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A numerical and experimental analysis of the methodology of thermal conductivity measurements in fluids by concentric cylinders

  • Henrique C. B. Costa
  • Danylo O. Silva
  • Luiz Gustavo M. Vieira
Original

Abstract

A study of thermal conductivity measurements of fluids, using the technique of steady-state heat transfer in concentric cylinders, is presented. In order to evaluate the effect of convective flow on the measured value of conductivity, numerical results, which were obtained using computational fluid dynamics (CFD) in three dimensions, are compared with experimental data and analytical results of temperature profiles. This latter was obtained considering the hypothesis of heat transfer mechanism being entirely diffusive and solely in the radial direction. An experimental design was proposed aiming to analyze the effects of glycerol mass fraction (0%, 50 and 100%), annuli size (2.525, 4.525 and 6.525 mm) and heat rate (5, 10 and 15 W) in the formation of convective streamlines. The ratio between effective and absolute conductivities (kef/k) was used as a response to evaluate the convection intensity. The results were compared with empirical equations that correlate the ratio kef/k with the dimensionless numbers of Prandtl and Rayleigh, which are in the rate 4.37 ≤ Pr ≤ 3.8 × 103 and 9.0 ≤ Ra ≤ 4.4 × 104. An evaluation of the accuracy in measuring kef is showed based on the simulated data of temperature profiles in the axial, radial and angular directions.

Nomenclature

Symbol

Meaning Unit (I.S.)

A

Area of heat transfer: m2

b

Coefficients of the multiple regression equation: dimensionless

C, m

Correlating parameters for the Nusselt number based on Reynolds number: dimensionless

C1, C2

Integration constants: K

cp

Specific heat: J/(kg∙K)

Di

Outer diameter of the inner cylinder: m

Dii

Inner diameter of the inner cylinder: m

Do

Inner diameter of the outer cylinder: m

Doo

Outer diameter of the outer cylinder: m

g

Gravity: m2/s

h

External convective heat transfer coefficient: W/(m2∙K)

k

Thermal conductivity: W/(m∙K)

kef

Effective thermal conductivity: W/(m∙K)

keq

Ratio kef/k: dimensionless

L

Concentric cylinders length: m

Lc

Annuli width: m

M

Nylon lid width: m

NuDi

Nusselt number for conduction or convection within the annuli: dimensionless

NuDicond

Nusselt number for conduction within the annuli from the inner cylinder: dimensionless

NuDiconv

Nusselt number for convection within the annuli from the inner cylinder: dimensionless

NuDoo

Nusselt number for external cross flow in cylinders: dimensionless

P

Pressure: Pa

Pr

Prandtl number: dimensionless

Prs

Prandtl number given at cylinder external wall temperature: dimensionless

Q

Heat rate generated per unit volume: W/m3

q

Heat transfer rate: W

qA

Heat flux: W/m2

qL

Heat transfer rate per cell unit length: W/m

r,θ,z

Cylindrical coordinates: m, rad, m

Ra

Rayleigh number: dimensionless

RaDi, RaDo, RaLc

Rayleigh number based on characteristics lengths Di, Do and Lc.: dimensionless

ReDoo

Reynolds number for external cross flow in cylinders: dimensionless

T

Temperature: K

t

Time: s

T0

Reference temperature: K

T

External environment temperature (air): K

Tfi

Temperature at the most inner fluid layer (fluid/inner cylinder interface): K

Tfo

Temperature at the most outer fluid layer (fluid/outer cylinder interface): K

TM

Fluid layer mean temperature: K

Troom

Room temperature: K

Tsi

Temperature at the inner surface of the inner cylinder: K

Tso

Temperature at the outer surface of the outer cylinder: K

v

Velocity: m/s.

x,y,z

Cartesian coordinates: m

X1

Coded value of glycerol mass fraction: dimensionless

X2

Coded value of annuli width: dimensionless

X3

Coded value of heat transfer rate: dimensionless

Y

Mean value of kef/k for the multiple regression equation: dimensionless

α

Thermal diffusivity: m2/s

β

Volumetric thermal expansion coefficient: 1/K

ΔT

Temperature difference: K

ΔTf

Temperature difference between the most inner and outer fluid layer (Tfi-Tfo): K

μ

Dynamic viscosity: Pa∙s

ν

Kinematic viscosity: m2/s

ρ

Density: kg/m3

ρ0

Reference density: kg/m3

σ

Stefan-Boltzmann constant (σ = 5.67 × 10−8 W∙m−2∙K−4): W/(m2∙K4)

τ

Shear stress: Pa

Φ

Energy dissipation due to viscous forces: J/(kg∙m2)

