Advertisement

Numerical simulation for three-dimensional flow of Carreau nanofluid over a nonlinear stretching surface with convective heat and mass conditions

  • Tasawar Hayat
  • Arsalan AzizEmail author
  • Taseer Muhammad
  • Ahmed Alsaedi
Technical Paper
  • 37 Downloads

Abstract

This article addresses (3D) flow of Carreau liquid in the presence of nanomaterials induced by a nonlinearly extendable surface. A nonlinear extendable surface generates the flow. Heat and mass transport via convective process is considered. The novel characteristics in regard to Brownian dispersion and thermophoresis are retained. The variation in partial differential framework to nonlinear ordinary differential framework is done through reasonable transformations. The graphical representation of transformed nonlinear ordinary differential framework is developed for both situations (n < 1 and n > 1). An efficient numerical solver namely NDSolve is used to tackle the governing nonlinear framework. The contributions of various interesting variables are studied graphically. Physical amounts like surface drag coefficients, transfer of heat and mass rates are portrayed by numeric esteems.

Keywords

3D flow Carreau liquid Nanomaterials Convective heat and mass conditions Nonlinear stretched surface 

List of symbols

\( u, v,w \)

Velocity components

\( \mu \)

Dynamic viscosity

\( \nu \)

Kinematic viscosity

T

Temperature

\( T_{\infty } \)

Ambient fluid temperature

n

Flow behavior index

\( \left( {\rho c} \right)_{\text{p}} \)

Effective heat capacity of nanoparticles

\( D_{\text{B}} \)

Brownian diffusion coefficient

\( U_{w} , V_{w} \)

Surface velocities

\( \varGamma \)

Material time constant

\( h_{2} \)

Mass transfer coefficient

\( \theta \)

Dimensionless temperature

\( f^{\prime}, g' \)

Dimensionless velocities

\( We \)

Local Weissenberg number

m

Positive constant

\( \alpha \)

Ratio of stretching rates

\( N_{\text{b}} \)

Brownian motion parameter

Sc

Schmidt number

\( Nu_{x} \)

Local Nusselt number

\( x,y,z \)

Coordinate axes

\( \rho_{\text{f}} \)

Density of base fluid

\( \alpha^{*} \)

Thermal diffusivity

C

Concentration

\( C_{\infty } \)

Ambient fluid concentration

k

Thermal conductivity

\( \left( {\rho c} \right)_{\text{f}} \)

Heat capacity of fluid

\( D_{\text{T}} \)

Thermophoretic diffusion coefficient

\( a, b \)

Positive constants

\( h_{1} \)

Heat transfer coefficient

\( \zeta \)

Dimensionless variable

\( \phi \)

Dimensionless concentration

\( \gamma_{1} \)

Thermal Biot number

\( \gamma_{2} \)

Concentration Biot number

\( Sh_{x} \)

Local Sherwood number

\( Pr \)

Prandtl number

\( N_{\text{t}} \)

Thermophoresis parameter

\( C_{\text{fx}} , C_{\text{fy}} \)

Skin friction coefficients

\( Re_{x} , Re_{y} \)

