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Numerical Flow Analysis in \(\Gamma\) Shaped Enclosure: Energy Streamlines and Field Synergy

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Problems of Geocosmos–2020

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Abstract

Understanding heat transfer becomes more important as the severity of climate, either hot or cold, increases. Managing heat flows is critical to occupant’s thermal comfort, durability, energy efficiency, and, increasingly, thermal resilience during periods of extended power outages. In the present study, the convective air flow in the differentially heated gamma (\({\Gamma }\)) shaped enclosure is simulated numerically. Isothermal temperature conditions are assumed at the vertical walls of the enclosure in which the temperature of the step wall is higher than that of other vertical walls. Top and bottom walls of the enclosure are considered to be adiabatic. The governing equations of the problem are discretized using the finite volume approach. To accelerate these simulations, the message passing interface (MPI) protocols are employed using the OpenMPI standard library. High-resolution simulation results are presented. We compare our results with those obtained by state-of-the-art methods to validate the performance of employed numerical methods. The flow behavior is elucidated with the aid of streamlines, isotherms, energy streamlines and synergy between the velocity and temperature gradient vectors by varying the control parameter, Rayleigh number, in the laminar regime.

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References

  1. Jue, T.C.: Analysis of flows driven by a torsionally-oscillatory lid in a fluid-saturated porous enclosure with thermal stable stratification. Int. J. Therm. Sci. 41, 795–804 (2002). https://doi.org/10.1016/S1290-0729(02)01373-X

    Article  Google Scholar 

  2. Mansour, R.B., Nguyen, C.T., Galanis, N.: Numerical study of transient heat and mass transfer and stability in a salt-gradient solar pond. Int. J. Therm. Sci. 43, 779–790 (2004). https://doi.org/10.1016/j.ijthermalsci.2004.02.018

    Article  Google Scholar 

  3. Prieto, M., Diaz, J., Egusquiza, E.: Analysis of the fluid-dynamic and thermal behaviour of a tin bath in float glass manufacturing. Int. J. Therm. Sci. 41, 348–359 (2002). https://doi.org/10.1016/S1290-0729(02)01325-X

    Article  Google Scholar 

  4. Bagchi, A., Kulacki, F.A.: Natural Convection in Superposed Fluid-Porous Layers. Springer, New York (2014)

    Book  Google Scholar 

  5. Jansen, J.D.: A Systems Description of Flow Through Porous Media. Springer, New York (2013)

    Book  Google Scholar 

  6. Poulikakos, D.: Natural convection in a confined fluid-filled space driven by a single vertical wall with warm and cold regions. ASME J. Heat Transf. 107, 867–876 (1985). https://doi.org/10.1115/1.3247515

    Article  Google Scholar 

  7. Lage, J.I., Bejan, A.: The resonance of natural convection in an enclosure heated periodically from the side. Int. J. Heat Mass Transf. 36, 2027–2038 (1993). https://doi.org/10.1016/S0017-9310(05)80134-6

    Article  Google Scholar 

  8. Bilgen, E., Wang, X., Vasseur, P., Meng, F., Robillard, L.: Periodic conditions to simulate mixed convection heat transfer in horizontal channels. Numer. Heat Transf. A 27, 461–472 (1995). https://doi.org/10.1080/10407789508913712

  9. Sarris, I.E., Lekakis, I., Vlachos, N.S.: Natural convection in a 2D enclosure with sinusoidal upper wall temperature. Numer. Heat Transf. A 42, 513–530 (2002). https://doi.org/10.1080/10407780290059675

  10. Mohebbi, R., Izadi, M., Sajjadi, H., Delouei, A.A., Sheremet, M.A.: Examining of nanofluid natural convection heat transfer in a Γ-shaped enclosure including a rectangular hot obstacle using the lattice Boltzmann method. Physica A 526, 120831 (2019). https://doi.org/10.1016/j.physa.2019.04.067

    Article  Google Scholar 

  11. Mahmud, S., Fraser, R.: Visualizing energy flows through energy streamlines and pathlines. Int. J. Heat Mass Transf. 50, 3990–4002 (2007). https://doi.org/10.1016/j.ijheatmasstransfer.2007.01.032

    Article  Google Scholar 

  12. Tasnim, S.H., Collins, M.R.: Suppressing natural convection in a differentially heated square cavity with an arc shaped baffle. Int. Commun. Heat Mass Transf. 32, 94–106 (2005). https://doi.org/10.1016/j.icheatmasstransfer.2004.05.022

