Calculation of Surface Radiation Entropy Generation by Developing the Net Radiation Method in an Inclined Enclosure with Natural Convection

Document Type : Original Article

Authors

Mehdi Fathipour ¹

Ali Safavinejad ²

¹ Department of Mechanical Engineering, University of Birjand, Birjand, Iran

² Department of Mechanical Engineering, University of Birjand

10.22067/jacsm.2023.80207.1151

Abstract

In this article, by developing the net radiation method, the entropy generation of surface radiation in an inclined enclosure with natural convection has been investigated. The governing equations are solved by the stream-vorticity function with the finite difference method and the surface radiation equations are solved with the net spectral radiation method. Surface radiation entropy generation includes radiation entropy in the field and in the matter. In this method, by solving the equations of net radiation in a spectral form, the intensity of the incoming and outgoing radiation from the surfaces is obtained, then the radiation entropy in the matter and the intensity of the spectral radiation entropy are calculated, and finally, the radiation entropy in the field is calculated using the intensity of the spectral radiation entropy. In order to accurately calculate the entropy generation of surface radiation, the developed net radiation method has been validated with the second law of thermodynamics. The effect of Rayleigh number, emissivity and enclosure angle on entropy generation is investigated. The results show that the surface radiation entropy generation decreases with the increase of the enclosure angle. The lowest entropy generation occurs at an angle of 90 degrees, when the hot wall is the lower wall of the enclosure. Also, 85% of the total entropy generation is due to surface radiation. So that the entropy generation due to the effect of surface radiation increases by 520% compared to the case where surface radiation is ignored.

