Study of water based nanofluid flows in annular tubes using numerical simulation and sensitivity analysis

Original
First Online:
Received:
Accepted:
  • 9 Downloads

Abstract

Convective heat transfer, entropy generation and pressure drop of two water based nanofluids (Cu-water and Al2O3-water) in horizontal annular tubes are scrutinized by means of computational fluids dynamics, response surface methodology and sensitivity analysis. First, central composite design is used to perform a series of experiments with diameter ratio, length to diameter ratio, Reynolds number and solid volume fraction. Then, CFD is used to calculate the Nusselt Number, Euler number and entropy generation. After that, RSM is applied to fit second order polynomials on responses. Finally, sensitivity analysis is conducted to manage the above mentioned parameters inside tube. Totally, 62 different cases are examined. CFD results show that Cu-water and Al2O3-water have the highest and lowest heat transfer rate, respectively. In addition, analysis of variances indicates that increase in solid volume fraction increases dimensionless pressure drop for Al2O3-water. Moreover, it has a significant negative and insignificant effects on Cu-water Nusselt and Euler numbers, respectively. Analysis of Bejan number indicates that frictional and thermal entropy generations are the dominant irreversibility in Al2O3-water and Cu-water flows, respectively. Sensitivity analysis indicates dimensionless pressure drop sensitivity to tube length for Cu-water is independent of its diameter ratio at different Reynolds numbers.

Nomenclature

A

Constant (=0.01)

a

Diameter ratio (=D o /D i )

B

Constant (=5)

Be

Bejan number (−)

Cp

Specific heat (J/kg.K)

DH

Hydraulic diameter (=0.008 m)

e

Absolute error ([f])

F

Coefficient (−)

f

Friction coefficient (−)

f

key parameter (Pa)

I

Turbulent intensity (%)

i

Grid index (−)

K

Constant (−)

k

Conduction coefficient (W/m.K)

k1

Constant (−)

L

Tube length (m)

N

Cell number (−)

Nu

Nusselt number (−)

n

Constant (=3)

P

Apparent order of discretization scheme (−)

Pr

Prandtl number (−)

q”

Heat flux (=197.5 W)

Re

Reynolds number (−)

r

Ratio of cell numbers (−)

S.”‘

Volumetric entropy generation (W/m 3 .K)

T

Temperature (K)

u

x-velocity (m/s)

V

Velocity magnitude (m/s)

v

y-velocity (m/s)

x,y

Coordinate directions (−)

y+

y-plus (−)

Greek letters

Γ

Blending function (−)

ε

Relative error (−)

μ

Dynamic viscosity (Pa.sec)

ρ

Density (kg/m3)

ϕ

Solid volume fraction (−)