    Article  Google Scholar 

  13. Tasnim, S.H., Fraser, R.A.: Flow and energy fields in a resonant channel. Int. Commun. Heat. Mass Transf. 36, 539–546 (2009). https://doi.org/10.1016/j.icheatmasstransfer.2009.03.016

    Article  Google Scholar 

  14. Tasnim, S.H., Fraser, R.A.: Computations of the flow and thermal fields in a thermosacoustic refrigerator. Int. Commun. Heat Mass Transf. 37, 748–755 (2010). https://doi.org/10.1016/J.ICHEATMASSTRANSFER.2010.04.006

    Article  Google Scholar 

  15. Cao, N., Olson, J.R., Swift, G.W., Chen, S.: Energy flux density in a thermoacoustic couple. J. Acoust. Soc. Am. 99, 3456–3464 (1996). https://doi.org/10.1121/1.414992

    Article  Google Scholar 

  16. Ishikawa, H., Mee, D.J.: Numerical investigation of flow and energy fields near a thermosacoustic couple. J. Acoust. Soc. Am. 111, 831–839 (2002). https://doi.org/10.1121/1.1430687

    Article  Google Scholar 

  17. Ziapour, B.M., Dehnavi, R.: Finite-volume method for solving the entropy generation due to air natural convection in γ-shaped enclosure with circular corners. Math. Comput. Model. 54(5–6), 1286–1299 (2011). https://doi.org/10.1016/j.mcm.2011.03.039

    Article  Google Scholar 

  18. Mahmoodi, M.: Numerical simulation of free convection of a nanofluid in L-shaped cavities. Int. J. Therm. Sci. 50, 1731–1740 (2011). https://doi.org/10.1016/j.ijthermalsci.2011.04.009

    Article  Google Scholar 

  19. Mahmud, S.: Free convection inside an L-shaped enclosure. Int. Commun. Heat Mass Transf. 29(7), 1005–1013 (2002). https://doi.org/10.1016/S0735-1933(02)00420-7

    Article  Google Scholar 

  20. Kalteh, M., Hasani, H.: Lattice Boltzmann simulation of nanofluid free convection heat transfer in an L-shaped enclosure. Superlattices Microstruct. 66, 112–128 (2014). https://doi.org/10.1016/j.spmi.2013.12.004

    Article  Google Scholar 

  21. Rani, H.P., Narayana, V., Rameshwar, Y., Starchenko, S.V.: Aspect ratio effects on bottom heated 2D cavity using energy streamlines and field synergy principle. Latin Am. Appl. Res. 50, 41–46 (2020). https://doi.org/10.52292/j.laar.2020.164

  22. Narayana, V., Rani, H.P.: Analysis of visualization techniques of bottom heated lid-driven square cavity. Heat Transf. 49, 3549–3559 (2020). https://doi.org/10.1002/htj.21787

    Article  Google Scholar 

  23. Rani, H.P., Naresh, K., Narayana, V.: Differentially heated cubical cavity using energy pathlines and field synergy. Heat Transf. 49, 3683–3701 (2020). https://doi.org/10.1002/htj.21795

    Article  Google Scholar 

  24. Kimura, S., Bejan, A.: The boundary layer natural convection regime in a rectangular cavity with uniform heat flux from the side. J. Heat Transf. 106(1), 98–103 (1984). https://doi.org/10.1115/1.3246666

    Article  Google Scholar 

  25. Bejan, A.: Convection Heat Transfer. Wiley, New York (1984)

    Google Scholar 

  26. Eckert, E.R., Drake, G.R.M., Jr.: Analysis of Heat and Mass Transfer. McGraw-Hill, New York (1972)

    Google Scholar 

  27. Bello-Ochende, F.L.: A heat function formulation for thermal convection in a square cavity. Int. Commun. Heat Mass Transf. 15, 193–202 (1988). https://doi.org/10.1016/0735-1933(88)90065-6

    Article  Google Scholar 

  28. Morega, A.M., Bejan, A.: Heatline visualization of forced convection laminar boundary layers. Int. J. Heat Mass Transf. 36, 3957–3966 (1993). https://doi.org/10.1016/0017-9310(93)90146-W

    Article  Google Scholar 

  29. Zhao, F.Y., Liu, D., Tang, G.F.: Application issues of the streamline, heatline and massline for conjugate heat and mass transfer. Int. J. Heat Mass Transf. 50, 320–334 (2007). https://doi.org/10.1016/j.ijheatmasstransfer.2006.06.026

    Article  Google Scholar 

  30. Costa, V.A.F.: Heatline and massline visualization of laminar natural convection boundary layers near a vertical wall. Int. J. Heat Mass Transf. 43, 3765–3774 (2000). https://doi.org/10.1016/S0017-9310(00)00028-4

