Skip to main content
SpringerLink
Log in

Investigating the mixed convection heat transfer of a nanofluid in a square chamber with a rotating blade

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

Mixed convection heat transfer of water–alumina nanofluid in a square chamber with a rotating blade in its center is studied numerically. The governing equations are discretized by using a finite-difference method and solved simultaneously using the SIMPLE algorithm. The blade thickness is assumed to be negligible, the vertical walls of the chamber are at constant temperature of \(T_{\text{c}}\) and \(T_{\text{h}}\), and the horizontal walls are insulated. The effects of Rayleigh number (\(10^{3} \le Ra \le 10^{6}\)) and Richardson (\(0.1 \le Ri \le 100\)) number, the dimensionless length of the blade (\(0.6 \le a \le 0.8\)) and the volumetric percentage of nanoparticles (\(0 \le \varphi \le 0.03\)) on flow and thermal fields are investigated. The results show that an increase in Rayleigh number, volumetric percentage of nanofluid and blade length leads to heat transfer increasing in most cases, but an increase in Richardson number results in a reduction in heat transfer. It is revealed that the maximum blade rotation occurs at small Richardson numbers.

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

Abbreviations

a :

Blade length (m)

C p :

Specific heat capacity (J kg−1 K−1)

g :

Acceleration of gravity (m s−2)

k :

Thermal conductivity (W m−1 K−1)

L :

Enclosure dimension (m)

n :

Number of iteration

Nu :

Local Nusselt number

Nu m :

Average Nusselt number

p :

Pressure (Pa)

Pr :

Prandtl number

Ra :

Rayleigh number

Re :

Reynolds number

Ri :

Richardson number

t :

Time (s)

T :

Temperature (K)

u :

Velocity component in the x-direction (m s−1)

v :

Velocity component in the y-direction (m s−1)

c, y :

Spatial coordinates (m)

α :

Diffusion coefficient (m2 s−1)

β :

Thermal expansion coefficient (K−1)

θ :

Dimensionless temperature

μ :

Dynamic viscosity (Pa s)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

τ :

Dimensionless time

φ :

Volume fraction of nanoparticles

Φ :

General variables

ω :

Angular velocity (rad s−1)

c :

Cold

f :

Fluid

h :

Hot

nf:

Nanofluid

p :

Nanoparticle

References

  1. Haddad Z, Oztop HF, Abu-Nada E, Mataoui A. A review on natural convective heat transfer of nanofluids. Renew Sustain Energy Rev. 2012;16:5363–78.

    Article  CAS  Google Scholar 

  2. Saitoh T, Hirose K. High-accuracy benchmark solutions to natural convection in a square cavity. Comput Mech. 1989;4:417–27.

    Article  Google Scholar 

  3. Davis DV. Natural convection of air in a square cavity: a benchmark solution. Int J Numer Methods Fluids. 1983;3:249–64.

    Article  Google Scholar 

  4. Oztop HF, Abu-Nada E, Varol Y, Al-Salem KH. Computational analysis of non-isothermal temperature distribution on natural convection in nanofluid filled enclosures. Superlattices Microstruct. 2011;49:453–67.

    Article  CAS  Google Scholar 

  5. Sun YS, Emery AF. Effects of wall conduction, internal heat sources and an internal baffle on natural convection heat transfer in a rectangular enclosure. Int J Heat Mass Transf. 1997;40:915–29.

    Article  Google Scholar 

  6. Sheikhzadeh GA, Arefmanesh A, Kheirkhah MH, Abdollahi R. Natural convection of Cu–water nanofluid in a cavity with partially active side walls. Eur J Mech B/Fluids. 2011;30:166–76.

    Article  Google Scholar 

  7. Hussain SH, Jabbar MY, Mohamad AS. Influence of presence of inclined centered baffle and corrugation frequency on natural convection heat transfer flow of air inside a square enclosure with corrugated side walls. Int J Therm Sci. 2011;50:1799–808.

    Article  Google Scholar 

  8. Hasib MH, Saddam MD, Saha S. Effect of tilt angle on pure mixed convection flow in trapezoidal cavities filled with water–Al2O3 nanofluid. Procedia Eng. 2015;105:388–97.

    Article  CAS  Google Scholar 

  9. Billah MM, Rahman MM, Sharif UM, Rahim NA, Saidur R, Hasanuzzaman M. Numerical analysis of fluid flow due to mixed convection in a lid-driven cavity having a heated circular hollow cylinder. Int Commun Heat Mass Transf. 2011;38:1093–103.

    Article  Google Scholar 

  10. Mamourian M, Shirvan KM, Ellahi R, Rahimi AB. Optimization of mixed convection heat transfer with entropy generation in a wavy surface square lid-driven cavity by means of Taguchi approach. Int J Heat Mass Transf. 2016;102:544–54.

