponential stretchable curved surface flow is originated.Heat source is present. Xue relation of nanoliquid is employed to explore the feature of CNTs(single and multi-wall).Transformation technique is adopted in order to achieve non-linear ordinary differential systems. The governing systems are solved numerically. Effects of involved parameters on flow, temperature, concentration, heat transfer rate(Nusselt number) with addition of skin friction coefficient are illustrated graphically. Decay in velocity is noted with an increment in Forchheimer number and porosity parameter while opposite impact is seen for temperature. Moreover, role of MWCNTs is prominent when compared with SWCNTs.
Present work reports chemically reacting Darcy-Forchheimer flow of nanotubes. Water is utilized as base liquid while carbon nanotubes are considered nanomaterial. An exponential stretchable curved surface flow is originated.Heat source is present. Xue relation of nanoliquid is employed to explore the feature of CNTs(single and multi-wall).Transformation technique is adopted in order to achieve non-linear ordinary differential systems. The governing systems are solved numerically. Effects of involved parameters on flow, temperature, concentration, heat transfer rate(Nusselt number) with addition of skin friction coefficient are illustrated graphically. Decay in velocity is noted with an increment in Forchheimer number and porosity parameter while opposite impact is seen for temperature. Moreover, role of MWCNTs is prominent when compared with SWCNTs.
引文
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[13]HAYAT T,MUHAMMAD K,ALSAEDI A,ASGHAR S.Numerical study for melting heat transfer and homogeneousheterogeneous reactions in flow involving carbon nanotubes[J].Results in Physics,2018,8:415-421.
[14]KHAN M I,HAYAT T,KHAN M I,ALSAEDI A.Amodified homogeneous-heterogeneous reaction for MHDstagnation flow with viscous dissipation and Joule heating[J].International Journal of Heat and Mass Transfer,2017,113:310-317.
[15]SHEIKHOLESLAMI M,HAYAT T,ALSAEDI A,ABELMAN S.Numerical analysis of EHD nanofluid force convective heat transfer considering electric field dependent viscosity[J].International Journal of Heat and Mass Transfer,Part B,2017,108:2558-2565.
[16]SELIMEFENDIGIL F,?ZTOP H F.Corrugated conductive partition effects on MHD free convection of CNT-water nanofluid in a cavity[J].International Journal of Heat and Mass Transfer,2019,129:265-277.
[17]SHEIKHOLESLAMI M,JAFARYAR M,LI Z.Second law analysis for nanofluid turbulent flow inside a circular duct in presence of twisted tape turbulators[J].Journal of Molecular Liquids,2018,263:489-500.
[18]SELIMEFENDIGIL F,?ZTOP H F.Numerical analysis and ANFIS modeling for mixed convection of CNT-water nanofluid filled branching channel with an annulus and a rotating inner surface at the junction[J].International Journal of Heat and Mass Transfer,2018,127:583-599.
[19]SHEIKHOLESLAMI M,HAYAT T,ALSAEDI A.MHDfree convection of Al2O3-water nanofluid considering thermal radiation:A numerical study[J].International Journal of Heat and Mass Transfer,2016,96:513-524.
[20]SELIMEFENDIGIL F,?ZTOP H F.Forced convection and thermal predictions of pulsating nanofluid flow over a backward facing step with a corrugated bottom wall[J].International Journal of Heat and Mass Transfer,2017,110:231-247.
[21]SHEIKHOLESLAMI M,HAYAT T,ALSAEDI A.Numerical simulation of nanofluid forced convection heat transfer improvement in existence of magnetic field using lattice Boltzmann method[J].International Journal of Heat and Mass Transfer,2017,108:1870-1883.
[22]MAJID S,MOHAMMAD J.Optimal selection of annulus radius ratio to enhance heat transfer with minimum entropy generation in developing laminar forced convection of water-Al2O3 nanofluid flow[J].Journal of Central South University,2017,24:1850-1865.
[23]SHEIKHOLESLAMI M,HAYAT T,ALSAEDI A.Numerical study for external magnetic source influence on water based nanofluid convective heat transfer[J].International Journal of Heat and Mass Transfer,2017,106:745-755.
[24]SARI M R,KEZZAR M,ADJABI R.Heat transfer of copper/water nanofluid flow through converging-diverging channel[J].Journal of Central South University,2016,23:484-496.
[25]SIAVASHI M,GHASEMI K,YOUSOFV R,DERAKHSHAN S.Computational analysis of SWCNHnanofluid-based direct absorption solar collector with a metal sheet[J].Solar Energy,2018,170:252-262.
