Skip to main content
SpringerLink
Log in

Unsteady nanofluid flow and heat transfer in presence of magnetic field considering thermal radiation

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

In this study, heat and mass transfer characteristic of unsteady nanofluid flow between two parallel plates is investigated considering thermal radiation. Two phase model is considered in order to simulate nanofluid. The basic partial differential equations are reduced to ordinary differential equations which are solved numerically using the fourth-order Runge–Kutta method. The effects of the squeeze number, radiation parameter, Schmidt number, Brownian motion parameter, thermophoretic parameter and Eckert number on flow, heat and mass transfer are considered. Results indicate that concentration boundary-layer thickness increases with increase of Radiation parameter. Also it can be found that Nusselt number has direct relationship with Eckert number, Schmidt number, squeeze parameter and Radiation parameter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Abbreviations

\( C \) :

Nanofluid concentration

\( c_{\text{p}} \) :

Specific heat at constant pressure

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

Brownian diffusion coefficient

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

Thermophoretic diffusion coefficient

\( {\text{Ec}} \) :

Eckert number \( \left( { = \frac{1}{{c_{\text{p}} }}\,\left( {\frac{\beta x}{{2\left( {1 - \beta t} \right)}}} \right)^{2} } \right) \)

\( k \) :

Thermal conductivity

\( \text{Nb} \) :

Brownian motion parameter \( ( = (\rho c)_{\text{p}} D_{\text{B}} (\phi_{\text{h}} - \phi_{\text{c}} )/(\rho c)_{f} \alpha ) \)

\( \text{Nt} \) :

Thermophoretic parameter \( ( = (\rho c)_{\text{p}} D_{\text{T}} (T_{\text{h}} - T_{\text{c}} )/[(\rho c)_{f} \alpha T_{\text{c}} ]) \)

\( \text{Nu} \) :

Nusselt number

\( q_{\text{r}} \) :

Radiation heat flux

\( \text{Rd} \) :

Radiation parameter \( \left( { = 4\sigma_{\text{e}} T_{\text{c}}^{3} /\left( {\beta_{\text{R}} k} \right)} \right) \)

\( \text{Pr} \) :

Prandtl number \( ( = \mu /\rho_{f} \alpha ) \)

P :

Pressure

\( S \) :

Squeeze number \( \left( { = \beta l^{2} \rho_{f} /2\mu } \right) \)

\( \text{Sc} \) :

Lewis number \( ( = \alpha /D_{\text{B}} ) \)

\( T \) :

Fluid temperature

\( u,v \) :

Velocity components in the x-direction and y-direction

\( x,y \) :

Space coordinates

\( \alpha \) :

Thermal diffusivity \( \left( { = \frac{k}{{\left( {\rho c_{P} } \right)_{f} }}} \right) \)

\( \mu \) :

Dynamic viscosity of nanofluid

\( \theta \) :

Dimensionless temperature \( \left( { = T/T_{\text{H}} } \right) \)

\( \phi \) :

Dimensionless concentration (=C/C H)

\( \rho \) :

Density

\( \sigma_{\text{e}} \) :

Stefan–Boltzmann constant

\( \beta_{\text{R}} \) :

Mean absorption coefficient

c:

Cold

H:

Hot

h:

High

f:

Base fluid

References

  1. Khanafer K, Vafai K, Lightstone M (2003) Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf 46:3639–3653

    Article  MATH  Google Scholar 

  2. Abu-Nada E, Masoud Z, Hijazi A (2008) Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids. Int Commun Heat Mass Transf 35:657–665

    Article  Google Scholar 

  3. Rashidi MM, Abelman S, Freidooni Mehr N (2013) Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. Int J Heat Mass Transf 62:515–525

    Article  Google Scholar 

  4. Ellahi R (2013) The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: analytical solutions. Appl Math Model 37(3):1451–1467

    Article  MathSciNet  Google Scholar 

  5. Gorji-Bandpy Mofid, Yahyazadeh-Jelodar Hossein, Khalili Mohammadtaghi (2011) Optimization of heat exchanger network. Appl Therm Eng 31:779–784

    Article  Google Scholar 

  6. Sheikholeslami M, Gorji-Bandpay M, Ganji DD (2012) Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid. Int Commun Heat Mass Transf 39:978–986

    Article  Google Scholar 

  7. Sheikholeslami M, Gorji-Bandpy M, Ganji DD (2014) S Soleimani, Natural convection heat transfer in a nanofluid filled inclined L-shaped enclosure. IJST. Trans Mech Eng 38:217–226

    Google Scholar 

  8. Sheikholeslami M, Gorji-Bandpy M, Ganji DD, Soleimani S (2014) Heat flux boundary condition for nanofluid filled enclosure in presence of magnetic field. J Mol Liq 193:174–184

