碳纳米管指数拉伸曲面上Darcy-Forchheimer流动的数值处理（英文）
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摘要
本文对碳水纳米流体的二维流动进行了数值模拟。流体是由指数扩展曲面引起的。本文用Darcy-Forchheimer方法描述了渗透空间中的黏性液体。通过适当的变换,将偏微分方程的后续排列转化为常微分框架。采用NDSolve程序建立了控制框架的数值排布。考察了不同参数对温度和速度的影响,并对表面摩擦和传热速率进行监测。
This article gives a numerical report to two dimensional(2D) Darcy-Forchheimer flow of carbon-water nanofluid. Flow is instigated by exponential extending curved surface. Viscous liquid in permeable space is described by Darcy-Forchheimer. The subsequent arrangement of partial differential equations is changed into ordinary differential framework through proper transformations. Numerical arrangements of governing frameworks are set up by NDSolve procedure. Outcomes of different sundry parameters on temperature and velocity are examined. Skin friction and heat transfer rate are also shown and inspected.
This article gives a numerical report to two dimensional(2D) Darcy-Forchheimer flow of carbon-water nanofluid. Flow is instigated by exponential extending curved surface. Viscous liquid in permeable space is described by Darcy-Forchheimer. The subsequent arrangement of partial differential equations is changed into ordinary differential framework through proper transformations. Numerical arrangements of governing frameworks are set up by NDSolve procedure. Outcomes of different sundry parameters on temperature and velocity are examined. Skin friction and heat transfer rate are also shown and inspected.
引文
[1] CHOI S U S, ZHANG Z G, YU W, LOCKWOOD F E,GRUKLE E A. Anomalous thermal conductivity enhancement in nanotube suspensions[J]. Applied Physics Letters, 2001, 79:2252.
[2] XUE Q Z. Model for thermal conductivity of carbon nanotube-based composites[J]. Physica B:Condensed Matter, 2005, 368:302-307.
[3] DING Y, ALIAS H, WEN D, WILLIAMS R A. Heat transfer of aqueous suspensions of carbon nanotubes(CNT nanofluids)[J]. International Journal of Heat and Mass Transfer, 2006,49:240-250.
[4] WANG J, ZHU J, ZHANG X, CHEN Y. Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows[J]. Experimental Thermal and Fluid Sciences,2013,44:716-721.
[5] SAFAEI M R, TOGUN H, VAFAI K, KAZI S N,BADARUDIN A. Investigation of heat transfer enhancement in a forward-facing contracting channel using FMWCNT nanofluids[J]. Numerical Heat Transfer, Part A, 2014, 66:1321-1340.
[6] ELLAHI R, HASSAN M, ZEESHAN A. Study of natural convection MHD nanofluid by means of single and multi walled carbon nanotubes suspended in a salt water solutions[J]. IEEE Transactions on Nanotechnology, 2015, 14:726-734.
[7] HAYAT T, HUSSAIN Z, MUHAMMAD T, ALSAEDI A.Effects of homogeneous and heterogeneous reactions in flow of nanofluids over a nonlinear stretching surface with variable surface thickness[J]. Journal of Molecular Liquids,2016,221:1121-1127.
[8] IQBAL Z, AZHAR E, MARAJ E N. Transport phenomena of carbon nanotubes and bioconvection nanoparticles on stagnation point flow in presence of induced magnetic field[J]. Physica E:Low-dimensional Systems and Nanostructures, 2017,91:128-135.
[9] KHAN U, AHMED N, MOHYUD-DIN S T. Numerical investigation for three dimensional squeezing flow of nanofluid in a rotating channel with lower stretching wallsuspended by carbon nanotubes[J]. Applied Thermal Engineering, 2017, 113:1107-1117.
[10] HAYAT T, HAIDER F, MUHAMMAD T, ALSAEDI A. On Darcy-Forchheimer flow of carbon nanotubes due to a rotating disk[J]. International Journal of Heat and Mass Transfer, 2017, 112:248-254.
[11] HAYAT T, MUHAMMAD T, ALSAEDI A, ALHUTHALI M S. Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation[J]. Journal of Magnetism and Magnetic Materials,2015,385:222-229.