[26]SIAVASHI M,RASAM H,IZADI A.Similarity solution of air and nanofluid impingement cooling of a cylindrical porous heat sink[J].J Therm Anal Calorim,2018,135:1399-1415.DOI:doi.org/10.1007/s10973-018-7540-0.
[27]HAYAT T,MUHAMMAD K,ULLAH I,ALSAEDI A,ASGHAR S.Rotating squeezed flow with carbon nanotubes and melting heat[J].Physysica Scripta,2018.DOI:doi.org/10.1088/1402-4896/aaef66.
[28]MAHIAN O,KOLSI L,AMANI M,ESTELLéP,AHMADIG,KLEINSTREUER C,MARSHALL J S,TAYLOR R A,ABU-NADA E,RASHIDI S,NIAZMAND H,WONGWISES S,HAYAT T,KASAEIAN A,POP I.Recent advances in modeling and simulation of nanofluid flows-Part II:Applications[J].Physics Reports,2018,791:1-59.DOI:doi.org/10.1016/j.physrep.2018.11.003.
[29]CRANE L J.Flow past a stretching plate[J].Zeitschrift fur Angewandte Mathematik und Physik,1970,21:645-641.
[30]HAYAT T,MUHAMMAD T ALSAEDI A.Impact of Cattaneo-Christov heat flux in three-dimensional flow of second grade fluid over a stretching surface[J].Chinese Journal of Physics,2017,55:1242-1251.
[31]SHIEKHOLESLAMI M,ELLAHI R,ASHORYNEJAD H R,DOMAIRRY G,HAYAT T.Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium[J].J Comput Theor Nanos,2014,11:486-496.
[32]HAYAT T,MUHAMMAD K,FAROOQ M,ALSAEDI A.Squeezed flow subject to Cattaneo-Christov heat flux and rotating frame[J].Journal of Molecular Liquids,2016,220:216-222.
[33]SAJID M,ALI N,JAVED T,ABBAS Z.Stretching a curved surface in a viscous fluid[J].Chin Phys Lett,2010,27:024703.
[34]HAYAT T,SAIF R S,ELLAHI R,MUHAMMAD T,AHMAD B.Numerical study of boundary-layer flow due to a nonlinear curved stretching sheet with convective heat and mass conditions[J].Results in Physics,2017,7:2601-2606.
[35]HAYAT T,HAIDER F,MUHAMMAD T,ALSAEDI A.Darcy-Forchheimer flow due to a curved stretching surface with Cattaneo-Christov double diffusion:A numerical study[J].Results in Physics,2017,7:2663-2670.
[36]NAVEED M,ABBAS Z,SAJID M.Hydromagnetic flow over an unsteady curved stretching surface[J].Engineering Science and Technology,an International Journal,2016,19:841-845.
[37]HAYAT T,AZIZ A,MUHAMMAD T,ALSAEDI A.Numerical study for nanofluid flow due to a nonlinear curved stretching surface with convective heat and mass conditions[J].Results in Physics,2017,7:3100-3106.
[38]OKECHI N F,JALILA M,AND ASGHAR S.Flow of viscous fluid along an exponentially stretching curved surface[J].Results in Physics,2017,7:2851-2854.
[39]MERKIN J H.A model for isothermal homogenousheterogenous reactions in boundarylayer flow[J].Math Computer Model,1996,24:125-136.
[40]KHAN M I,HAYAT T,ALSAEDI A.Numerical analysis for Darcy-Forchheimer flow in presence of homogeneousheterogeneous reactions[J].Results in Physics,2017,7:2644-2650.
[41]HAYAT T,KHAN,I,ALSAEDI A,KHAN M I.Homogeneous-heterogeneous reactions and melting heat transfer effects in the MHD flow by a stretching surface with variable thickness[J].J Mol Liq,2016,223:960-968.
[42]IMTIAZ M,HAYAT T,ALSAEDI A.MHD convective flow of Jeffrey fluid due to a curved stretching surface with homogeneous-heterogeneous reactions[J].PLOS One,2016,9:e0161641.
[43]HAYAT T,AYUB T,MUHAMMAD T,ALSAEDI A.Three-dimensional flow with Cattaneo-Christov double diffusion and homogeneous-heterogeneous reactions[J].Results in Physics,2017,7:2812-2820.