    Article  Google Scholar 

  9. Sheikholeslami M, Ganji DD, Gorji-Bandpy M, Soleimani S (2014) Nanofluid flow and heat transfer using KKL model. J Taiwan Inst Chem Eng 45:795–807

    Article  Google Scholar 

  10. Sheikholeslami M, Gorji Bandpy M, Ellahi R, Hassan M, Soleimani S (2014) Effects of MHD on Cu–water nanofluid flow and heat transfer by means of CVFEM. J Mag Mag Mater 349:188–200

    Article  Google Scholar 

  11. Sheikholeslami M, Gorji-Bandpy M, Pop I, Soleimani S (2013) Numerical study of natural convection between a circular enclosure and a sinusoidal cylinder using control volume based finite element method. Int J Therm Sci 72:147–158

    Article  Google Scholar 

  12. Sheikholeslami M, Gorji-Bandpy M, Ganji DD, Soleimani S (2014) Magnetic field. J Taiwan Inst Chem Eng 45:40–49

    Article  Google Scholar 

  13. Sheikholeslami M, Hashim I, Soleimani S (2013) Numerical investigation of the effect of magnetic field on natural convection in a curved-shape enclosure, Hindawi Publishing Corporation Mathematical Problems in Engineering. Vol. 2013, Article ID 831725, p 11. doi:10.1155/2013/831725

  14. Sheikholeslami M, Gorji-Bandpy M, Ganji DD, Soleimani S (2013) Effect of a magnetic field on natural convection in an inclined half-annulus enclosure filled with Cu–water nanofluid using CVFEM. Adv Powder Technol 24:980–991

    Article  Google Scholar 

  15. Sheikholeslami M, Gorji-Bandpy M, Ganji DD, Soheil Soleimani S (2014) MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM. Neural Comput Appl 24:873–882

    Article  Google Scholar 

  16. Sheikholeslami M, Gorji-Bandpy M, Ganji DD, Soleimani S, Seyyedi SM (2012) Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field. Int Commun Heat Mass Transf 39:1435–1443

    Article  Google Scholar 

  17. Soleimani Soheil, Sheikholeslami M, Ganji DD, Gorji-Bandpay M (2012) Natural convection heat transfer in a nanofluid filled semi-annulus enclosure. Int Commun Heat Mass Transf 39:565–574

    Article  Google Scholar 

  18. Sheikholeslami M, GorjiBandpy M, Ellahi R, Zeeshan A (2014) Simulation of MHD CuO–water nanofluid flow and convective heat transfer considering Lorentz forces. J Magn Magn Mater 369:69–80

    Article  Google Scholar 

  19. Sheikholeslami M, Gorji-Bandpy M, Ganji DD (2014) MHD free convection in an eccentric semi-annulus filled with nanofluid. J Taiwan Inst Chem Eng 45:1204–1216

    Article  Google Scholar 

  20. Sheikholeslami Mohsen, Gorji-Bandpy Mofid (2014) Free convection of ferrofluid in a cavity heated from below in the presence of an external magnetic field. Powder Technol 256:490–498

    Article  Google Scholar 

  21. Sheikholeslami M, Gorji-Bandpy M, Ganji DD (2014) Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid. Powder Technol 254:82–93

    Article  Google Scholar 

  22. Sheikholeslami M, Gorji-Bandpy M, Ganji DD (2013) Numerical investigation of MHD effects on Al2O3–water nanofluid flow and heat transfer in a semi-annulus enclosure using LBM. Energy 60:501–510

    Article  Google Scholar 

  23. Sheikholeslami M, Gorji-Bandpy M, Seyyedi SM, Ganji DD, Rokni HB, Soleimani S (2013) Application of LBM in simulation of natural convection in a nanofluid filled square cavity with curve boundaries. Powder Technol 247:87–94

    Article  Google Scholar 

  24. Sheikholeslami M, Gorji-Bandpy M, Ganji DD (2013) Natural convection in a nanofluid filled concentric annulus between an outer square cylinder and an inner elliptic cylinder. Sci Iran Trans B Mech Eng 20(4):1241–1253

    Google Scholar 

  25. Sheikholeslami M, Gorji-Bandpy M, Domairry G (2013) Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM). Appl Math Mech Engl Ed 34(7):1–15

    Article  Google Scholar 

  26. Sheikholeslami M, Ganji DD (2014) Magnetohydrodynamic flow in a permeable channel filled with nanofluid. Sci Iran B 21(1):203–212

    Google Scholar 

  27. Hatami M, Sheikholeslami M, Ganji DD (2014) Nanofluid flow and heat transfer in an asymmetric porous channel with expanding or contracting wall. J Mol Liq 195:230–239

    Article  Google Scholar 

  28. Hatami M, Sheikholeslami M, Ganji DD (2014) Laminar flow and heat transfer of nanofluid between contracting and rotating disks by least square method. Powder Technol 253:769–779