    Article  Google Scholar 

  31. Costa, V.A.F.: Unification of the streamline, heatline and massline methods for the visualization of two-dimensional heat and mass transfer in anisotropic media. Int. J. Heat Mass Transf. 46, 1309–1320 (2003). https://doi.org/10.1016/S0017-9310(02)00404-0

    Article  Google Scholar 

  32. Hooman, K.: Energy flux vectors as a new tool for convection visualization. Int. J. Numer. Methods Heat Fluid Flow 20, 240–249 (2010). https://doi.org/10.1108/09615531011016984

  33. Guo, G., Li, D., Wang, B.: A novel concept for convective heat transfer enhancement. Int. J. Heat Mass Transf. 41, 2221–2225 (1998). https://doi.org/10.1016/S0017-9310(97)00272-X

    Article  Google Scholar 

  34. Guo, Z., Tao, W., Shah, R.: The field synergy (coordination) principle and its applications in enhancing single phase convective heat transfer. Int. J. Heat Mass Transf. 48, 1797–1807 (2005). https://doi.org/10.1016/j.ijheatmasstransfer.2004.11.007

    Article  Google Scholar 

  35. Li, Y., Liu, G., Rao, Z., Liao, S.: Field synergy principle analysis for reducing natural convection heat loss of a solar cavity receiver. Renew. Energy 75, 257–265 (2015). https://doi.org/10.1016/j.renene.2014.09.055

    Article  Google Scholar 

  36. Chen, L., Chu, Y., Zhang, Y., Han, F., Zhang, J.: Analysis of heat transfer characteristics of fractured surrounding rock in deep underground spaces. Math. Probl. Eng. Article ID 1926728, 1–11(2019). https://doi.org/10.1155/2019/1926728

  37. https://www.openfoam.com/

  38. Roe, P.L.: Large scale computations in fluid mechanics. Part 2 Lect. Appl. Math. 22, 163–193 (1985)

    Google Scholar 

  39. de Vahl Davis, G., Jones, I.P.: Natural convection in a square cavity: a comparison exercise. Int. J. Numer. Meth. Fluids 3, 227–248 (1983). https://doi.org/10.1002/fld.1650030304

    Article  Google Scholar 

  40. Markatos, N.C., Pericleous, K.A.: Laminar and turbulent natural convection in an enclosed cavity. Int. J. Heat Mass Transf. 27, 755–772 (1984). https://doi.org/10.1016/0017-9310(84)90145-5

    Article  Google Scholar 

  41. Rincon-Casado, A., Sanchez de la Flor, Chacon Vera, E., Sanchez Ramos, J.: New natural convection heat transfer correlations in enclosures for building performance simulation. Eng. Appl. Comput. Fluid Mech. 11, 340–356 (2017). https://doi.org/10.1080/19942060.2017.1300107

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Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Warangal, India

    Hari Ponnamma Rani

  2. Department of Mathematics, Balaji Institute of Technology and Science, Narsampet, Warangal, India

    Vekamulla Narayana

  3. Department of Mathematics, University College of Engineering, Osmania University, Hyderabad, India

    Yadagiri Rameshwar

  4. IZMIRAN, Troitsk, Russia

    Sergey V. Starchenko

Authors
  1. Hari Ponnamma Rani
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  2. Vekamulla Narayana
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  3. Yadagiri Rameshwar
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  4. Sergey V. Starchenko
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Corresponding author

Correspondence to Hari Ponnamma Rani .

Editor information

Editors and Affiliations

  1. Earth Physics Department, Saint Petersburg State University, St. Petersburg, Russia

    Andrei Kosterov

  2. Saint Petersburg State University, St. Petersburg, Russia

    Nikita Bobrov

  3. Saint Petersburg State University, St. Petersburg, Russia

    Evgeniy Gordeev

  4. Centre for Earth Evolution and Dynamics, University of Oslo, Oslo, Norway

    Evgeniy Kulakov

  5. Saint Petersburg State University, St. Petersburg, Russia

    Evgeniya Lyskova

  6. Saint Petersburg State University, St. Petersburg, Russia

    Irina Mironova

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Rani, H.P., Narayana, V., Rameshwar, Y., Starchenko, S.V. (2022). Numerical Flow Analysis in \(\Gamma\) Shaped Enclosure: Energy Streamlines and Field Synergy. In: Kosterov, A., Bobrov, N., Gordeev, E., Kulakov, E., Lyskova, E., Mironova, I. (eds) Problems of Geocosmos–2020. Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-91467-7_16

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