[44]IMTIAZ M,HAYAT T ALSAEDI A.Convective flow of ferrofluid due to a curved stretching surface with homogeneous-heterogeneous reactions[J].Powder Technology,2017,310:154-162.
[45]HAYAT T,ULLAH I,ALSAEDI A,AHMAD B.Numerical simulation for homogeneous-heterogeneous reactions in flow of Sisko fluid[J].J Braz Soc Mech Sci Eng,2018,40:73.
[46]QAYYUM S,KHAN M I,HAYAT T,ALSAEDI A.Aframework for nonlinear thermal radiation and homogeneous-heterogeneous reactions flow based on silver-water and copper-water nanoparticles:A numerical model for probable error[J].Results Phys,2017,7:1907-1914.
[47]HAYAT T,ULLAH I,WAQAS M,ALSAEDI A.Flow of chemically reactive magneto Cross nanoliquid with temperature-dependent conductivity[J].Appl Nanosci,2018.DOI:doi.org/10.1007/s13204-018-0813.
[48]XUE Q.Model for thermal conductivity of carbon nanotube based composites[J].Phys B:Condens Matter,2005,368:302-307.
[49]KHAN M I,QAYYUM S,HAYAT T,WAQAS M,KHAN MI,ALSAEDI A.Entropy generation minimization and binary chemical reaction with Arrhenius activation energy in MHDradiative flow of nanomaterial[J].Journal of Molecular Liquids,2018,259:274-283.
[50]PRAKASH J,RAMESH K,TRIPATHI D,KUMAR R.Numerical simulation of heat transfer in blood flow altered by electroosmosis through tapered micro-vessels[J].Microvascular Research,2018,118:162-172.
[2]ELIAS M M,MIQDAD M,MAHABUBUL I M,SAIDURR,KAMALISAVESTANI M,SOHEL M R,HAPBASLI A,RAHIM N A,AMALINA M A.Effect of nanoparticle shape on the heat transfer and thermodynamic performance of a shell and tube heat exchanger[J].International Communications in Heat and Mass Transfer,2013,44:93-99.
[3]VOLDER M F L D,TAWFIC S H,BAUGHMAN R H,HART A J.Carbon nanotubes:Present and future commercial applications[J].Science,2013,339:535-539.
[4]HAYAT T,MUHAMMAD K,FAROOQ M,ALSAEDI A.Unsteady squeezing flow of carbon nanotubes with convective boundary conditions[J].PLOS One,2016,11:0152923.
[5]TURKYILMAZOGLU M.Analytical solutions of single and multi-phase models for the condensation of nanofluid film flow and heat transfer[J].European Journal of Mechanics,B/Fluids,2015,53:272-277.
[6]HAYAT T,FAROOQ M,ALSAEDI A.Homogenousheterogenous reactions in the stagnation point ow of carbon nanotubes with Newtonian heating[J].AIP Advances,2015,5:027130.
[7]SHIEKHOLESLAMI M,ELLAHI R.Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid[J].International Journal of Heat and Mass Transfer,2015,89:799-808.
[8]HAYAT T,MUHAMMAD K,FAROOQ M,ALSAEDI A.Melting heat transfer in stagnation point flow of carbon nanotubes towards variable thickness surface[J].AIPAdvances,2016,6:015214.
[9]SOLTANI S,KASAEIAN A,SARRAFHA H,WEN D.An experimental investigation of a hybrid photovoltaic/thermoelectric system with nanofluid application[J].Solar Energy,2017,115:1033-1043.
[10]HAYAT T,AHMED S,MUHAMMAD T,ALSAEDI A.Modern aspects of homogeneous-heterogeneous reactions and variable thickness in nanofluids through carbon nanotubes[J].Physica E:Low-dimensional Systems and Nanostructures,2017,94:70-77.
[11]HAYAT T,MUHAMMAD K,MUHAMMAD T,ALSAEDIA.Melting heat in radiative flow of carbon nanotubes with homogeneous-heterogeneous Reactions[J].Communicatins in Theoritical Physics,2018,69:441-448.
[12]KHAN M I,ULLAH S,HAYAT T,KHAN M I,ALSAEDIA.Entropy generation minimization(EGM)for convection nanomaterial flow with nonlinear radiative heat flux[J].Journal of Molecular Liquids,260,2018:279-291.
[13]HAYAT T,MUHAMMAD K,ALSAEDI A,ASGHAR S.Numerical study for melting heat transfer and homogeneousheterogeneous reactions in flow involving carbon nanotubes[J].Results in Physics,2018,8:415-421.