[12] SULOCHANA C, SANDEEP N,SUGUNAMMA V,KUMAR B R. Aligned magnetic field and cross-diffusion effects of a nanofluid over an exponentially stretching surface in porous medium[J]. Applied Nanoscience, 2016, 6:737-746.
[13] SANDEEP N, CHAMKHA A J, ANIMASAUN I L.Numerical exploration of magnetohydrodynamic nanofluid flow suspended with magnetite nanoparticles[J]. Journal of Brazilian Society of Mechanical Sciences and Engineering,2017, 39:3635-3644.
[14] BABU M J, SANDEEP N, SALEEM S. Free convective MHD Cattaneo-Christov flow over three different geometries with thermophoresis and Brownian motion[J]. Alexandria Engineering Journal, 2017, 56:659-669.
[15] KUMAR M S, SANDEEP N, KUMAR B R, DINESH P A.A comparative analysis of magnetohydrodynamic nonNewtonian fluids flow over an exponential stretched sheet[J].Alexandria Engineering Journal, 2018, 57:2093-2100.https://doi.org/10. 1016/j.aej.2017.06.002.
[16] SUCHARITHA G, LAKSMINNARAYANA P, SANDEEP N.Joule heating and wall flexibility effects on the peristaltic flow of magnetohydrodynamic nanofluid[J]. International Journal of Mechanical Sciences, 2017, 131:52-62.
[17] REDDY J V R, SUGUNAMMA V, SANDEEP N. Dual solutions for nanofluid flow past a curved surface with nonlinear radiation, Soret and Dufour effect[J]. Journal of Physics:Conference Series, 2018, 1000:012152.
[18] SHEIKHOLESLAMI M, HAYAT T, MUHAMMAD T,ALSAEDI A. MHD forced convection flow of nanofluid in a porous cavity with hot elliptic obstacle by means of Lattice Boltzmann method[J]. International Journal of Mechanical Sciences, 2018, 135:532-540.
[19] HAYAT T, MUHAMMAD K, MUHAMMAD T, ALSAEDI A, Melting heat in radiative flow of carbon nanotubes with homogeneous-heterogeneous reactions[J]. Communications in Theoretical Physics, 2018, 69:441.
[20] HAYAT T, HAIDER F, MUHAMMAD T, ALSAEDI A.Darcy-Forchheimer squeezed flow of carbon nanotubes with thermal radiation[J]. Journal of Physics and Chemistry of Solids, 2018, 120:79-86.
[21] FORCHHEIMER P. Water movement through ground[J].Journal of the Association of German Engineers, 1901, 45:1782-1788.
[22] MUSKAT M. The flow of homogeneous fluids through porous media[M]. Edwards, MI. 1946.
[23] SEDDEEK M A. Influence of viscous dissipation and thermophoresis on Darcy-Forchheimer mixed convection in a fluid saturated porous media[J]. Journal of Colloid and Interface Science, 2006, 293:137--142.
[24] SADIQ M A, HAYAT T. Darcy-Forchheimer flow of magneto Maxwell liquid bounded by convectively heated sheet[J]. Results in Physics, 2016, 6:884-890.
[25] BAKAR S A, ARIFIN N M, NAZAR R, ALI F M, POP I.Forced convection boundary layer stagnation-point flow in Darcy-Forchheimer porous medium past a shrinking sheet[J].Frontiers in Heat and Mass Transfer, 2016, 7:38.
[26] HAYAT T, MUHAMMAD T, AL-MEZAL S, LIAO S J.Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux[J]. International Journal of Numerical Methods for Heat and Fluid Flow, 2016, 26:2355-2369.
[27] UMAVATHI J C, OJJELA O, VAJRAVELU K. Numerical analysis of natural convective flow and heat transfer of nanofluids in a vertical rectangular duct using DarcyForchheimer-Brinkman model[J]. International Journal of Thermal Sciences, 2017, 111:511-524.
[28] 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.
[29] HAYAT T, AZIZ A, MUHAMMAD T, ALSAEDI A.Darcy-Forchheimer three-dimensional flow of Williamson nanofluid over a convectively heated nonlinear stretching surface[J]. Communication in Theoretical Physics, 2017, 68:387.
[30] MUHAMMAD T, ALSAEDI A, SHEHZAD S A, HAYAT T.A revised model for Darcy-Forchheimer flow Maxwell nanofluid subject to convective boundary condition[J].Chinese Journal of Physics, 2017, 55:963-976.
