Numerical investigation of nanofluid laminar forced convection heat transfer between two horizontal concentric cylinders in the presence of porous medium


In this paper, the finite volume method is used to investigate the laminar forced convection of water–copper nanofluid between two porous horizontal concentric cylinders. The effects of Reynolds number, the volume fraction of nanoparticles, the geometry, and the porous medium porosity on heat transfer have been studied. The problem is investigated in two different geometries and Re = 10, 25, 50, 75,100, and volume fraction of nanoparticles 0, 0.2, 0.5, 2, and 5% that were related to Copper nanoparticles and the porous medium porosity of 0.5, 0.9. The results indicated that in each geometry, the corresponding Nusselt number increase in the porosity of 0.9 is greater than that of the case with the porosity of 0.5. The results show that the increase in the heat transfer coefficient in the second geometry is greater than the first geometry and in porosity 0.9 is greater than porosity 0.5. These increase values are 6 and 3%, respectively. The increase in the average temperature of the inner cylinder surface in the five mentioned Reynolds values and both geometries is investigated. This increase in temperature in Re = 10 is greater than other Reynolds numbers. The corresponding temperature increases of Re = 10, for the first and second geometries, are 1.8 and 2.2%, respectively. Investigation of the effects of volume fraction of nanoparticles on Nusselt number and heat transfer coefficient shows that both parameters increase by increasing in the volume fraction of nanoparticles. The results show that the increase in the volume fraction of nanoparticles causes the increase in average temperature of the surface. The results show that these increases of temperature that take place in the volume fractions of 0.5, 2, and 5% of nanoparticles are equal to 0.6, 1.14, and 2.3% and relative to the water, respectively.

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C f :

Coefficient of friction

C p :

Heat capacity (J kg−1 K−1)

g :

Gravitational acceleration (m s−2)

h :

Local heat transfer coefficient (W m−2 K−1)

k :

Thermal conductivity coefficient (Wm−1 K−1)


Nusselt number


Reynolds number

T :

Temperature (K)

u, v, w :

Velocity components in x, y, z directions (ms−1)

φ :

Volume fraction of nanoparticles

μ :

Dynamic viscosity (Pa s−1)

ε :


ρ :

Density (kg m−3)

υ :

Kinematics viscosity (m2 s−1)






Base fluid (pure water)






Solid nanoparticles


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This study is partially supported by the Fujian Province Natural Science Foundation (No: 2018J01506), University-industry cooperation program of Department of Science and Technology of Fujian Province (No. 2019H6018), Fuzhou Science and Technology Planning Project (No: 2018S113, 2018G92), the Educational Research Projects of Young Teachers of Fujian Province(No. JK2017038, JAT170439), and the 2017 Outstanding Young Scientist Training Program of Colleges in Fujian Province.

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Correspondence to Masoud Afrand.

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Liu, X., Toghraie, D., Hekmatifar, M. et al. Numerical investigation of nanofluid laminar forced convection heat transfer between two horizontal concentric cylinders in the presence of porous medium. J Therm Anal Calorim 141, 2095–2108 (2020).

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  • Nanofluid
  • Forced convection
  • Laminar flow
  • Nusselt number
  • Porous medium