    Article  Google Scholar 

  29. Sheikholeslami M, Hatami M, Ganji DD (2014) Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field. J Mol Liq 190:112–120

    Article  Google Scholar 

  30. Sheikholeslami M, Ganji DD (2013) Heat transfer of Cu–water nanofluid flow between parallel plates. Powder Technol 235:873–879

    Article  Google Scholar 

  31. Sheikholeslami M, Ganji DD, Rokni HB (2013) Nanofluid flow in a semi-porous channel in the presence of uniform magnetic field. IJE Trans C Asp 26(6):653–662

    Google Scholar 

  32. Nield DA, Kuznetsov AV (2009) Thermal instability in a porous medium layer saturated by a nanofluid. Int J Heat Mass Transf 52:5796–5801

    Article  MATH  Google Scholar 

  33. Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477–2483

    Article  MATH  Google Scholar 

  34. Hassani M, Mohammad Tabar M, Nemati H, Domairry G, Noori F (2011) An analytical solution for boundary layer flow of a nanofluid past a stretching sheet. Int J Therm Sci 50:2256–2263

    Article  Google Scholar 

  35. Sheikholeslami M, Gorji-Bandpy M, Soleimani S (2013) Two phase simulation of nanofluid flow and heat transfer using heatline analysis. Int Commun Heat Mass Transf 47:73–81

    Article  Google Scholar 

  36. Sheikholeslami M, Gorji-Bandpy M, Ganji DD, Rana P, Soleimani S (2014) Magnetohydrodynamic free convection of Al2O3–water nanofluid considering thermophoresis and Brownian motion effects. Comput Fluids 94:147–160

    Article  MathSciNet  Google Scholar 

  37. Sheikholeslami M, Gorji-Bandpy M, Ganji DD, Soleimani S (2014) Nanofluid using two phase model. J Mol Liq 194:179–187

    Article  Google Scholar 

  38. Sheikholeslami M, Ganji DD (2014) Three dimensional heat and mass transfer in a rotating system using nanofluid. Powder Technol 253:789–796

    Article  Google Scholar 

  39. Sheikholeslami M, Ganji DD (2014) Numerical investigation for two phase modeling of nanofluid in a rotating system with permeable sheet. J Mol Liq 194:13–19

    Article  Google Scholar 

  40. Bakier AY (2001) Thermal radiation effect on mixed convection from vertical surface in saturated porous media. Int Commun Heat Mass Transf 28(1):119–126

    Article  Google Scholar 

  41. Damseh RA (2006) Magnetohydrodynamics-mixed convection from radiate vertical isothermal surface embedded in a saturated porous media. J Appl Mech 73:54–59

    Article  MATH  Google Scholar 

  42. Hossain MA, Takhar HS (1996) Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat Mass Transf 31:243–248

    Article  Google Scholar 

  43. Zahmatkesh I (2007) Influence of thermal radiation on free convection inside a porous enclosure. Emir J Eng Res 12(2):47–52

    Google Scholar 

  44. Hayat T, Abbas Z, Pop I, Asghar S (2010) Effects of radiation and magnetic field on the mixed convection stagnation-point flow over a vertical stretching sheet in a porous medium. Int J Heat Mass Transf 53:466–474

    Article  MATH  Google Scholar 

  45. Hayat T, Qasim M (2010) Influence of thermal radiation and Joule heating on MHD flow of a Maxwell fluid in the presence of thermophoresis. Int J Heat Mass Transf 53:4780–4788

    Article  MATH  Google Scholar 

  46. Moradi A, Ahmadikia H, Hayat T, Alsaedi A (2013) On mixed convection radiation interaction about an inclined plate through a porous medium. Int J Therm Sci 64:129–136

    Article  Google Scholar 

  47. Pal D, Mondal H (2009) Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity. Meccanica 44:133–144

    Article  MATH  MathSciNet  Google Scholar 

  48. Raptis A (1998) Radiation and free convection flow through a porous medium. Int Commun Heat Mass Transf 25:289–295

    Article  Google Scholar 

  49. Mustafa M, Hayat T, Obaidat S (2012) On heat and mass transfer in the unsteady squeezing flow between parallel plates. Meccanica doi:10.1007/s11012-012-9536-3

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Babol University of Technology, Babol, Iran

    Mohsen Sheikholeslami & Davood Domiri Ganji

Authors
  1. Mohsen Sheikholeslami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Davood Domiri Ganji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohsen Sheikholeslami.

Additional information

Technical Editor: Francisco Ricardo Cunha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheikholeslami, M., Ganji, D.D. Unsteady nanofluid flow and heat transfer in presence of magnetic field considering thermal radiation. J Braz. Soc. Mech. Sci. Eng. 37, 895–902 (2015). https://doi.org/10.1007/s40430-014-0228-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-014-0228-x

Keywords

Search

Navigation