Subscripts

ann

Annulus

bf

Base fluid

f

Frictional

gen

Generation

i

Inner

in

Inlet

n

Non dimensional

nf

Nanofluid

o

Outer

p

Particle

T

Thermal

This is a preview of subscription content, log in to check access

Notes

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

References

  1. 1.
    Abu-Nada E, Masoud Z, Hijazi A (2008) Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids. International Communications in Heat and Mass Transfer 35:657–665.  https://doi.org/10.1016/j.icheatmasstransfer.2007.11.004 CrossRefGoogle Scholar
  2. 2.
    Afrand M (2017) Using a magnetic field to reduce natural convection in a vertical cylindrical annulus. Int J Therm Sci 118:12–23.  https://doi.org/10.1016/j.ijthermalsci.2017.04.012 CrossRefGoogle Scholar
  3. 3.
    Akbarzadeh M, Rashidi S, Bovand M, Ellahi R (2016) A sensitivity analysis on thermal and pumping power for the flow of nanofluid inside a wavy channel. J Mol Liq 220:1–13.  https://doi.org/10.1016/j.molliq.2016.04.058 CrossRefGoogle Scholar
  4. 4.
    Amani E, Nobari MRH (2011) A numerical investigation of entropy generation in the entrance region of curved pipes at constant wall temperature. Energy 36:4909–4918.  https://doi.org/10.1016/j.energy.2011.05.035 CrossRefGoogle Scholar
  5. 5.
    Brinkman H (1952) The viscosity of concentrated suspensions and solutions. J Chem Phys 20:571–571CrossRefGoogle Scholar
  6. 6.
    Buongiorno J (2006) Convective transport in nanofluids. J Heat Transf 128:240–250CrossRefGoogle Scholar
  7. 7.
    Ebrahimi A, Rikhtegar F, Sabaghan A, Roohi E (2016) Heat transfer and entropy generation in a microchannel with longitudinal vortex generators using nanofluids. Energy 101:190–201.  https://doi.org/10.1016/j.energy.2016.01.102 CrossRefGoogle Scholar
  8. 8.
    El Maakoul A, Laknizi A, Saadeddine S, Ben Abdellah A, Meziane M, El Metoui M (2017) Numerical design and investigation of heat transfer enhancement and performance for an annulus with continuous helical baffles in a double-pipe heat exchanger. Energy Convers Manag 133:76–86.  https://doi.org/10.1016/j.enconman.2016.12.002 CrossRefGoogle Scholar
  9. 9.
    Gnielinski V (1976) New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem Eng 16:359–368Google Scholar
  10. 10.
    Gnielinski V (2009) Heat transfer coefficients for turbulent flow in concentric annular ducts. Heat Transfer Engineering 30:431–436.  https://doi.org/10.1080/01457630802528661 CrossRefGoogle Scholar
  11. 11.
    Haghighi EB et al (2014) Experimental study on convective heat transfer of nanofluids in turbulent flow: methods of comparison of their performance. Exp Thermal Fluid Sci 57:378–387.  https://doi.org/10.1016/j.expthermflusci.2014.05.019 CrossRefGoogle Scholar
  12. 12.
    Hamilton R, Crosser O (1962) Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam 1:187–191CrossRefGoogle Scholar
  13. 13.
    Kader BA (1981) Temperature and concentration profiles in fully turbulent boundary layers. Int J Heat Mass Transf 24:1541–1544.  https://doi.org/10.1016/0017-9310(81)90220-9 CrossRefGoogle Scholar
  14. 14.
    Kuehn TH, Goldstein RJ (2006) An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders. J Fluid Mech 74:695–719.  https://doi.org/10.1017/S0022112076002012 CrossRefMATHGoogle Scholar
  15. 15.
    Lee YN, Minkowycz WJ (1989) Heat transfer characteristics of the annulus of twocoaxial cylinders with one cylinder rotating. Int J Heat Mass Transf 32:711–722.  https://doi.org/10.1016/0017-9310(89)90218-4 CrossRefGoogle Scholar
  16. 16.
    Malvandi A, Heysiattalab S, Ganji DD (2016) Thermophoresis and Brownian motion effects on heat transfer enhancement at film boiling of nanofluids over a vertical cylinder. J Mol Liq 216:503–509.  https://doi.org/10.1016/j.molliq.2016.01.030 CrossRefGoogle Scholar
  17. 17.
    Ndenguma DD, Dirker J, Meyer JP (2017) Heat transfer and pressure drop in annuli with approximately uniform internal wall temperatures in the transitional flow regime. Int J Heat Mass Transf 111:429–441.  https://doi.org/10.1016/j.ijheatmasstransfer.2017.02.064 CrossRefGoogle Scholar
  18. 18.
    Pak BC, Cho YI (1998) Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Experimental Heat Transfer 11:151–170.  https://doi.org/10.1080/08916159808946559 CrossRefGoogle Scholar
  19. 19.
    Pakravan HA, Yaghoubi M (2013) Analysis of nanoparticles migration on natural convective heat transfer of nanofluids. Int J Therm Sci 68:79–93.  https://doi.org/10.1016/j.ijthermalsci.2012.12.012 CrossRefGoogle Scholar
  20. 20.
    Ravi Kumar NT, Bhramara P, Addis BM, Sundar LS, Singh MK, Sousa ACM (2017) Heat transfer, friction factor and effectiveness analysis of Fe3O4/water nanofluid flow in a double pipe heat exchanger with return bend. International Communications in Heat and Mass Transfer 81:155–163.  https://doi.org/10.1016/j.icheatmasstransfer.2016.12.019 CrossRefGoogle Scholar
  21. 21.
    Richardson LF, Gaunt JA (1927) The deferred approach to the limit. Part I. Single lattice. Part II. Interpenetrating lattices. Philosophical Transactions of the Royal Society of London Series A, containing papers of a mathematical or physical character 226:299–361Google Scholar
  22. 22.
    Roache PJ (1997) Quantification of uncertainty in computational fluid dynamics. Annu Rev Fluid Mech 29:123–160MathSciNetCrossRefGoogle Scholar
  23. 23.
    Saha G, Paul MC (2015) Heat transfer and entropy generation of turbulent forced convection flow of nanofluids in a heated pipe. International Communications in Heat and Mass Transfer 61:26–36.  https://doi.org/10.1016/j.icheatmasstransfer.2014.11.007 CrossRefGoogle Scholar
  24. 24.
    Saqr KM, Shehata AI, Taha AA, Abo ElAzm MM (2016) CFD modelling of entropy generation in turbulent pipe flow: Effects of temperature difference and swirl intensity. Appl Therm Eng 100:999–1006.  https://doi.org/10.1016/j.applthermaleng.2016.02.014 CrossRefGoogle Scholar
  25. 25.
    Shalchi-Tabrizi A, Seyf HR (2012) Analysis of entropy generation and convective heat transfer of Al2O3 nanofluid flow in a tangential micro heat sink. Int J Heat Mass Transf 55:4366–4375.  https://doi.org/10.1016/j.ijheatmasstransfer.2012.04.005 CrossRefGoogle Scholar
  26. 26.
    Sheikholeslami M, Rokni HB (2017) Numerical modeling of nanofluid natural convection in a semi annulus in existence of Lorentz force. Comput Methods Appl Mech Eng 317:419–430.  https://doi.org/10.1016/j.cma.2016.12.028 MathSciNetCrossRefGoogle Scholar
  27. 27.
    Siavashi M, Jamali M (2016) Heat transfer and entropy generation analysis of turbulent flow of TiO2-water nanofluid inside annuli with different radius ratios using two-phase mixture model. Appl Therm Eng 100:1149–1160.  https://doi.org/10.1016/j.applthermaleng.2016.02.093 CrossRefGoogle Scholar
  28. 28.
    Siavashi M, Talesh Bahrami HR, Saffari H (2015) Numerical investigation of flow characteristics, heat transfer and entropy generation of nanofluid flow inside an annular pipe partially or completely filled with porous media using two-phase mixture model. Energy 93:2451–2466.  https://doi.org/10.1016/j.energy.2015.10.100 CrossRefGoogle Scholar
  29. 29.
    Xuan Y, Roetzel W (2000) Conceptions for heat transfer correlation of nanofluids. Int J Heat Mass Transf 43:3701–3707.  https://doi.org/10.1016/S0017-9310(99)00369-5 CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMalek-Ashtar University of TechnologyShahin-ShahrIslamic Republic of Iran
  2. 2.Department of Applied ChemistryMalek-Ashtar University of TechnologyShahin-ShahrIslamic Republic of Iran

Personalised recommendations