    Article  CAS  Google Scholar 

  11. Alipanah M, Hasannasab P, Hosseinizadeh SF, Darbandi M. Entropy generation for compressible natural convection with high gradient temperature in a square cavity. Int Commun Heat Mass Transf. 2010;37:1388–95.

    Article  Google Scholar 

  12. Chamkha AJ, Abu-Nada E. Mixed convection flow in single-and double-lid driven square cavities filled with water–Al2O3 nanofluid: effect of viscosity models. Eur J Mech B/Fluids. 2012;36:82–96.

    Article  Google Scholar 

  13. Roy M, Roy S, Basak T. Analysis of entropy generation on mixed convection in square enclosures for various horizontal or vertical moving walls. Int Commun Heat Mass Transf. 2015;68:258–66.

    Article  CAS  Google Scholar 

  14. Talebi F, Mahmoudi AH, Shahi M. Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid. Int Commun Heat Mass Transf. 2010;37:79–90.

    Article  Google Scholar 

  15. Hemmat M, Ghadak F, Mirtalebi Esforjani SS, Haghiri A. Numerical study of mixed convection flows in a two-sided inclined lid-driven cavity utilizing nano-fluid with various inclination angles and ununiformed temperature. Aerosp Mech J. 2012;8:69–83.

  16. Khorasanizadeh H, Nikfar M, Amani J. Entropy generation of Cu–water nanofluid mixed convection in a cavity. Eur J Mech B/Fluids. 2013;37:143–52.

    Article  Google Scholar 

  17. Costa VA, Raimundo AM. Steady mixed convection in a differentially heated square enclosure with an active rotating circular cylinder. Int J Heat Mass Transf. 2010;53:1208–19.

    Article  CAS  Google Scholar 

  18. Hussain SH, Hussein AK. Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations. Int Commun Heat Mass Transf. 2011;38:263–74.

    Article  Google Scholar 

  19. Khanafer K, Aithal SM. Laminar mixed convection flow and heat transfer characteristics in a lid driven cavity with a circular cylinder. Int J Heat Mass Transf. 2013;66:200–9.

    Article  Google Scholar 

  20. Bansal S, Dipankar C. Magneto-convective transport of nanofluid in a vertical lid-driven cavity including a heat-conducting rotating circularcylinder. Numer Heat Transf Part A Appl. 2015;68:411–31.

    Article  CAS  Google Scholar 

  21. Selimefendigil F, Öztop HF, Abu-Hamdeh N. Mixed convection due to rotating cylinder in an internally heated and flexible walled cavity filled with SiO2–water nanofluids: effect of nanoparticle shape. Int Commun Heat Mass Transf. 2016;71:9–19.

    Article  CAS  Google Scholar 

  22. Safaei MR, Goshayshi HR. Numerical simulation of laminar and turbulent mixed convection in rectangular enclosure with hot upper moving wall. Int J Adv Des Manuf Technol Majlesi J Mech Eng. 2010;3(2):49–57.

    Google Scholar 

  23. Nourollahi B, Zafarmand MR, Safaei MR, Maghmoumi Y. An investigation of lid driven cavity flow by using large eddy simulation. Int J Adv Des Manuf Technol Majlesi J Mech Eng. 2008;2(1):25–36.

    Google Scholar 

  24. Safaei MR, Saleh SR, Goodarzi M. Numerical studies of laminar natural convection in a square cavity with orthogonal grid mesh by finite volume. Int J Adv Des Manuf Technol Majlesi J Mech Eng. 2008;1(2):13–21.

    Google Scholar 

  25. Safaei MR, Saleh SR, Goodarzi M. Finite volume solutions of 2-D steady incompressible Navier–Stokes equations in driven skewed cavity flow with non-orthogonal grid mesh. Int J Adv Des Manuf Technol Majlesi J Mech Eng. 2007;1(1):35–43.

    Google Scholar 

  26. Safaei MR, Jahanbin AM, Kianifar A, Gharehkhani S, Kherbeet AS, Goodarzi M, Dahari M. Mathematical modeling for nanofluids simulation: a review of the latest works, modeling and simulation in engineering sciences. In: Akbar NS, editors. InTech. 2016. https://doi.org/10.5772/64154.

  27. Safaei MR, Safdari Shadloo M, Goodarzi MS, Hadjadj A, Goshayeshi HR, Afrand M, Kazi SN. A survey on experimental and numerical studies of convection heat transfer of nanofluids inside closed conduits. Adv Mech Eng. 2016;8(10):1–14.

    Article  CAS  Google Scholar 

  28. Kherbeet AS, Safaei MR, Mohammed HA, Salman BH, Ahmed HE, Alawi OA, Al-Asadi MT. Heat transfer and fluid flow over microscale backward and forward facing step: a review. Int Commun Heat Mass Transf. 2016;76:237–44.