Local Reynolds number

References

  1. 1.
    Choi SUS, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress & Exposisition, American Society of Mechanical Engineers, San FranciscoGoogle Scholar
  2. 2.
    Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transf 128:240–250CrossRefGoogle Scholar
  3. 3.
    Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluid. Int J Heat Mass Transf 50:2002–2018CrossRefGoogle Scholar
  4. 4.
    Kakac S, Pramuanjaroenkij A (2009) Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transf 52:3187–3196CrossRefGoogle Scholar
  5. 5.
    Abu-Nada E, Oztop HF (2009) Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid. Int J Heat Fluid Flow 30:669–678CrossRefGoogle Scholar
  6. 6.
    Mustafa M, Hayat T, Pop I, Asghar S, Obaidat S (2011) Stagnation-point flow of a nanofluid towards a stretching sheet. Int J Heat Mass Transf 54:5588–5594CrossRefGoogle Scholar
  7. 7.
    Turkyilmazoglu M (2012) Exact analytical solutions for heat and mass transfer of MHD slip flow in nanofluids. Chem Eng Sci 84:182–187CrossRefGoogle Scholar
  8. 8.
    Rashad AM, Chamkha AJ, Abdou MMM (2013) Mixed convection flow of non-Newtonian fluid from vertical surface saturated in a porous medium filled with a nanofluid. J Appl Fluid Mech 6:301–309Google Scholar
  9. 9.
    Murthy PVSN, RamReddy Ch, Chamkha AJ, Rashad AM (2013) Magnetic effect on thermally stratified nanofluid saturated non-Darcy porous medium under convective boundary condition. Int Commun Heat Mass Transf 47:41–48CrossRefGoogle Scholar
  10. 10.
    Turkyilmazoglu M, Pop I (2013) Heat and mass transfer of unsteady natural convection flow of some nanofluids past a vertical infinite flat plate with radiation effect. Int J Heat Mass Transf 59:167–171CrossRefGoogle Scholar
  11. 11.
    Hsiao KL (2014) Nanofluid flow with multimedia physical features for conjugate mixed convection and radiation. Comput Fluids 104:1–8MathSciNetCrossRefGoogle Scholar
  12. 12.
    Togun H, Safaei MR, Sadri R, Kazi SN, Badarudin A, Hooman K, Sadeghinezhad E (2014) Numerical simulation of laminar to turbulent nanofluid flow and heat transfer over a backward-facing step. Appl Math Comput 239:153–170MathSciNetzbMATHGoogle Scholar
  13. 13.
    Chamkha A, Abbasbandy S, Rashad AM (2015) Non-Darcy natural convection flow for non-Newtonian nanofluid over cone saturated in porous medium with uniform heat and volume fraction fluxes. Int J Numer Methods Heat Fluid Flow 25:422–437MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hayat T, Muhammad T, Alsaedi A, Alhuthali MS (2015) Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. J Magn Magn Mater 385:222–229CrossRefGoogle Scholar
  15. 15.
    Lin Y, Zheng L, Zhang X, Ma L, Chen G (2015) MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation. Int J Heat Mass Transf 84:903–911CrossRefGoogle Scholar
  16. 16.
    El-Kabeir SMM, Chamkha AJ, Rashad AM (2015) Unsteady slip flow of a nanofluid due to a contracting cylinder with newtonian heating. J Nanofluids 4:394–401CrossRefGoogle Scholar
  17. 17.
    Hayat T, Aziz A, Muhammad T, Alsaedi A (2016) On magnetohydrodynamic three-dimensional flow of nanofluid over a convectively heated nonlinear stretching surface. Int J Heat Mass Transf 100:566–572CrossRefGoogle Scholar
  18. 18.
    Eid MR (2016) Chemical reaction effect on MHD boundary-layer flow of two-phase nanofluid model over an exponentially stretching sheet with a heat generation. J Mol Liq 220:718–725CrossRefGoogle Scholar
  19. 19.
    Hayat T, Aziz A, Muhammad T, Alsaedi A, Mustafa M (2016) On magnetohydrodynamic flow of second grade nanofluid over a convectively heated nonlinear stretching surface. Adv Powder Technol 27:1992–2004CrossRefGoogle Scholar
  20. 20.
    Eid MR, Alsaedi A, Muhammad T, Hayat T (2017) Comprehensive analysis of heat transfer of gold-blood nanofluid (Sisko-model) with thermal radiation. Results Phys 7:4388–4393CrossRefGoogle Scholar
  21. 21.
