Advertisement

Journal of Thermal Analysis and Calorimetry

, Volume 137, Issue 6, pp 1939–1949 | Cite as

Darcy–Forchheimer flow of carbon nanotubes due to a convectively heated rotating disk with homogeneous–heterogeneous reactions

  • Tasawar Hayat
  • Farwa Haider
  • Taseer MuhammadEmail author
  • Bashir Ahmad
Article
  • 56 Downloads

Abstract

Here, Darcy–Forchheimer flow of dissipating SWCNT and MWCNT nanofluids induced by rotation of disk with homogeneous–heterogeneous reactions and convective boundary condition is examined. Xue model of nanofluid is implemented in mathematical modeling. The resulting problems are computed for convergent optimal series solutions. Graphical results have been presented for physical quantities. Our findings indicate that skin friction coefficients and local Nusselt number are enhanced for larger values of nanoparticle volume fraction.

Keywords

CNTs (SWCNTs and MWCNTs) Darcy–Forchheimer flow Homogeneous–heterogeneous reactions Convective boundary condition Rotating disk OHAM 

Notes

References

  1. 1.
    Von Karman T. Uber laminare and turbulente Reibung. ZAMM Z Angew Math Mech. 1921;1:233–52.CrossRefGoogle Scholar
  2. 2.
    Turkyilmazoglu M, Senel P. Heat and mass transfer of the flow due to a rotating rough and porous disk. Int J Therm Sci. 2013;63:146–58.CrossRefGoogle Scholar
  3. 3.
    Rashidi MM, Kavyani N, Abelman S. Investigation of entropy generation in MHD and slip flow over rotating porous disk with variable properties. Int J Heat Mass Transf. 2014;70:892–917.CrossRefGoogle Scholar
  4. 4.
    Turkyilmazoglu M. Nanofluid flow and heat transfer due to a rotating disk. Comput Fluids. 2014;94:139–46.CrossRefGoogle Scholar
  5. 5.
    Hatami M, Sheikholeslami M, Gangi DD. Laminar flow and heat transfer of nanofluids between contracting and rotating disks by least square method. Power Technol. 2014;253:769–79.CrossRefGoogle Scholar
  6. 6.
    Mustafa M, Khan JA, Hayat T, Alsaedi A. On Bödewadt flow and heat transfer of nanofluids over a stretching stationary disk. J Mol Liq. 2015;211:119–25.CrossRefGoogle Scholar
  7. 7.
    Sheikholeslami M, Hatami M, Ganji DD. Numerical investigation of nanofluid spraying on an inclined rotating disk for cooling process. J Mol Liq. 2015;211:577–83.CrossRefGoogle Scholar
  8. 8.
    Khan JA, Mustafa M, Hayat T, Turkyilmazoglu M, Alsaedi A. Numerical study of nanofluid flow and heat transfer over a rotating disk using Buongiorno’s model. Int J Numer Methods Heat Fluid Flow. 2017;27:221–34.CrossRefGoogle Scholar
  9. 9.
    Mustafa M, Khan JA. Numerical study of partial slip effects on MHD flow of nanofluids near a convectively heated stretchable rotating disk. J Mol Liq. 2017;234:287–95.CrossRefGoogle Scholar
  10. 10.
    Hayat T, Muhammad T, Shehzad SA, Alsaedi A. On magnetohydrodynamic flow of nanofluid due to a rotating disk with slip effect: a numerical study. Comput Methods Appl Mech Eng. 2017;315:467–77.CrossRefGoogle Scholar
  11. 11.
    Choi SUS, Zhang ZG, Yu W, Lockwood FE, Grulke EA. Anomalous thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett. 2001;79:2252.CrossRefGoogle Scholar
  12. 12.
    Ramasubramaniam R, Chen J, Liu H. Homogeneous carbon nanotube/polymer composites for electrical applications. Appl Phys Lett. 2003;83:2928.CrossRefGoogle Scholar
  13. 13.
    Xue QZ. Model for thermal conductivity of carbon nanotube-based composites. Physica B. 2005;368:302–7.CrossRefGoogle Scholar
  14. 14.
    Ding Y, Alias H, Wen D, Williams RA. Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids). Int J Heat Mass Transf. 2006;49:240–50.CrossRefGoogle Scholar
  15. 15.
    Kamali R, Binesh A. Numerical investigation of heat transfer enhancement using carbon nanotube-based non-Newtonian nanofluids. Int Commun Heat Mass Transf. 2010;37:1153–7.CrossRefGoogle Scholar