[14]KHAN M I,HAYAT T,KHAN M I,ALSAEDI A.Amodified homogeneous-heterogeneous reaction for MHDstagnation flow with viscous dissipation and Joule heating[J].International Journal of Heat and Mass Transfer,2017,113:310-317.
[15]SHEIKHOLESLAMI M,HAYAT T,ALSAEDI A,ABELMAN S.Numerical analysis of EHD nanofluid force convective heat transfer considering electric field dependent viscosity[J].International Journal of Heat and Mass Transfer,Part B,2017,108:2558-2565.
[16]SELIMEFENDIGIL F,?ZTOP H F.Corrugated conductive partition effects on MHD free convection of CNT-water nanofluid in a cavity[J].International Journal of Heat and Mass Transfer,2019,129:265-277.
[17]SHEIKHOLESLAMI M,JAFARYAR M,LI Z.Second law analysis for nanofluid turbulent flow inside a circular duct in presence of twisted tape turbulators[J].Journal of Molecular Liquids,2018,263:489-500.
[18]SELIMEFENDIGIL F,?ZTOP H F.Numerical analysis and ANFIS modeling for mixed convection of CNT-water nanofluid filled branching channel with an annulus and a rotating inner surface at the junction[J].International Journal of Heat and Mass Transfer,2018,127:583-599.
[19]SHEIKHOLESLAMI M,HAYAT T,ALSAEDI A.MHDfree convection of Al2O3-water nanofluid considering thermal radiation:A numerical study[J].International Journal of Heat and Mass Transfer,2016,96:513-524.
[20]SELIMEFENDIGIL F,?ZTOP H F.Forced convection and thermal predictions of pulsating nanofluid flow over a backward facing step with a corrugated bottom wall[J].International Journal of Heat and Mass Transfer,2017,110:231-247.
[21]SHEIKHOLESLAMI M,HAYAT T,ALSAEDI A.Numerical simulation of nanofluid forced convection heat transfer improvement in existence of magnetic field using lattice Boltzmann method[J].International Journal of Heat and Mass Transfer,2017,108:1870-1883.
[22]MAJID S,MOHAMMAD J.Optimal selection of annulus radius ratio to enhance heat transfer with minimum entropy generation in developing laminar forced convection of water-Al2O3 nanofluid flow[J].Journal of Central South University,2017,24:1850-1865.
[23]SHEIKHOLESLAMI M,HAYAT T,ALSAEDI A.Numerical study for external magnetic source influence on water based nanofluid convective heat transfer[J].International Journal of Heat and Mass Transfer,2017,106:745-755.
[24]SARI M R,KEZZAR M,ADJABI R.Heat transfer of copper/water nanofluid flow through converging-diverging channel[J].Journal of Central South University,2016,23:484-496.
[25]SIAVASHI M,GHASEMI K,YOUSOFV R,DERAKHSHAN S.Computational analysis of SWCNHnanofluid-based direct absorption solar collector with a metal sheet[J].Solar Energy,2018,170:252-262.
[26]SIAVASHI M,RASAM H,IZADI A.Similarity solution of air and nanofluid impingement cooling of a cylindrical porous heat sink[J].J Therm Anal Calorim,2018,135:1399-1415.DOI:doi.org/10.1007/s10973-018-7540-0.
[27]HAYAT T,MUHAMMAD K,ULLAH I,ALSAEDI A,ASGHAR S.Rotating squeezed flow with carbon nanotubes and melting heat[J].Physysica Scripta,2018.DOI:doi.org/10.1088/1402-4896/aaef66.
[28]MAHIAN O,KOLSI L,AMANI M,ESTELLéP,AHMADIG,KLEINSTREUER C,MARSHALL J S,TAYLOR R A,ABU-NADA E,RASHIDI S,NIAZMAND H,WONGWISES S,HAYAT T,KASAEIAN A,POP I.Recent advances in modeling and simulation of nanofluid flows-Part II:Applications[J].Physics Reports,2018,791:1-59.DOI:doi.org/10.1016/j.physrep.2018.11.003.
[29]CRANE L J.Flow past a stretching plate[J].Zeitschrift fur Angewandte Mathematik und Physik,1970,21:645-641.
[30]HAYAT T,MUHAMMAD T ALSAEDI A.Impact of Cattaneo-Christov heat flux in three-dimensional flow of second grade fluid over a stretching surface[J].Chinese Journal of Physics,2017,55:1242-1251.
