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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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Abstract

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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Abbreviations

CF:

Forchheimer coefficient

d :

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

d*:

Porous layer thickness (m)

Da:

Darcy number

e :

Non-dimensional porous layer thickness (m)

e*:

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)

Nu:

Average Nusselt number

Nub :

Nusselt number without using porous medium

Nulocal :

Local Nusselt number

P :

Dimensionless pressure

P*:

Pressure (Pa)

Pr:

Prandtl number

PR:

Radial ratio

r :

Dimensionless radial coordinate

r*:

Radial coordinate (m)

Ra:

Rayleigh number

R c :

Thermal conductivity ratio

Re:

Reynolds number

r i :

Inner cylinder radius (m)

Ri:

Richardson number

r o :

Outer cylinder radius (m)

T :

Dimensionless temperature

T*:

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*:

x coordinate (m)

α :

Heat diffusion coefficient (m2 s−1)

β :

Thermal diffusion coefficient (k−1)

ε :

Porosity

θ :

Cross-radial coordinate (°)

θ*:

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)

Φ:

Angular coordinate (°)

ω :

Angular velocity (s−1)

c:

Cold

eff:

Effective

f:

Fluid

h:

Hot

s:

Solid

References

  1. Talesh Bahrami HR, Zarei S, Saffari H. The effect of droplet morphology on the heat transfer performance of micro-, nanostructured surfaces in dropwise condensation. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08318-1.

    Article  Google Scholar 

  2. Sheikholeslami M. New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media. Comput Methods Appl Mech Eng. 2019;344:319–33.

    Article  Google Scholar 

  3. Sheikholeslami M. Numerical approach for MHD Al2O3–water nanofluid transportation inside a permeable medium using innovative computer method. Comput Methods Appl Mech Eng. 2019;344:306–18.

    Article  Google Scholar 

  4. Gholamalipour P, Siavashi M, Doranehgard MH. Eccentricity effects of heat source inside a porous annulus on the natural convection heat transfer and entropy generation of Cu–water nanofluid. Int Commun Heat Mass Transf. 2019;109:104367.

    Article  CAS  Google Scholar 

  5. Mohamad AA. Heat transfer enhancements in heat exchangers fitted with porous media part I: constant wall temperature. Int J Therm Sci. 2003;42:385–95.

    Article  Google Scholar 

  6. Yang Y-T, Hwang M-L. Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media. Int J Heat Mass Transf. 2009;52:2956–65.

    Article  Google Scholar 

  7. Hekmat MH, Rabiee MB, Ziarati KK. Numerical investigation of the mixed convection of a magnetic nanofluid in an annulus between two vertical concentric cylinders under the influence of a non-uniform external magnetic field. J Therm Anal Calorim. 2019;138:1745–59.

    Article  CAS  Google Scholar 

  8. Shahsavar A, Rashidi M, Mosghani MM, Toghraie D, Talebizadehsardari P. A numerical investigation on the influence of nanoadditive shape on the natural convection and entropy generation inside a rectangle-shaped finned concentric annulus filled with boehmite alumina nanofluid using two-phase mixture model. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-09076-w.

    Article  Google Scholar 

  9. Shirazi M, Shateri A, Bayareh M. Numerical investigation of mixed convection heat transfer of a nanofluid in a circular enclosure with a rotating inner cylinder. J Therm Anal Calorim. 2018;133:1061–73.

    Article  CAS  Google Scholar 

  10. Siavashi M, Karimi K, Xiong Q, Doranehgard MH. Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder. J Therm Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7945-9.

    Article  Google Scholar 

  11. Khanafer K, Chamkha AJ. Mixed convection within a porous heat generating horizontal annulus. Int J Heat Mass Transf. 2003;46:1725–35.

    Article  Google Scholar 

  12. Leong JC, Lai FC. Mixed convection in a rotating concentric annulus with a porous sleeve. J Thermophys Heat Transf. 2019;33:483–94.

    Article  CAS  Google Scholar 

  13. Luo Y, Peden JM. Flow of drilling fluids through eccentric annuli. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers; 1987.

  14. Siavashi M, Talesh Bahrami HR, Saffari H. 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. 2015;93:2451–66.

    Article  CAS  Google Scholar 

  15. Siavashi M, Bahrami HRT, Saffari H. Numerical investigation of porous rib arrangement on heat transfer and entropy generation of nanofluid flow in an annulus using a two-phase mixture model. Numer Heat Transf Part A Appl. 2017;71:1251–73.

    Article  CAS  Google Scholar 

  16. Mozayyeni HR, Rahimi AB. Mixed convection in cylindrical annulus with rotating outer cylinder and constant magnetic field with an effect in the radial direction. Sci Iran. 2012;19:91–105.

    Article  Google Scholar 

  17. Liao C-C, Lin C-A. Mixed convection of a heated rotating cylinder in a square enclosure. Int J Heat Mass Transf. 2014;72:9–22.

    Article  Google Scholar 

  18. Salman Ahmed NJ, Badruddin IA, Kanesan J, Zainal ZA, Nazim Ahamed KS. Study of mixed convection in an annular vertical cylinder filled with saturated porous medium, using thermal non-equilibrium model. Int J Heat Mass Transf. 2011;54:3822–5.

    Article  Google Scholar 

  19. Moderres M, Abboudi S, Ihdene M, Aberkane S, Ghezal A. Numerical investigation of double-diffusive mixed convection in horizontal annulus partially filled with a porous medium. Int J Numer Methods Heat Fluid Flow. 2017;27:773–94.

    Article  Google Scholar 

  20. Minkowycz WJ, Haji-Sheikh A, Vafai KF. On departure from local thermal equilibrium in porous media due to a rapidly changing heat source: the Sparrow number. Int J Heat Mass Transf. 1999;42:3373–85.

    Article  CAS  Google Scholar 

  21. Rashidi S, Tamayol A, Valipour MS, Shokri N. Fluid flow and forced convection heat transfer around a solid cylinder wrapped with a porous ring. Int J Heat Mass Transf. 2013;63:91–100.

    Article  Google Scholar 

  22. Alazmi B, Vafai K. Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer. Int J Heat Mass Transf. 2001;44:1735–49.

    Article  Google Scholar 

  23. Saada MA, Chikh S, Campo A. Natural convection around a horizontal solid cylinder wrapped with a layer of fibrous or porous material. Int J Heat Fluid Flow. 2007;28:483–95.

    Article  Google Scholar 

  24. Pavel BI, Mohamad AA. An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media. Int J Heat Mass Transf. 2004;47:4939–52.

    Article  CAS  Google Scholar 

  25. Aminossadati SM, Ghasemi B. Natural convection of water–CuO nanofluid in a cavity with two pairs of heat source–sink. Int Commun Heat Mass Transf. 2011;38:672–8.

    Article  CAS  Google Scholar 

  26. Nasrin R, Alim MA, Chamkha AJ. Buoyancy-driven heat transfer of water–Al2O3 nanofluid in a closed chamber: effects of solid volume fraction, Prandtl number and aspect ratio. Int J Heat Mass Transf. 2012;55:7355–65.

    Article  CAS  Google Scholar 

  27. Thevenin J, Sadaoui D. About enhancement of heat transfer over a circular cylinder embedded in a porous medium. Int Commun Heat Mass Transf. 1995;22:295–304.

    Article  Google Scholar 

Download references

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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). https://doi.org/10.1007/s10973-020-09532-y

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