[31] CRANE L J. Flow past a stretching plate[J]. Journal of Applied Mathematics and Physics(ZAMP), 1970, 21:645-647.
[32] SAJID M, ALI N, JAVED T,ABBAS Z. Stretching a curved surface in a viscous fluid[J]. Chinese Physics Letters, 2010,27:024703.
[33] ROSCA N C,POP I. Unsteady boundary layer flow over a permeable curved stretching/shrinking surface[J]. European Journal of Mechanics-B/Fluids, 2015, 51:61-67.
[34] NAVEED M,ABBAS Z,SAJID M. MHD flow of a microploar fluid due to curved stretching surface with thermal radiation[J]. Journal of Applied Fluid Mechanics,2016,9:131-138.
[35] ABBAS Z, NAVEED M, SAJID M, Hydromagnetic slip flow of nanofluid over a curved stretching surface with heatgeneration and thermal radiation[J]. Journal of Molecular Liquids, 2016,215:756-762.
[36] IMTIAZ M, HAYAT T, ALSAEDI A, HOBINY A.Homogeneous-heterogeneous reactions in MHD flow due to an unsteady curved stretching surface[J]. Journal of Molecular Liquids, 2016, 221:245-253.
[37] HAYAT T, SAJJAD R, ELLAHI R, ALSAEDI A,MUHAMMAD T. Homogeneous-heterogeneous reactions in MHD flow of micropolar fluid by a curved stretching surface[J]. Journal of Molecular Liquids, 2017,240:209-220.
[38] SANNI K M, ASGHAR S, JALIL M, OKECHIN F. Flow of viscous fluid along nonlinearly stretching curved surface[J].Results in Physics, 2017, 7:1-4.
[39] OKECHI N F, JALIL M, ASGHAR S. Flow of viscous fluid along an exponentially stretching curved surface[J]. Results in Physics, 2017, 7:2851-2854.
[40] HAYAT T, SAIF R S, ELLAHI R, MUHAMMAD T,AHMAD B. Numerical study for Darcy-Forchheimer flow due to a curved stretching surface with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions[J].Results in Physics, 2017, 7:2886-2892.
[41] 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.
[42] 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.
[43] 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.
[44] HAYAT T, RAFIQUE K, MUHAMMAD T, ALSAEDI A,AYUB M. Carbon nanotubes significance in DarcyForchheimer flow[J]. Results in Physics, 2018, 8:26-33.
[45] HAYAT T, HAIDER F, MUHAMMAD T,ALSAEDI A.Numerical study for Darcy-Forchheimer flow of nanofluid due to an exponentially stretching curved surface[J]. Results in Physics, 2018, 8:764-771.
[46] JAVED M, FAROOQ M, AHMAD S, ANJUM A. Melting heat transfer with radiative effects and homogeneousheterogeneous reaction in thermally stratified stagnation flow embedded in porous medium[J]. Journal of Central South University, 2018,25:2701-2711.
[2] XUE Q Z. Model for thermal conductivity of carbon nanotube-based composites[J]. Physica B:Condensed Matter, 2005, 368:302-307.
[3] DING Y, ALIAS H, WEN D, WILLIAMS R A. Heat transfer of aqueous suspensions of carbon nanotubes(CNT nanofluids)[J]. International Journal of Heat and Mass Transfer, 2006,49:240-250.
[4] WANG J, ZHU J, ZHANG X, CHEN Y. Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows[J]. Experimental Thermal and Fluid Sciences,2013,44:716-721.
[5] SAFAEI M R, TOGUN H, VAFAI K, KAZI S N,BADARUDIN A. Investigation of heat transfer enhancement in a forward-facing contracting channel using FMWCNT nanofluids[J]. Numerical Heat Transfer, Part A, 2014, 66:1321-1340.
[6] ELLAHI R, HASSAN M, ZEESHAN A. Study of natural convection MHD nanofluid by means of single and multi walled carbon nanotubes suspended in a salt water solutions[J]. IEEE Transactions on Nanotechnology, 2015, 14:726-734.
