Effect of fibrous porous material on natural convection heat transfer from a horizontal circular cylinder located in a square enclosure

Abstract

A numerical simulation study was carried out to investigate a steady two-dimensional laminar natural convective heat transfer from a uniformly heated inner circular cylinder placed inside an air-filled square enclosure with a porous material. The enclosure’s side and upper walls were isothermal, while the bottom wall was adiabatic. All the numerical calculations were performed in the range of Rayleigh numbers between 103 and 107. The material porosity (ε), the solid to fluid thermal conductivity ratio (kr), and Darcy number in the present study were 1.0, 0.5, and 0.01, respectively. The results showed that for Rayleigh numbers that are less than 106, the isotherms are almost parallel inside the three cold walls except for the corners of the adiabatic bottom wall. The rates of vertical velocity are higher than the horizontal velocity, especially at higher Grashof numbers. Also, the use of fibrous porous material with low thermal conductivity relative to the fluid thermal conductivity reduces the values of average Nusselt number, in addition to reducing the horizontal and vertical velocities along the horizontal axis.

Keywords

• Natural convection
• Square cavity
• Porous media

References

1. [1] Dalal A, Das MK. Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature. International Journal of Heat and Mass Transfer 2005;48:3833–54. [CrossRef]
2. [2] Ding H, Shu C, Yeo KS, Lu ZL. Simulation of natural convection in eccentric annuli between a square outer cylinder and a circular inner cylinder using local MQ-DQ method. Numerical Heat Transfer, Part A: Applications 2005;47:291–313. [CrossRef]
3. [3] Mezrhab A, Jami M, Abid C, Bouzidi MH, Lallemand P. Lattice-Boltzmann modelling of natural convection in an inclined square enclosure with partitions attached to its cold wall. International Journal of Heat and Fluid Flow 2006;27:456–465. [CrossRef]
4. [4] Varol Y, Oztop HF, Yilmaz T. Two-dimensional natural convection in a porous triangular enclosure with a square body. International communications in heat and mass transfer. 2007;34:238–247. [CrossRef]
5. [5] Ben-Nakhi A, Chamkha AJ. Conjugate natural convection in a square enclosure with inclined thin fin of arbitrary length”, International Journal of Thermal Sciences 2007;46:467–78. [CrossRef]
6. [6] Oztop HF, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow 2008;29:1326–36. [CrossRef]
7. [7] Xu X, Sun G, Yu Z, Hu Y, Fan L, Cen K. Numerical investigation of laminar natural convective heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure. International Journal of Heat and Mass Transfer 2009;52:3176–86. [CrossRef]
8. [8] Hussain SH., Hussein AK. Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations. International Communications in Heat and Mass Transfer 2010;37:1115–26. [CrossRef]

9. [9] Yu ZT., Xu X., Hu YC., Fan LW., Cen KF. Unsteady natural convection heat transfer from a heated horizontal circular cylinder to its air-filled coaxial triangular enclosure. International Journal of Heat and Mass Transfer 2011;54:1563–71. [CrossRef]
10. [10] Sheikholeslami M, Hashim I, Soleimani S. Numerical investigation of the effect of magnetic field on natural convection in a curved-shape enclosure. Mathematical Problems in Engineering 2013;1-10. [CrossRef]
11. [11] Balamurugan S, Krishnakanth K. Numerical Study of Convective Heat Transfer for Different Shapes of Hot Sources inside an Enclosure. Research and Reviews: Journal of Engineering and Technology RRJET 2015;4:18–34.
12. [12] Ravnik J, Škerget L. A numerical study of nanofluid natural convection in a cubic enclosure with a circular and an ellipsoidal cylinder. International Journal of Heat and Mass Transfer 2015;89:596–605. [CrossRef]
13. [13] Chowdhury R, Khan MAH, Siddiki MNAA. Natural convection in porous triangular enclosure with a circular obstacle in presence of heat generation. American Journal of Applied Mathematics 2015;3:51–58. [CrossRef]
14. [14] Yuan X, Tavakkoli F, Vafai K. Analysis of natural convection in horizontal concentric annuli of variable inner shape. Numerical Heat Transfer, Part A 2015;68:1155–74. [CrossRef]
15. [15] Ho YT, Yu TH, Lin KC. Laminar natural convection over a heated cylinder in a cubic – a Lattice Boltzmann study. Proceedings of IASTEM International Conference, Chengdu, China, 17th–18th Jun 2017, 4–8.
16. [16] Gangawane KM., Manikandan B. Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids. Chinese Journal of Chemical Engineering 2017;25:555–71. [CrossRef]
17. [17] Zadkhast M., Toghraie D., Karimipour A. Developing a new correlation to estimate the thermal conductivity of MWCNT-CuO/water hybrid nanofluid via an experimental investigation. J Therm Anal Calorim 2017;129:859–867. [CrossRef]
18. [18] Abdulkadhim A, Abed AM, Mohsen AM, Al-Farhany K. Effect of partially thermally active wall on natural convection in porous enclosure. Mathematical Modeling of Engineering Problems 2018;5:395-406. [CrossRef]
19. [19] Geridönmez BP. Numerical simulation of natural convection in a porous cavity filled with free of fluid in presence of magnatic source. Journal of Thermal Engineering 2018;4:1756–69. [CrossRef]
20. [20] Ataei-Dadavi I, Chakkingal M, Kenjeres S, Kleijn CR, Tummers MJ. Flow and heat transfer measurements in natural convection in coarse-grained porous media. International Journal of Heat and Mass Transfer 2019;130:575–84. [CrossRef]
21. [21] Zahmatkesh I, Ardekani RA. Effect of magnetic field orientation on nanofluid free convection in a porous cavity: A heat visualization study. Journal of Thermal Engineering 2020;6:170–86. [CrossRef]
22. [22] Fletcher CAJ. Computational Galerkin methods. New York: Springer-Verlag; 1984. [CrossRef]
23. [23] Pop I., Kumari M, Nath G. Free convection about cylinders of elliptic cross section embedded in a porous medium. International Journal of Engineering Sciences 1992;30:35–45. [CrossRef]
24. [24] Yih K. Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium. International Communications of Heat and Mass Transfer 1999;26:431–440. [CrossRef]
25. [25] Kumari M, Jayanthi S. Non-darcy non-­newtonian free convection flow over a horizontal cylinder in a saturated porous medium. International Communications of Heat and Mass Transfer 2004;31:1219-1226. [CrossRef]
26. [26] Abbas AH, Messaoud H, Saada D, Abdennacer B. Numerical study of laminar natural convection in porous media: Darcy -Brinkman-Forcheimer model. International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES15, Energy Procedia 2015;74:77–86. [CrossRef]