Keywords

surface radiation entropy

developed net radiation method

An inclined enclosure

Subjects

• Heat transfer

---

References

1. F. Oztop, K. Al-Salem, "A review on entropy generation in natural and mixed convection heat transfer for energy systems", Renewable and Sustainable Energy Reviews, vol. 16, no. 1, Pp. 911-920, (2012). https://doi.org/10.1016/j.rser.2011.09.012
2. Balaji, S. P. Venkateshan, "Interaction of Surface Radiation with Free Convection in a Square Cavity", International Journal of Heat and Fluid Flow, Vol. 14, No. 3, Pp. 260-267, (1993). https://doi.org/10.1016/0142-727X(93)90057-T
3. Akiyama, Q. P. Chong, "Numerical Analysis of Natural Convection with Surface Radiation in a Square Enclosure", Numerical Heat Transfer, Part A: Applications, Vol. 32, No. 4, Pp. 419-433, (1997). https://doi.org/10.1080/10407789708913899.
4. Z. Shuja, B. S. Yilbas, and M. O. Budair, "Natural Convection in a Square Cavity with a Heat Generating Body: Entropy Consideration," Heat and Mass Transfer, journal article. Vol. 36, No. 4, Pp. 343-350, (2000). https://doi.org/10.1007/s002310000075
5. Berrin Erbay, Z. Altaç and B. Sülüş, "Entropy Generation in a Square Enclosure with Partial Heating from a Vertical Lateral Wall", Heat and Mass Transfer, Vol. 40, No. 12, Pp. 909-918, (2004). https://doi.org/10.1007/s00231-003-0497-x
6. Varol, H. F. Oztop and A. Koca, "Entropy Generation due to Conjugate Natural Convection in Enclosures Bounded by Vertical Solid Walls with Different Thicknesses" International Communications in Heat and Mass Transfer, Vol. 35, No. 5, Pp. 648-656, (2008). https://doi.org/10.1016/j.icheatmasstransfer.2008.01.010
7. G. Ilis, M. Mobedi, and B. Sunden, "Effect of Aspect Ratio on Entropy Generation in a Rectangular Cavity with Differentially Heated Vertical Walls", International Communications in Heat and Mass Transfer, Vol. 35, No. 6, Pp. 696-703, (2008). https://doi.org/10.1016/j.icheatmasstransfer.2008.02.002
8. D. C. Oliveski, R, M. H. Macagnan and J. B. Copetti, "Entropy Generation and Natural Convection in Rectangular Cavities", Applied Thermal Engineering, Vol. 29, No. 8, Pp. 1417-1425, (2009). https://doi.org/10.1016/j.applthermaleng.2008.07.012.
9. Alipanah, P. Hasannasab, S. F. Hosseinizadeh and M. Darbandi, "Entropy Generation for Compressible Natural Convection with High Gradient Temperature in a Square Cavity", International Communications in Heat and Mass Transfer, Vol. 37, No. 9, Pp. 1388-1395, (2010). https://doi.org/10.1016/j.icheatmasstransfer.2010.07.020
10. Bouabid, M. Magherbi, N. Hidouri and A. B. Brahim, A, "Entropy Generation at Natural Convection in an Inclined Rectangular Cavity", Entropy, Vol. 13, No. 5, Pp. 1020-1033, (2011).https://doi.org/10.3390/e13051020
11. S. Bondareva, M. A. Sheremet, H. F. Oztop, and N. Abu-Hamdeh, "Entropy Generation due to Natural Convection of a Nanofluid in a Partially Open Triangular Cavity," Advanced Powder Technology, Vol. 28, No. 1, Pp. 244-255, (2017). https://doi.org/10.1016/j.apt.2016.09.030
12. C. Cho, "Heat Transfer and Entropy Generation of Mixed Convection Flow in Cu-water Nanofluid-filled Lid-driven Cavity with Wavy Surface", International Journal of Heat and Mass Transfer, Vol. 119, Pp. 163-174, (2018).https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.090
13. M. Seyyedi, A. S. Dogonchi, M. Hashemi-Tilehnoee, M. Waqas and D. D. Ganji, D. D., "Investigation of Entropy Generation in a Square Inclined Cavity Using Control Volume Finite Element Method with Aided Quadratic Lagrange Interpolation Functions", International Communications in Heat and Mass Transfer, Vol. 110, P. 104398, (2020) . https://doi.org/10.1016/j.icheatmasstransfer.2019.104398
14. Iftikhar, T. Javed and M. A. Siddiqu, "Entropy Generation Analysis During MHD Mixed Convection Flow of Non-Newtonian Fluid Saturated Inside the Square Cavity", Journal of Computational Science, Vol. 66, P. 101907, (2023). https://doi.org/10.1016/j.jocs.2022.101907
15. Amraqui, A. Mezrhab, and C. Abid, "Combined Natural Convection and Surface Radiation in Solar Collector Equipped with Partitions", Applied Solar Energy, Vol. 47, No. 1, Pp. 36-47, (2011). https://doi.org/10.3103/S0003701X11010051
16. A. Dashti and A. Safavinejad, "Optimal Design with Entropy Generation Minimization Approach in Combined Natural Convection with Surface Radiation in a Two‐dimensional Enclosure", Heat Transfer—Asian Research, Vol. 48, No. 8, Pp. 4049-4073,(2019). https://doi.org/10.1002/htj.21582.
17. F. Hinojosa, D. Buentello, J. Xamán and M. Pérez-Tello, "The Effect of Surface Thermal Radiation on Entropy Generation in an Open Cavity with Natural Convection", International Communications in Heat and Mass Transfer, Vol. 81, Pp. 164-17, (2017). https://doi.org/10.1016/j.icheatmasstransfer.2016.12.018
18. Sadeghi and A. Safavinejad, "Radiative entropy generation in a gray absorbing, emitting, and scattering planar medium at radiative equilibrium", Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 201, Pp. 17-29, (2017). https://doi.org/10.1016/j.jqsrt.2017.06.023
19. Bejan, Convection Heat Transfer. Wiley, (2013).
20. Montiel Gonzalez, Hinojosa Palafox, J., and Estrada, C. A., "Numerical study of heat transfer by natural convection and surface thermal radiation in an open cavity receiver," Solar Energy, vol. 86, no. 4, pp. 1118-1128, (2012). https://doi.org/10.1016/j.solener.2012.01.005
21. R. Howell, M. P. Menguc and R. Siegel, Thermal Radiation Heat Transfer, 5th Edition.CRC Press, (2010). https://doi.org/10.1201/9780429327308
22. Aejan, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-size Systems and Finite-time Processes. CRC press, (2013). https://doi.org/10.1201/9781482239171
23. Planck, The theory of heat radiation. Blakiston, (1914).
24. Liu, S. Chu, "Verification of Numerical Simulation Method for Entropy Generation of Radiation Heat Transfer in Semitransparent Medium," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 103, No. 1, Pp. 43-56, (2007). https://doi.org/10.1016/j.jqsrt.2006.07.004
25. de Vahl Davis, "Natural Convection of Air in a Square Cavity: a Bench Mark Numerical Solution", International Journal for numerical methods in fluids, Vol. 3, No. 3, Pp. 249-264, (1983).
26. Behnia, J. Reizes and G. de Vahl Davis, "Combined Radiation and Natural Convection in a Rectangular Cavity with a Transparent Wall and Containing a Non‐participating Fluid", International Journal for Numerical Methods in Fluids, Vol. 10, No. 3, Pp. 305-325, (1990). https://doi.org/10.1002/fld.1650100306
27. G. Martyushev and M. A. Sheremet, "Numerical Analysis of Conjugate Natural Convection and Surface Radiation in an Enclosure with Local Heat Source" Computational Thermal Sciences: An International Journal, Vol. 5, No. 1, (2013). https:// doi.org/10.1615/ComputThermalScien.2012006040