  16. 16.
    Wang J, Zhu J, Zhang X, Chen Y. Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows. Exp Therm Fluid Sci. 2013;44:716–21.CrossRefGoogle Scholar
  17. 17.
    Safaei MR, Togun H, Vafai K, Kazi SN, Badarudin A. Investigation of heat transfer enhancement in a forward-facing contracting channel using FMWCNT nanofluids. Numer Heat Transf Part A. 2014;66:1321–40.CrossRefGoogle Scholar
  18. 18.
    Hayat T, Farooq M, Alsaedi A. Homogeneous–heterogeneous reactions in the stagnation point flow of carbon nanotubes with Newtonian heating. AIP Adv. 2015;5:027130.CrossRefGoogle Scholar
  19. 19.
    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. IEEE Trans Nanotechnol. 2015;14:726–34.CrossRefGoogle Scholar
  20. 20.
    Karimipour A, Taghipour A, Malvandi A. Developing the laminar MHD forced convection flow of water/FMWNT carbon nanotubes in a microchannel imposed the uniform heat flux. J Magn Magn Mater. 2016;419:420–8.CrossRefGoogle Scholar
  21. 21.
    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 Mol Liq. 2016;21:1121–7.CrossRefGoogle Scholar
  22. 22.
    Imtiaz M, Hayat T, Alsaedi A, Ahmad B. Convective flow of carbon nanotubes between rotating stretchable disks with thermal radiation effects. Int J Heat Mass Transf. 2016;101:948–57.CrossRefGoogle Scholar
  23. 23.
    Kandasamy R, Muhaimin I, Mohammad R. Single walled carbon nanotubes on MHD unsteady flow over a porous wedge with thermal radiation with variable stream conditions. Alex Eng J. 2016;55:275–85.CrossRefGoogle Scholar
  24. 24.
    Khan U, Ahmed N, Mohyud-Din ST. Numerical investigation for three dimensional squeezing flow of nanofluid in a rotating channel with lower stretching wall suspended by carbon nanotubes. Appl Therm Eng. 2017;113:1107–17.CrossRefGoogle Scholar
  25. 25.
    Haq RU, Shahzad F, Al-Mdallal QM. MHD pulsatile flow of engine oil based carbon nanotubes between two concentric cylinders. Results Phys. 2017;7:57–68.CrossRefGoogle Scholar
  26. 26.
    Hayat T, Haider F, Muhammad T, Alsaedi A. On Darcy-Forchheimer flow of carbon nanotubes due to a rotating disk. Int J Heat Mass Transf. 2017;112:248–54.CrossRefGoogle Scholar
  27. 27.
    Turkyilmazoglu M. A note on the correspondence between certain nanofluid flows and standard fluid flows. J Heat Transf. 2015;137:024501.CrossRefGoogle Scholar
  28. 28.
    Mahanthesh B, Gireesha BJ, PrasannaKumara BC, Shashikumar NS. Marangoni convection radiative flow of dusty nanoliquid with exponential space dependent heat source. Nucl Eng Technol. 2017;49:1660–8.CrossRefGoogle Scholar
  29. 29.
    Mahanthesh B, Mabood F, Gireesha BJ, Gorla RSR. Effects of chemical reaction and partial slip on the three-dimensional flow of a nanofluid impinging on an exponentially stretching surface. Eur Phys J Plus. 2017;132:113.CrossRefGoogle Scholar
  30. 30.
    Mahanthesh B, Gireesha BJ, Shashikumar NS, Shehzad SA. Marangoni convective MHD flow of SWCNT and MWCNT nanoliquids due to a disk with solar radiation and irregular heat source. Physica E. 2017;94:25–30.CrossRefGoogle Scholar
  31. 31.
    Gireesha BJ, Mahanthesh B, Thammanna GT, Sampathkumar PB. Hall effects on dusty nanofluid two-phase transient flow past a stretching sheet using KVL model. J Mol Liq. 2018;256:139–47.CrossRefGoogle Scholar
  32. 32.
    Mahanthesh B, Gireesha BJ, Gorla RSR, Makinde OD. Magnetohydrodynamic three-dimensional flow of nanofluids with slip and thermal radiation over a nonlinear stretching sheet: a numerical study. Neural Comput Appl. 2018;30:1557–67.CrossRefGoogle Scholar
  33. 33.
    Kumar PBS, Mahanthesh B, Gireesha BJ, Shehzad SA. Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo–Christov double diffusion. Appl Math Mech. 2018;39:1311–26.CrossRefGoogle Scholar
