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Heat transfer enhancement inside an eccentric cylinder with an inner rotating wall using porous media: a numerical study

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Porous media insert is a simple technique to enhance heat transfer, which has been used in different applications. This useful passive improvement technique could be applied on the rotating/fixed inner/outer wall of a/an concentric/eccentric cylinder to improve heat transfer. This configuration has extensive applications in different fields, especially in the bearing technology. In the current study, a numerical research has been done to explore the effect of inserting a porous layer on the inner rotating wall of an eccentric cylinder on the heat transfer. The effects of different parameters including Richardson number, Rayleigh number, Darcy number, the eccentricity, and the inner wall peripheral location are investigated. The results show that using porous media with higher Darcy numbers enhances more heat transfer (for example, about 70% at Da = 10−3 with respect to 30% at Da = 10−6). Also, porous media insert improves heat transfer by about 90% in the medium Richardson numbers (Ri = 0.1). The results show that the effect of porous media insert becomes very considerable as the Rayleigh number increases. For example, porous media insert could augment heat transfer by three times at Ra = 9 × 104.

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Forchheimer coefficient

d :

Normalized porous cover thickness (d* r−1i )


Porous layer thickness (m)


Darcy number

e :

Non-dimensional porous layer thickness (m)


Porous layer thickness (m)

h :

Heat transfer coefficient (W m−2 K−1)

K :

Permeability (m2)

k :

Thermal conductivity (W m−1 K−1)

k eff :

Effective thermal conductivity (W m−1 K−1)

L :

Specific length (m)


Average Nusselt number

Nub :

Nusselt number without using porous medium

Nulocal :

Local Nusselt number

P :

Dimensionless pressure


Pressure (Pa)


Prandtl number


Radial ratio

r :

Dimensionless radial coordinate


Radial coordinate (m)


Rayleigh number

R c :

Thermal conductivity ratio


Reynolds number

r i :

Inner cylinder radius (m)


Richardson number

r o :

Outer cylinder radius (m)

T :

Dimensionless temperature


Temperature (K)

T c :

Inner cylinder temperature (K)

T h :

Outer cylinder temperature (K)

u*, v*:

Velocity component in r and theta directions, respectively

u, v :

Dimensionless velocity component in r and theta directions, respectively

V :

Dimensionless velocity magnitude

u c :

Characteristic velocity (m s−1)


x coordinate (m)

α :

Heat diffusion coefficient (m2 s−1)

β :

Thermal diffusion coefficient (k−1)

ε :


θ :

Cross-radial coordinate (°)


Normalized cross-radial coordinate

μ :

Dynamic viscosity (kg m−1 s−1)

μ eff :

Effective dynamic viscosity (kg m−1 s−1)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Fluid density (kg m−3)

ρ 0 :

Reference fluid density (kg m−3)


Angular coordinate (°)

ω :

Angular velocity (s−1)












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Correspondence to Hamid Reza Talesh Bahrami.

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Talesh Bahrami, H.R., Safikhani, H. Heat transfer enhancement inside an eccentric cylinder with an inner rotating wall using porous media: a numerical study. J Therm Anal Calorim 141, 1905–1917 (2020).

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