Notes

Compliance with ethical standards

Conflicts of interest

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

References

  1. 1.
    Sharqawy MH (2013) New correlations for seawater and pure water thermal conductivity at different temperatures and salinities. Desalination 313:97–104.  https://doi.org/10.1016/j.desal.2012.12.010 CrossRefGoogle Scholar
  2. 2.
    Takamatsu H, Wang H, Fukunaga T, Kurata K (2018) Measurement of fluid thermal conductivity using micro-beam MEMS sensor. Int J Heat Mass Transf 117:30–35.  https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.117 CrossRefGoogle Scholar
  3. 3.
    Babu SK, Praveen KS, Raja B, Damodharan P (2013) Measurement of thermal conductivity of fluid using single and dual wire transient techniques. Measurement 46:2746–2752.  https://doi.org/10.1016/j.measurement.2013.05.017 CrossRefGoogle Scholar
  4. 4.
    Turgut A, Tavman I, Tavman S (2009) Measurement of thermal conductivity of edible oils using transient hot wire method. Int J Food Prop 12:741–747.  https://doi.org/10.1080/10942910802023242 CrossRefGoogle Scholar
  5. 5.
    Bon J, Váquiro H, Benedito J, Telis-Romero J (2010) Thermophysical properties of mango pulp (Mangifera indica L. cv. Tommy Atkins). J Food Eng 97:563–568.  https://doi.org/10.1016/j.jfoodeng.2009.12.001 CrossRefGoogle Scholar
  6. 6.
    Gratão ACA, Silveira Júnior V, Polizelli MA, Telis-romero J (2005) Thermal properties of passion fruit juice as affected by temperature and water content. J Food Process Eng 27:413–431CrossRefGoogle Scholar
  7. 7.
    Akhmedova-Azizova LA (2006) Thermal conductivity and viscosity of aqueous of Mg(NO3)2, Sr(NO3)2, Ca(NO3)2 and Ba(NO3)2 solutions. J Chem Eng Data 51:2088–2090.  https://doi.org/10.1021/je060202w
  8. 8.
    Dawood HK, Mohammed HA, Azwadi N et al (2015) Forced, natural and mixed-convection heat transfer and fluid flow in annulus: a review. Int Commun Heat Mass Transf 62:45–57CrossRefGoogle Scholar
  9. 9.
    Huang L, Liu L-S (2009) Simultaneous determination of thermal conductivity and thermal diffusivity of food and agricultural materials using a transient plane-source method. J Food Eng 95:179–185.  https://doi.org/10.1016/j.jfoodeng.2009.04.024 CrossRefGoogle Scholar
  10. 10.
    Zhu S, Ramaswamy HS, Marcotte M et al (2007) Evaluation of thermal properties of food materials at high pressures using a dual-needle line-heat-source method. J Food Sci 72.  https://doi.org/10.1111/j.1750-3841.2006.00243.x
  11. 11.
    Cordioli M, Rinaldi M, Copelli G et al (2015) Computational fluid dynamics (CFD) modelling and experimental validation of thermal processing of canned fruit salad in glass jar. J Food Eng 150:62–69.  https://doi.org/10.1016/j.jfoodeng.2014.11.003 CrossRefGoogle Scholar
  12. 12.
    Kannan A, Sandaka PCG (2008) Heat transfer analysis of canned food sterilization in a still retort. J Food Eng 88:213–228.  https://doi.org/10.1016/j.jfoodeng.2008.02.007 CrossRefGoogle Scholar
  13. 13.
    Atayılmaz ŞÖ (2011) Experimental and numerical study of natural convection heat transfer from horizontal concentric cylinders. Int J Therm Sci 50:1472–1483.  https://doi.org/10.1016/j.ijthermalsci.2011.03.019 CrossRefGoogle Scholar
  14. 14.
    Yuan X, Tavakkoli F, Vafai K (2015) Analysis of natural convection in horizontal concentric annuli of varying inner shape. Numer Heat Transf Part A Appl 68:1155–1174.  https://doi.org/10.1080/10407782.2015.1032016 CrossRefGoogle Scholar
  15. 15.
    Raithby GD, Hollands KGT (1975) A general method of obtaining approximate solutions to laminar and turbulent free convection problems. Adv Heat Tran 11:265–315.  https://doi.org/10.1016/S0065-2717(08)70076-5 CrossRefGoogle Scholar
  16. 16.
    Sambamurthy NB, Shaija A, Narasimham GSVL, Murthy MVK (2008) Laminar conjugate natural convection in horizontal annuli. Int J Heat Fluid Flow 29:1347–1359.  https://doi.org/10.1016/j.ijheatfluidflow.2008.04.003 CrossRefGoogle Scholar
  17. 17.
    Žukauskas A (1972) Heat transfer from tubes in cross flow. Adv Heat Tran 8:93–160.  https://doi.org/10.1016/S0065-2717(08)70038-8 CrossRefGoogle Scholar
  18. 18.
    Kreith F, Manglik RM, Bohn MS (2011) Principles of heat transfer, 7th edn. Cengage Learning, StamfordGoogle Scholar
  19. 19.
    Kuehn TH, Goldstein RJ (1976) Correlating equations for natural convection heat transfer between horizontal circular cylinders. Int J Heat Mass Transf 19:1127–1134.  https://doi.org/10.1016/0017-9310(76)90145-9 CrossRefGoogle Scholar
  20. 20.
    Clemes SB, Hollands KGT, Brunger AP (1994) Natural convection heat transfers from long horizontal isothermal cylinders. J Heat Transf 116:96–104.  https://doi.org/10.1115/1.2910890 CrossRefGoogle Scholar
  21. 21.
    Atayılmaz ŞÖ, Demir H, Sevindir MK et al (2017) Natural convection heat transfer from horizontal concentric and eccentric cylinder systems cooling in the ambient air and determination of inner cylinder location. Heat Mass Transf 53:2677–2692.  https://doi.org/10.1007/s00231-017-2012-9 CrossRefGoogle Scholar
  22. 22.
    Glycerin Producers Association (1963) Physical properties of glycerin and its solutions. New YorkGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Food EngineeringFederal University of São João del ReiSete LagoasBrazil
  2. 2.School of Chemical EngineeringFederal University of UberlândiaUberlândiaBrazil

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