  34. 34.
    Muhammad T, Lu DC, Mahanthesh B, Eid MR, Ramzan M, Dar A. Significance of Darcy–Forchheimer porous medium in nanofluid through carbon nanotubes. Commun Theor Phys. 2018;70:361.CrossRefGoogle Scholar
  35. 35.
    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. Int J Mech Sci. 2018;135:532–40.CrossRefGoogle Scholar
  36. 36.
    Hayat T, Aziz A, Muhammad T, Alsaedi A. An optimal analysis for Darcy–Forchheimer 3D flow of Carreau nanofluid with convectively heated surface. Results Phys. 2018;9:598–608.CrossRefGoogle Scholar
  37. 37.
    Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2018;131:2027–39.CrossRefGoogle Scholar
  38. 38.
    Rashidi S, Eskandarian M, Mahian O, Poncet S. Combination of nanofluid and inserts for heat transfer enhancement. J Therm Anal Calorim. 2018.  https://doi.org/10.1007/s10973-018-7070-9.Google Scholar
  39. 39.
    Hayat T, Aziz A, Muhammad T, Alsaedi A. Effects of binary chemical reaction and Arrhenius activation energy in Darcy-Forchheimer three-dimensional flow of nanofluid subject to rotating frame. J Therm Anal Calorim. 2018.  https://doi.org/10.1007/s10973-018-7822-6.Google Scholar
  40. 40.
    Hayat T, Aziz A, Muhammad T, Alsaedi A. Numerical simulation for Darcy-Forchheimer three-dimensional rotating flow of nanofluid with prescribed heat and mass flux conditions. J Therm Anal Calorim. 2018.  https://doi.org/10.1007/s10973-018-7847-x.Google Scholar
  41. 41.
    Forchheimer P. Wasserbewegung durch boden. Z Ver Dtsch Ing. 1901;45:1782–8.Google Scholar
  42. 42.
    Muskat M. The flow of homogeneous fluids through porous media. Ann Arbor: Edwards; 1946.Google Scholar
  43. 43.
    Seddeek MA. Influence of viscous dissipation and thermophoresis on Darcy–Forchheimer mixed convection in a fluid saturated porous media. J Colloid Interface Sci. 2006;293:137–42.CrossRefGoogle Scholar
  44. 44.
    Jha BK, Kaurangini ML. Approximate analytical solutions for the nonlinear Brinkman–Forchheimer-extended Darcy flow model. Appl Math. 2011;2:1432–6.CrossRefGoogle Scholar
  45. 45.
    Pal D, Mondal H. Hydromagnetic convective diffusion of species in Darcy–Forchheimer porous medium with non-uniform heat source/sink and variable viscosity. Int Commun Heat Mass Transf. 2012;39:913–7.CrossRefGoogle Scholar
  46. 46.
    Sadiq MA, Hayat T. Darcy–Forchheimer flow of magneto Maxwell liquid bounded by convectively heated sheet. Results Phys. 2016;6:884–90.CrossRefGoogle Scholar
  47. 47.
    Shehzad SA, Abbasi FM, Hayat T, Alsaedi A. Cattaneo–Christov heat flux model for Darcy–Forchheimer flow of an Oldroyd-B fluid with variable conductivity and non-linear convection. J Mol Liq. 2016;224:274–8.CrossRefGoogle Scholar
  48. 48.
    Bakar SA, Arifin NM, Nazar R, Ali FM, Pop I. Forced convection boundary layer stagnation-point flow in Darcy–Forchheimer porous medium past a shrinking sheet. Front Heat Mass Transf. 2016;7:38.Google Scholar
  49. 49.
    Hayat T, Muhammad T, Al-Mezal S, Liao SJ. Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux. Int J Numer Methods Heat Fluid Flow. 2016;26:2355–69.CrossRefGoogle Scholar
  50. 50.
    Umavathi JC, Ojjela O, Vajravelu K. Numerical analysis of natural convective flow and heat transfer of nanofluids in a vertical rectangular duct using Darcy–Forchheimer–Brinkman model. Int J Therm Sci. 2017;111:511–24.CrossRefGoogle Scholar
  51. 51.
    Hayat T, Haider F, Muhammad T, Alsaedi A. On Darcy–Forchheimer flow of viscoelastic nanofluids: a comparative study. J Mol Liq. 2017;233:278–87.CrossRefGoogle Scholar
  52. 52.
    Muhammad T, Alsaedi A, Shehzad SA, Hayat T. A revised model for Darcy–Forchheimer flow of Maxwell nanofluid subject to convective boundary condition. Chin J Phys. 2017;55:963–76.CrossRefGoogle Scholar
  53. 53.