    Hayat T, Aziz A, Muhammad T, Alsaedi A (2017) Three-dimensional flow of nanofluid with heat and mass flux boundary conditions. Chin J Phys 55:1495–1510CrossRefGoogle Scholar
  22. 22.
    Sheikholeslami M, Hayat T, Muhammad T, Alsaedi A (2018) MHD forced convection flow of nanofluid in a porous cavity with hot elliptic obstacle by means of Lattice Boltzmann method. Int J Mech Sci 135:532–540CrossRefGoogle Scholar
  23. 23.
    Rashad AM (2017) Unsteady nanofluid flow over an inclined stretching surface with convective boundary condition and anisotropic slip impact. Int J Heat Technol 35(1):82–90CrossRefGoogle Scholar
  24. 24.
    Nabwey HA, Boumazgour M, Rashad AM (2017) Group method analysis of mixed convection stagnation-point flow of non-Newtonian nanofluid over a vertical stretching surface. Ind J Phys 91:731–742CrossRefGoogle Scholar
  25. 25.
    Aziz A, Alsaedi A, Muhammad T, Hayat T (2018) Numerical study for heat generation/absorption in flow of nanofluid by a rotating disk. Results Phys 8:785–792CrossRefGoogle Scholar
  26. 26.
    Vajravelu K (2001) Viscous flow over a nonlinearly stretching sheet. Appl Math Comput 124:281–288MathSciNetzbMATHGoogle Scholar
  27. 27.
    Cortell R (2007) Viscous flow and heat transfer over a nonlinearly stretching sheet. Appl Math Comput 184:864–873MathSciNetzbMATHGoogle Scholar
  28. 28.
    Cortell R (2008) Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys Lett A 372:631–636CrossRefGoogle Scholar
  29. 29.
    Hayat T, Hussain Q, Javed T (2009) The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet. Nonlinear Anal Real World Appl 10:966–973MathSciNetCrossRefGoogle Scholar
  30. 30.
    Rana P, Bhargava R (2012) Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study. Commun Nonlinear Sci Numer Simul 17:212–226MathSciNetCrossRefGoogle Scholar
  31. 31.
    Mukhopadhyay S (2013) Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at the boundary. Alex Eng J 52:563–569CrossRefGoogle Scholar
  32. 32.
    Mustafa M, Khan JA, Hayat T, Alsaedi A (2015) Analytical and numerical solutions for axisymmetric flow of nanofluid due to non-linearly stretching sheet. Int J Non-Linear Mech 71:22–29CrossRefGoogle Scholar
  33. 33.
    Mabood F, Khan WA, Ismail AIM (2015) MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: a numerical study. J Magn Magn Mater 374:569–576CrossRefGoogle Scholar
  34. 34.
    Hayat T, Aziz A, Muhammad T, Alsaedi A, Mustafa M (2016) On magnetohydrodynamic flow of second grade nanofluid over a convectively heated nonlinear stretching surface. Adv Powder Technol 27:1992–2004CrossRefGoogle Scholar
  35. 35.
    Hayat T, Aziz A, Muhammad T, Alsaedi A (2017) Darcy-Forchheimer three-dimensional flow of Williamson nanofluid over a convectively heated nonlinear stretching surface. Commun Theor Phys 68:387–394CrossRefGoogle Scholar
  36. 36.
    Carreau PJ (1972) Rheological equations from molecular network theories. Trans Soc Rheol 116:99–127CrossRefGoogle Scholar
  37. 37.
    Sulochana C, Ashwinkumar GP, Sandeep N (2016) Transpiration effect on stagnation-point flow of a Carreau nanofluid in the presence of thermophoresis and Brownian motion. Alex Eng J 55:1151–1157CrossRefGoogle Scholar
  38. 38.
    Hsiao KL (2017) To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-nanofluid with parameters control method. Energy 130:486–499CrossRefGoogle Scholar
  39. 39.
    Eid MR, Mahny KL, Muhammad T, Sheikholeslami M (2018) Numerical treatment for Carreau nanofluid flow over a porous nonlinear stretching surface. Results Phys 8:1185–1193CrossRefGoogle Scholar
  40. 40.
    Hayat T, Aziz A, Muhammad T, Alsaedi A (2018) An optimal analysis for Darcy–Forchheimer 3D flow of Carreau nanofluid with convectively heated surface. Results Phys 9:598–608CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Tasawar Hayat
    • 1
    • 2
  • Arsalan Aziz
    • 1
    Email author
  • Taseer Muhammad
    • 3
  • Ahmed Alsaedi
    • 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