[7] HAYAT T, HUSSAIN Z, MUHAMMAD T, ALSAEDI A.Effects of homogeneous and heterogeneous reactions in flow of nanofluids over a nonlinear stretching surface with variable surface thickness[J]. Journal of Molecular Liquids,2016,221:1121-1127.
[8] IQBAL Z, AZHAR E, MARAJ E N. Transport phenomena of carbon nanotubes and bioconvection nanoparticles on stagnation point flow in presence of induced magnetic field[J]. Physica E:Low-dimensional Systems and Nanostructures, 2017,91:128-135.
[9] KHAN U, AHMED N, MOHYUD-DIN S T. Numerical investigation for three dimensional squeezing flow of nanofluid in a rotating channel with lower stretching wallsuspended by carbon nanotubes[J]. Applied Thermal Engineering, 2017, 113:1107-1117.
[10] HAYAT T, HAIDER F, MUHAMMAD T, ALSAEDI A. On Darcy-Forchheimer flow of carbon nanotubes due to a rotating disk[J]. International Journal of Heat and Mass Transfer, 2017, 112:248-254.
[11] HAYAT T, MUHAMMAD T, ALSAEDI A, ALHUTHALI M S. Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation[J]. Journal of Magnetism and Magnetic Materials,2015,385:222-229.
[12] SULOCHANA C, SANDEEP N,SUGUNAMMA V,KUMAR B R. Aligned magnetic field and cross-diffusion effects of a nanofluid over an exponentially stretching surface in porous medium[J]. Applied Nanoscience, 2016, 6:737-746.
[13] SANDEEP N, CHAMKHA A J, ANIMASAUN I L.Numerical exploration of magnetohydrodynamic nanofluid flow suspended with magnetite nanoparticles[J]. Journal of Brazilian Society of Mechanical Sciences and Engineering,2017, 39:3635-3644.
[14] BABU M J, SANDEEP N, SALEEM S. Free convective MHD Cattaneo-Christov flow over three different geometries with thermophoresis and Brownian motion[J]. Alexandria Engineering Journal, 2017, 56:659-669.
[15] KUMAR M S, SANDEEP N, KUMAR B R, DINESH P A.A comparative analysis of magnetohydrodynamic nonNewtonian fluids flow over an exponential stretched sheet[J].Alexandria Engineering Journal, 2018, 57:2093-2100.https://doi.org/10. 1016/j.aej.2017.06.002.
[16] SUCHARITHA G, LAKSMINNARAYANA P, SANDEEP N.Joule heating and wall flexibility effects on the peristaltic flow of magnetohydrodynamic nanofluid[J]. International Journal of Mechanical Sciences, 2017, 131:52-62.
[17] REDDY J V R, SUGUNAMMA V, SANDEEP N. Dual solutions for nanofluid flow past a curved surface with nonlinear radiation, Soret and Dufour effect[J]. Journal of Physics:Conference Series, 2018, 1000:012152.
[18] SHEIKHOLESLAMI M, HAYAT T, MUHAMMAD T,ALSAEDI A. MHD forced convection flow of nanofluid in a porous cavity with hot elliptic obstacle by means of Lattice Boltzmann method[J]. International Journal of Mechanical Sciences, 2018, 135:532-540.
[19] HAYAT T, MUHAMMAD K, MUHAMMAD T, ALSAEDI A, Melting heat in radiative flow of carbon nanotubes with homogeneous-heterogeneous reactions[J]. Communications in Theoretical Physics, 2018, 69:441.
[20] HAYAT T, HAIDER F, MUHAMMAD T, ALSAEDI A.Darcy-Forchheimer squeezed flow of carbon nanotubes with thermal radiation[J]. Journal of Physics and Chemistry of Solids, 2018, 120:79-86.
[21] FORCHHEIMER P. Water movement through ground[J].Journal of the Association of German Engineers, 1901, 45:1782-1788.
[22] MUSKAT M. The flow of homogeneous fluids through porous media[M]. Edwards, MI. 1946.
[23] SEDDEEK M A. Influence of viscous dissipation and thermophoresis on Darcy-Forchheimer mixed convection in a fluid saturated porous media[J]. Journal of Colloid and Interface Science, 2006, 293:137--142.
[24] SADIQ M A, HAYAT T. Darcy-Forchheimer flow of magneto Maxwell liquid bounded by convectively heated sheet[J]. Results in Physics, 2016, 6:884-890.
