Abstract
A freely moving elastic ring is used to enhance mixed convection heat transfer in a two-dimensional square cavity with three different Richardson (Ri) numbers of 0.1, 1.0, and 10. The multiple-relaxation time lattice Boltzmann method combined with the immersed boundary method is employed to simulate the mixed convection heat transfer and its interaction with the elastic ring in the cavity. Two different thermal conditions for the elastic ring, i.e., with and without thermal interaction, are considered. The results are given in terms of streamlines, isotherms, temperature distribution, and Nusselt (Nu) number. It was found that at the steady state, the ring accords to one of the streamlines in the cavity. In addition, for each investigated case, the Nu number decreases as the Ri number increases. Besides, the presence of the ring leads to a much higher heat transfer (Nu number) and a much earlier steady state as compared to the case with no ring. Finally, the values of the Nu number for both thermal conditions of the ring are about the same being slightly higher for the ring with thermal interaction.
Graphical abstract
Similar content being viewed by others
References
Boutra, A., Ragui, K., Benkahla, Y.K.: Numerical study of mixed convection heat transfer in a lid-driven cavity filled with a nanofluid. Mech. Ind. 16(5), 505 (2015)
Boutra, A., Ragui, K., Benkahla, Y.K., Labsi, N.: Mixed convection of a Bingham fluid in differentially heated square enclosure with partitions. Theor. Found. Chem. Eng. 52(2), 286–294 (2018)
Gibanov, N.S., Sheremet, M.A., Oztop, H.F., Abu-Hamdeh, N.: Effect of uniform inclined magnetic field on mixed convection in a lid-driven cavity having a horizontal porous layer saturated with a ferrofluid. Int. J. Heat Mass Transf. 114, 1086–1097 (2017)
Khanafer, K., Aithal, S.M.: Laminar mixed convection flow and heat transfer characteristics in a lid-driven cavity with a circular cylinder. Int. J. Heat Mass Transf. 66, 200–209 (2013)
Gangawane, K.M., Oztop, H.F., Abu-Hamdeh, N.: Mixed convection characteristic in a lid-driven cavity containing heated triangular block: effect of location and size of block. Int. J. Heat Mass Transf. 124, 860–875 (2018)
Nithyadevi, N., Begum, A.S., Oztop, H.F., Abu-Hamdeh, N.: Mixed convection analysis in heat transfer enhancement of a nanofluid filled porous enclosure with various wall speed ratios. Int. J. Heat Mass Transf. 113, 716–729 (2017)
Al-Amiri, A., Khanafer, K.: Fluid-structure interaction analysis of mixed convection heat transfer in a lid-driven cavity with a flexible bottom wall. Int. J. Heat Mass Transf. 54(17–18), 3826–3836 (2011)
Khanafer, K.: Fluid-structure interaction analysis of non-Darcian effects on natural convection in a porous enclosure. Int. J. Heat Mass Transf. 58(1–2), 382–394 (2013)
Jamesahar, E., Ghalambaz, M., Chamkha, A.J.: Fluid–solid interaction in natural convection heat transfer in a square cavity with a perfectly thermal-conductive flexible diagonal partition. Int. J. Heat Mass Transf. 100, 303–319 (2016)
Ghalambaz, M., Jamesahar, E., Ismael, M.A., Chamkha, A.J.: Fluid-structure interaction study of natural convection heat transfer over a flexible oscillating fin in a square cavity. Int. J. Therm. Sci. 111, 256–273 (2017)
Mehryan, S.A.M., Ghalambaz, M., Ismael, M.A., Chamkha, A.J.: Analysis of fluid–solid interaction in MHD natural convection in a square cavity equally partitioned by a vertical flexible membrane. J. Magn. Magn. Mater. 424, 161–173 (2017)
Khanafer, K., Aithal, S.M.: Mixed convection heat transfer in a lid-driven cavity with a rotating circular cylinder. Int. Commun. Heat Mass Transf. 86, 131–142 (2017)
Arun, S., Satheesh, A.: Analysis of flow behavior in a two sided lid driven cavity using lattice Boltzmann technique. Alex. Eng. J. 54, 795–806 (2015)
Oztop, H.F., Zhao, Z., Yu, B.: Fluid flow due to combined convection in lid-driven enclosure having a circular body. Int. J. Heat Fluid Flow 30(5), 886–901 (2009)
Billah, M.M., Rahman, M.M., Sharif, U.M., Rahim, N.A., Saidur, R., Hasanuzzaman, M.: Numerical analysis of fluid flow due to mixed convection in a lid-driven cavity having a heated circular hollow cylinder. Int. Commun. Heat Mass Transf. 38(8), 1093–1103 (2011)
Sivasankaran, S., Sivakumar, V., Prakash, P.: Numerical study on mixed convection in a lid-driven cavity with non-uniform heating on both sidewalls. Int. J. Heat Mass Transf. 53(19–20), 4304–4315 (2010)
Waheed, M.A.: Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate. Int. J. Heat Mass Transf. 52(21–22), 5055–5063 (2009)
Sun, C., Yu, B., Oztop, H.F., Wang, Y., Wei, J.: Control of mixed convection in lid-driven enclosures using conductive triangular fins. Int. J. Heat Mass Transf. 54(4), 894–909 (2011)