    Merkin JH. A model for isothermal homogeneous–heterogeneous reactions in boundary-layer flow. Math Comput Model. 1996;24:125–36.CrossRefGoogle Scholar
  54. 54.
    Chaudhary MA, Merkin JH. A simple isothermal model for homogeneous–heterogeneous reactions in boundary-layer flow. II Different diffusivities for reactant and autocatalyst. Fluid Dyn Res. 1995;16:335–59.CrossRefGoogle Scholar
  55. 55.
    Bachok N, Ishak A, Pop I. On the stagnation-point flow towards a stretching sheet with homogeneous–heterogeneous reactions effects. Commun Nonlinear Sci Numer Simul. 2011;16:4296–302.CrossRefGoogle Scholar
  56. 56.
    Kameswaran PK, Shaw S, Sibanda P, Murthy PVSN. Homogeneous–heterogeneous reactions in a nanofluid flow due to porous stretching sheet. Int J Heat Mass Transf. 2013;57:465–72.CrossRefGoogle Scholar
  57. 57.
    Imtiaz M, Hayat T, Alsaedi A, Hobiny A. Homogeneous–heterogeneous reactions in MHD flow due to an unsteady curved stretching surface. J Mol Liq. 2016;221:245–53.CrossRefGoogle Scholar
  58. 58.
    Abbas Z, Sheikh M. Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition. Chin J Chem Eng. 2017;25:11–7.CrossRefGoogle Scholar
  59. 59.
    Sajid M, Iqbal SA, Naveed M, Abbas Z. Effect of homogeneous–heterogeneous reactions and magnetohydrodynamics on Fe3O4 nanofluid for the Blasius flow with thermal radiations. J Mol Liq. 2017;233:115–21.CrossRefGoogle Scholar
  60. 60.
    Hayat T, Haider F, Muhammad T, Alsaedi A. Darcy–Forchheimer flow with Cattaneo–Christov heat flux and homogeneous–heterogeneous reactions. PLoS ONE. 2017;12:e0174938.CrossRefGoogle Scholar
  61. 61.
    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 Mol Liq. 2017;240:209–20.CrossRefGoogle Scholar
  62. 62.
    Liao SJ. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Commun Nonlinear Sci Numer Simul. 2010;15:2003–16.CrossRefGoogle Scholar
  63. 63.
    Malvandi A, Hedayati F, Domairry G. Stagnation point flow of a nanofluid toward an exponentially stretching sheet with nonuniform heat generation/absorption. J Thermodyn. 2013;2013:764827.CrossRefGoogle Scholar
  64. 64.
    Abbasbandy S, Hayat T, Alsaedi A, Rashidi MM. Numerical and analytical solutions for Falkner–Skan flow of MHD Oldroyd-B fluid. Int J Numer Methods Heat Fluid Flow. 2014;24:390–401.CrossRefGoogle Scholar
  65. 65.
    Hayat T, Muhammad T, Alsaedi A, Alhuthali MS. Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. J Magn Magn Mater. 2015;385:222–9.CrossRefGoogle Scholar
  66. 66.
    Hayat T, Aziz A, Muhammad T, Alsaedi A. On magnetohydrodynamic three-dimensional flow of nanofluid over a convectively heated nonlinear stretching surface. Int J Heat Mass Transf. 2016;100:566–72.CrossRefGoogle Scholar
  67. 67.
    Turkyilmazoglu M. An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method. Filomat. 2016;30:1633–50.CrossRefGoogle Scholar
  68. 68.
    Hayat T, Aziz A, Muhammad T, Ahmad B. On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet. J Magn Magn Mater. 2016;408:99–106.CrossRefGoogle Scholar
  69. 69.
    Hayat T, Muhammad T, Shehzad SA, Alsaedi A. An analytical solution for magnetohydrodynamic Oldroyd-B nanofluid flow induced by a stretching sheet with heat generation/absorption. Int J Therm Sci. 2017;111:274–88.CrossRefGoogle Scholar
  70. 70.
    Hayat T, Ullah I, Muhammad T, Alsaedi A. Thermal and solutal stratification in mixed convection three-dimensional flow of an Oldroyd-B nanofluid. Results Phys. 2017;7:3797–805.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • Tasawar Hayat
    • 1
    • 2
  • Farwa Haider
    • 1
  • Taseer Muhammad
    • 3
    Email author
  • Bashir Ahmad
    • 2
  1. 1.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of MathematicsGovernment College Women UniversitySialkotPakistan

Personalised recommendations