[25] BAKAR S A, ARIFIN N M, NAZAR R, ALI F M, POP I.Forced convection boundary layer stagnation-point flow in Darcy-Forchheimer porous medium past a shrinking sheet[J].Frontiers in Heat and Mass Transfer, 2016, 7:38.
[26] HAYAT T, MUHAMMAD T, AL-MEZAL S, LIAO S J.Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux[J]. International Journal of Numerical Methods for Heat and Fluid Flow, 2016, 26:2355-2369.
[27] UMAVATHI J C, OJJELA O, VAJRAVELU K. Numerical analysis of natural convective flow and heat transfer of nanofluids in a vertical rectangular duct using DarcyForchheimer-Brinkman model[J]. International Journal of Thermal Sciences, 2017, 111:511-524.
[28] 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.
[29] HAYAT T, AZIZ A, MUHAMMAD T, ALSAEDI A.Darcy-Forchheimer three-dimensional flow of Williamson nanofluid over a convectively heated nonlinear stretching surface[J]. Communication in Theoretical Physics, 2017, 68:387.
[30] MUHAMMAD T, ALSAEDI A, SHEHZAD S A, HAYAT T.A revised model for Darcy-Forchheimer flow Maxwell nanofluid subject to convective boundary condition[J].Chinese Journal of Physics, 2017, 55:963-976.
[31] CRANE L J. Flow past a stretching plate[J]. Journal of Applied Mathematics and Physics(ZAMP), 1970, 21:645-647.
[32] SAJID M, ALI N, JAVED T,ABBAS Z. Stretching a curved surface in a viscous fluid[J]. Chinese Physics Letters, 2010,27:024703.
[33] ROSCA N C,POP I. Unsteady boundary layer flow over a permeable curved stretching/shrinking surface[J]. European Journal of Mechanics-B/Fluids, 2015, 51:61-67.
[34] NAVEED M,ABBAS Z,SAJID M. MHD flow of a microploar fluid due to curved stretching surface with thermal radiation[J]. Journal of Applied Fluid Mechanics,2016,9:131-138.
[35] ABBAS Z, NAVEED M, SAJID M, Hydromagnetic slip flow of nanofluid over a curved stretching surface with heatgeneration and thermal radiation[J]. Journal of Molecular Liquids, 2016,215:756-762.
[36] IMTIAZ M, HAYAT T, ALSAEDI A, HOBINY A.Homogeneous-heterogeneous reactions in MHD flow due to an unsteady curved stretching surface[J]. Journal of Molecular Liquids, 2016, 221:245-253.
[37] HAYAT T, SAJJAD R, ELLAHI R, ALSAEDI A,MUHAMMAD T. Homogeneous-heterogeneous reactions in MHD flow of micropolar fluid by a curved stretching surface[J]. Journal of Molecular Liquids, 2017,240:209-220.
[38] SANNI K M, ASGHAR S, JALIL M, OKECHIN F. Flow of viscous fluid along nonlinearly stretching curved surface[J].Results in Physics, 2017, 7:1-4.
[39] OKECHI N F, JALIL M, ASGHAR S. Flow of viscous fluid along an exponentially stretching curved surface[J]. Results in Physics, 2017, 7:2851-2854.
[40] HAYAT T, SAIF R S, ELLAHI R, MUHAMMAD T,AHMAD B. Numerical study for Darcy-Forchheimer flow due to a curved stretching surface with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions[J].Results in Physics, 2017, 7:2886-2892.
[41] 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.
[42] 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.
[43] 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.
[44] HAYAT T, RAFIQUE K, MUHAMMAD T, ALSAEDI A,AYUB M. Carbon nanotubes significance in DarcyForchheimer flow[J]. Results in Physics, 2018, 8:26-33.
[45] HAYAT T, HAIDER F, MUHAMMAD T,ALSAEDI A.Numerical study for Darcy-Forchheimer flow of nanofluid due to an exponentially stretching curved surface[J]. Results in Physics, 2018, 8:764-771.
[46] JAVED M, FAROOQ M, AHMAD S, ANJUM A. Melting heat transfer with radiative effects and homogeneousheterogeneous reaction in thermally stratified stagnation flow embedded in porous medium[J]. Journal of Central South University, 2018,25:2701-2711.