Islam, A.W., Sharif, M.A., Carlson, E.S.: Mixed convection in a lid driven square cavity with an isothermally heated square blockage inside. Int. J. Heat Mass Transf. 55(19–20), 5244–5255 (2012)
Bhattacharya, M., Basak, T., Oztop, H.F., Varol, Y.: Mixed convection and role of multiple solutions in lid-driven trapezoidal enclosures. Int. J. Heat Mass Transf. 63, 366–388 (2013)
Basak, T., Sharma, P.K., Pop, I.: Analysis of mixed convection flows within a square cavity with uniform and non-uniform heating of bottom wall. Int. J. Therm. Sci. 48(5), 891–912 (2009)
Chamkha, A.J., Selimefendigil, F., Ismael, M.A.: Mixed convection in a partially layered porous cavity with an inner rotating cylinder. Numer. Heat Transf. Part A Appl. 69(6), 659–675 (2016)
Gangawane, K.M.: Computational analysis of mixed convection heat transfer characteristics in lid-driven cavity containing triangular block with constant heat flux: Effect of Prandtl and Grashof numbers. Int. J. Heat Mass Transf. 105, 34–57 (2017)
Gangawane, K.M., Manikandan, B.: Mixed convection characteristics in lid-driven cavity containing heated triangular block. Chin. J. Chem. Eng. 25(10), 1381–1394 (2017)
Hammami, F., Souayeh, B., Ben-Cheikh, N., Ben-Beya, B.: Computational analysis of fluid flow due to a two-sided lid driven cavity with a circular cylinder. Comput. Fluids 15, 317–328 (2017)
Ali, F.H., Hamzah, H.K., Hussein, A.K., Jabbar, M.Y., Talebizadehsardari, P.: MHD mixed convection due to a rotating circular cylinder in a trapezoidal enclosure filled with a nanofluid saturated with a porous media. Int. J. Mech. Sci. 181, 105688 (2020)
Zadeh, S.M.H., Mehryan, S.A.M., Izadpanahi, E., Ghalambaz, M.: Impacts of the flexibility of a thin heater plate on the natural convection heat transfer. Int. J. Therm. Sci. 145, 106001 (2019)
Gangawane, K.M., Oztop, H.F., Ali, M.E.: Mixed convection in a lid-driven cavity containing triangular block with constant heat flux: effect of location of block. Int. J. Mech. Sci. 152, 492–511 (2019)
Dadvand, A., Baghalnezhad, M., Mirzaee, I., Khoo, B.C., Ghoreishi, S.: An immersed boundary-lattice Boltzmann approach to study the dynamics of elastic membranes in viscous shear flows. J. Comput. Sci. 5, 709–718 (2014)
Huang, R., Wu, H.: An immersed boundary-thermal lattice Boltzmann method for solid-liquid phase change. J. Comput. Phys. 227, 305–319 (2014)
Lallemand, P., Luo, L.: Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61(6), 6564 (2000)
Luo, L.S., Liao, W., Chen, X., Peng, Y., Zhang, W.: Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations. Phys. Rev. E 5(83), 056710 (2011)
Li, Z., Yang, M., Zhang, Y.: Double MRT thermal lattice Boltzmann method for simulating natural convection of low Prandtl number fluids. Int. J. Numer. Methods Heat Fluid Flow 26(6), 1889–1909 (2016)
Contrino, D., Lallemand, P., Asinari, P., Luo, L.S.: Lattice-Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers. J. Comput. Phys. 275, 257–272 (2014)
Dubois, F., Lin, C.A., Tekitek, M.M.: Anisotropic thermal lattice Boltzmann simulation of 2D natural convection in a square cavity. Comput. Fluids 124, 278–287 (2016)
Wang, J., Wang, D., Lallemand, P., Luo, L.S.: Lattice Boltzmann simulations of thermal convective flows in two dimensions. Comput. Math. Appl. 65(2), 262–286 (2013)
Ginzburg, I.: Truncation errors, exact and heuristic stability analysis of two-relaxation-times lattice Boltzmann schemes for anisotropic advection-diffusion equation. Commun. Comput. Phys. 11(5), 1439–1502 (2012)
Mohamad, A.A.: Lattice Boltzmann Method, p. 195. Springer, New York (2011)
Liu, C.-H., Lin, K.-H., Mai, H.-C., Lin, C.-A.: Thermal boundary conditions for thermal lattice Boltzmann simulations. Comput. Math. Appl. 59, 2178–2193 (2010)
Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S., Matsumoto, Y.: A full Eulerian finite difference approach for solving fluid–structure coupling problems. J. Comput. Phys. 230(3), 596–627 (2011)
Nayak, R.K., Bhattacharyya, S., Pop, I.: Numerical study on mixed convection and entropy generation of Cu-water nanofluid in a differentially heated skewed enclosure. Int. J. Heat Mass Transf. 85, 620–634 (2015)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Data availability
The data and code used in this work are currently proprietary and confidential; it will be considered for public release in the future.
Additional information
Communicated by Vassilios Theofilis.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Hoseyni, A., Dadvand, A., Rezazadeh, S. et al. Enhancement of mixed convection heat transfer in a square cavity via a freely moving elastic ring. Theor. Comput. Fluid Dyn. 37, 83–104 (2023). https://doi.org/10.1007/s00162-022-00637-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00162-022-00637-8