[31]SHIEKHOLESLAMI M,ELLAHI R,ASHORYNEJAD H R,DOMAIRRY G,HAYAT T.Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium[J].J Comput Theor Nanos,2014,11:486-496.
[32]HAYAT T,MUHAMMAD K,FAROOQ M,ALSAEDI A.Squeezed flow subject to Cattaneo-Christov heat flux and rotating frame[J].Journal of Molecular Liquids,2016,220:216-222.
[33]SAJID M,ALI N,JAVED T,ABBAS Z.Stretching a curved surface in a viscous fluid[J].Chin Phys Lett,2010,27:024703.
[34]HAYAT T,SAIF R S,ELLAHI R,MUHAMMAD T,AHMAD B.Numerical study of boundary-layer flow due to a nonlinear curved stretching sheet with convective heat and mass conditions[J].Results in Physics,2017,7:2601-2606.
[35]HAYAT T,HAIDER F,MUHAMMAD T,ALSAEDI A.Darcy-Forchheimer flow due to a curved stretching surface with Cattaneo-Christov double diffusion:A numerical study[J].Results in Physics,2017,7:2663-2670.
[36]NAVEED M,ABBAS Z,SAJID M.Hydromagnetic flow over an unsteady curved stretching surface[J].Engineering Science and Technology,an International Journal,2016,19:841-845.
[37]HAYAT T,AZIZ A,MUHAMMAD T,ALSAEDI A.Numerical study for nanofluid flow due to a nonlinear curved stretching surface with convective heat and mass conditions[J].Results in Physics,2017,7:3100-3106.
[38]OKECHI N F,JALILA M,AND ASGHAR S.Flow of viscous fluid along an exponentially stretching curved surface[J].Results in Physics,2017,7:2851-2854.
[39]MERKIN J H.A model for isothermal homogenousheterogenous reactions in boundarylayer flow[J].Math Computer Model,1996,24:125-136.
[40]KHAN M I,HAYAT T,ALSAEDI A.Numerical analysis for Darcy-Forchheimer flow in presence of homogeneousheterogeneous reactions[J].Results in Physics,2017,7:2644-2650.
[41]HAYAT T,KHAN,I,ALSAEDI A,KHAN M I.Homogeneous-heterogeneous reactions and melting heat transfer effects in the MHD flow by a stretching surface with variable thickness[J].J Mol Liq,2016,223:960-968.
[42]IMTIAZ M,HAYAT T,ALSAEDI A.MHD convective flow of Jeffrey fluid due to a curved stretching surface with homogeneous-heterogeneous reactions[J].PLOS One,2016,9:e0161641.
[43]HAYAT T,AYUB T,MUHAMMAD T,ALSAEDI A.Three-dimensional flow with Cattaneo-Christov double diffusion and homogeneous-heterogeneous reactions[J].Results in Physics,2017,7:2812-2820.
[44]IMTIAZ M,HAYAT T ALSAEDI A.Convective flow of ferrofluid due to a curved stretching surface with homogeneous-heterogeneous reactions[J].Powder Technology,2017,310:154-162.
[45]HAYAT T,ULLAH I,ALSAEDI A,AHMAD B.Numerical simulation for homogeneous-heterogeneous reactions in flow of Sisko fluid[J].J Braz Soc Mech Sci Eng,2018,40:73.
[46]QAYYUM S,KHAN M I,HAYAT T,ALSAEDI A.Aframework for nonlinear thermal radiation and homogeneous-heterogeneous reactions flow based on silver-water and copper-water nanoparticles:A numerical model for probable error[J].Results Phys,2017,7:1907-1914.
[47]HAYAT T,ULLAH I,WAQAS M,ALSAEDI A.Flow of chemically reactive magneto Cross nanoliquid with temperature-dependent conductivity[J].Appl Nanosci,2018.DOI:doi.org/10.1007/s13204-018-0813.
[48]XUE Q.Model for thermal conductivity of carbon nanotube based composites[J].Phys B:Condens Matter,2005,368:302-307.
[49]KHAN M I,QAYYUM S,HAYAT T,WAQAS M,KHAN MI,ALSAEDI A.Entropy generation minimization and binary chemical reaction with Arrhenius activation energy in MHDradiative flow of nanomaterial[J].Journal of Molecular Liquids,2018,259:274-283.
[50]PRAKASH J,RAMESH K,TRIPATHI D,KUMAR R.Numerical simulation of heat transfer in blood flow altered by electroosmosis through tapered micro-vessels[J].Microvascular Research,2018,118:162-172.