    Article  CAS  Google Scholar 

  29. Aboulhasan Alavi SM, Safaei MR, Mahian O, Goodarzi M, Dahari M, Yarmand H, Wongwises S. A hybrid finite element/finite difference scheme for solving the 3-D energy equation in transient non-isothermal fluid flow over a staggered tube bank. Numer Heat Transf Part B. 2015;68:169–83.

    Article  CAS  Google Scholar 

  30. Safaei MR, Togun H, Vafai K, Kazi SN, Badarudin A. Investigation of heat transfer enchantment in a forward-facing contracting channel using FMWCNT nanofluids. Numer Heat Transf Part A. 2014;66:1321–40.

    Article  CAS  Google Scholar 

  31. Safaei MR, Mahian O, Garoosi F, Hooman K, Karimipour A, Kazi SN, Gharehkhani S. Investigation of micro and nano-sized particle erosion in a 90° pipe bend using a two-phase discrete phase model. Sci World J. 2014; Article ID 740578.

  32. Safaei MR, Rahmanian B, Goodarzi M. Investigation of the coal diameter effect on pulverized coal combustion for pollutant reduction. J Math Comput Sci. 2014;12:143–51.

    Article  Google Scholar 

  33. Goodarzi M, Safaei MR, Vafai K, Ahmadi G, Dahari M, Jomhari N, Kazi SN. Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model. Int J Therm Sci. 2014;75:204–20.

    Article  CAS  Google Scholar 

  34. Rahmanian B, Safaei MR, Kazi SN, Ahmadi G, Oztop HF, Vafai K. Investigation of pollutant reduction by simulation of turbulent non-premixed pulverized coal combustion. Appl Therm Eng. 2014;73:1220–33.

    Article  CAS  Google Scholar 

  35. Goodarzi M, Safaei MR, Oztop HF, Karimipour A, Sadeghinezhad E, Dahari M, Kazi SN. Numerical study of entropy generation due to coupled laminar and turbulent mixed convection heat transfer and thermal radiation in a square enclosure filled with a semitransparent medium. Sci World J. 2014;2014:1–7.

  36. Goodarzi M, Safaei MR, Karimipour A, Hooman K, Dahari M, Kazi SN, Sadeghinezhad E. Comparison of the finite volume and lattice Boltzmann methods for solving natural convection heat transfer problems inside cavities and enclosures. Abstr Appl Anal. 2014;2014:1–15.

  37. Karimipour A, Afrand M, Akbari M, Safaei MR. Simulation of fluid flow and heat transfer in the inclined enclosure. Int J Mech Aerosp Eng. 2012;6:86–91.

    Google Scholar 

  38. Safaei MR, Goodarzi M, Mohammadi M. Numerical modeling of turbulence mixed convection heat transfer in air filled enclosures by finite volume method. Int J Multiphys. 2011;5(4):307–24.

    Article  Google Scholar 

  39. Safaei MR, Rahmanian B, Goodarzi M. Numerical study of laminar mixed convection heat transfer of power-law non-Newtonian fluids in square enclosures by finite volume method. Int J Phys Sci. 2011;6(33):7456–70.

    CAS  Google Scholar 

  40. Safaei MR, Goshayshi HR, Saeedi Razavi B, Goodarzi M. Numerical investigation of laminar and turbulent mixed convection in a shallow water-filled enclosure by various turbulence methods. Sci Res Essays. 2011;6(22):4826–38.

    Google Scholar 

  41. Nayak RK, Bhattacharyya S, Pop I. Heat transfer and entropy generation in mixed convection of a nanofluid within an inclined skewed cavity. Int J Heat Mass Transf. 2016;102:596–609.

    Article  CAS  Google Scholar 

  42. Zeibi Shirejini S, Rashidi S, Abolfazli Esfahani J. Recovery of drop in heat transfer rate for a rotating system by nanofluids. J Mol Liq. 2016;220:961–9.

    Article  CAS  Google Scholar 

  43. Parizad Laein R, Rashidi S, Abolfazli Esfahani J. Experimental investigation of nanofluid free convection over the vertical and horizontal flat plates with uniform heat flux by PIV. Adv Powder Technol. 2016;27:312–22.

    Article  CAS  Google Scholar 

  44. Akbarzadeh M, Rashidi S, Karimi N, Omar N. First and second laws of thermodynamics analysis of nanofluid flow inside a heat exchanger duct with wavy walls and a porous insert. J Therm Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7044-y.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran

    Mehran Sepyani, Alireza Shateri & Morteza Bayareh

Authors
  1. Mehran Sepyani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alireza Shateri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Morteza Bayareh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alireza Shateri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sepyani, M., Shateri, A. & Bayareh, M. Investigating the mixed convection heat transfer of a nanofluid in a square chamber with a rotating blade. J Therm Anal Calorim 135, 609–623 (2019). https://doi.org/10.1007/s10973-018-7098-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-018-7098-x

Keywords

Search

Navigation