Home / Regular Issue / JST Vol. 31 (3) Apr. 2023 / JST-3715-2022


Analysis of Influence of Vertical Vibration on Natural Heat Convection Coefficients from Horizontal Concentric and Eccentric Annulus

Baydaa Khalil Khudhair, Adel Mahmood Saleh and Ali Laftah Ekaid

Pertanika Journal of Science & Technology, Volume 31, Issue 3, April 2023

DOI: https://doi.org/10.47836/pjst.31.3.24

Keywords: Cylindrical annulus, heat convection, numerical validation, Rayleigh number, vertical vibration

Published on: 7 April 2023

The research looks at how heat transmission is improved when two horizontal cylinders are concentric or vertically eccentric, creating vertical motion. The inner cylinder is uniformly heated, whereas the outer cylinder is isothermal. Apart from Rayleigh’s number (102 ≥ Ra ≥ 106), eccentricity (normalized by the radius difference) at range (ϵ = 0, ±0.625 & ±0.333), and Prandtle number is fixed Pr = 0.7(air), the vibrational frequencies are changed from (ϖ = 0, 100, 1000 &10000). The steady-state, two-dimensional Navier-Stokes equations (with Boussineq approximation) are generated using central difference approximation and solved using the successive over-relaxation (LSOR) method line by line. The contour maps of streamlines and heat lines clearly illustrate the annuli’s heat and fluid flow patterns. According to the results, it is found that the vibration generally enhanced the heat transfer rate more than the stationary one for all values of frequency and different eccentricities with various rates of enhancement. Vibration thermal convection is prominent at low Rayleigh (Ra = 102, 103, 104), and the vibration significantly boosts the heat transfer rate within an annular annulus. In a high Rayleigh number situation, a high Rayleigh number situation (Ra=105 and 106), gravitational thermal convection predominates, and vibration motion does not significantly improve heat transmission. The vibration is a powerful augmentation tool for placing the inner cylinder towards the bottom of the outer cylinder (negative vertical eccentricity (ϵ = -0.625)), the heat rate enhancement more than 3.8-fold at Ra = 103, ϖ = 10000. The Nusselt number has been correlated in a dimensionless form as the Rayleigh number and the vibrational Rayleigh number.

  • Alawadhi, E. M. (2008). Natural convection flow in a horizontal annulus with an oscillating inner cylinder using Lagrangian–Eulerian kinematics. Computers & Fluids, 37, 1253-1261.

  • Al-Azzawi, M. M., Abdullah, A. R., Majel, B. M., & Habeeb, L. J. (2021). Experimental investigation of the effect of forced vibration on natural convection heat transfer in a concentric vertical cylinder. Journal of Mechanical Engineering Research and Developments, 44(3), 56-65.

  • Ali, M., Rad, M. M., Nuhait, A., Almuzaiqer, R., Alimoradi, A., & Tlili, I. (2020). New equations for Nusselt number and friction factor of the annulus side of the conically coiled tubes in tube heat exchangers. Applied Thermal Engineering, 164, Article 114545. https://doi.org/10.1016/j.applthermaleng.2019.114545

  • Bouzerzour, A., Tayebi, T., Chamkha, A. J., & Djezzar, M. (2020). Numerical investigation of natural convection nanofluid flow in an annular space between confocal elliptic cylinders at various geometrical orientations. Computational Thermal Sciences: An International Journal, 12(2), 99-114. https://doi.org/10.1615/computthermalscien.2020026938

  • Fu, W. S., & Huang, C. P. (2006). Effects of a vibrational heat surface on natural convection in a vertical channel flow. International Journal of Heat and Mass Transfer, 49(7-8), 1340-1349. https://doi.org/10.1016/j.ijheatmasstransfer.2005.10.028

  • Ho, C. J., Lin, Y. H., & Chen, T. C., (1989). A numerical study of natural convection in concentric and eccentric horizontal cylindrical annuli with mixed boundary conditions. International Journal of Heat and Fluid Flow, 10(1), 40-47. https://doi.org/10.1016/0142-727X(89)90053-2

  • Hosseinian, A., Meghdadi I. A. H., & Shirani, E. (2018). Experimental investigation of surface vibration effects on increasing the stability and heat transfer coefficient of MWCNTs-water nanofluid in a flexible double pipe heat exchanger. Experimental Thermal and Fluid Science, 90, 275-285. https://doi.org/10.1016/j.expthermflusci.2017.09.018

  • Imtiaz, H., & Mahfouz, F. M. (2017). Conjugated conduction-free convection heat transfer in an annulus heated at either constant wall temperature or constant heat flux. Journal of Engineering and Technology, 36(2), 273-288. https://doi.org/10.22581/muet1982.1702.06

  • Kim, S. K., Kim, S. Y., & Choi, Y. D. (2002). Resonance of natural convection in a side heated enclosure with a mechanically oscillating bottom wall. International Journal of Heat and Mass Transfer, 45(15), 3155-3162. https://doi.org/10.1016/S0017-9310(02)00030-3

  • Kuehn, T. H., & Coldstein., R. J. (1976). An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders. Journal of Fluid mechanics, 74(4), 695-719. https://doi.org/10.1017/S0022112076002012

  • Kuehn, T. H., & Goldstein, R. J. (1978). An experimental study of natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli. Journal of Heat and Mass Transfer, 100(4), 635-640. https://doi.org/10.1115/1.3450869

  • Liu, W., Yang, Z., Zhang, B., & Lv, P. (2017). Experimental study on the effects of mechanical vibration on the heat transfer characteristics of tubular laminar flow. International Journal of Heat and Mass Transfer, 115, 169-179. https://doi.org/10.1016/j.ijheatmasstransfer.2017.07.025

  • Mahfouz, F. M. (2012). Heat convection within an eccentric annulus heated at either constant wall temperature or constant heat flux. Journal of Heat Transfer, 134(8), Article 082502. https://doi.org/10.1115/1.4006170

  • Mahian, O., Pop, I., Sahin, A. Z., Oztop, H. F., & Wongwises, S. (2013). Irreversibility analysis of a vertical annulus using TiO2/water nanofluid with MHD flow effects. International Journal of Heat and Mass Transfer, 64, 671-679. https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.001

  • Nasrat, K. M., Hameed, D. L., & Sadiq, E. A. (2019). The effect of transverse vibration on the natural convection heat transfer in a rectangular enclosure. International Journal of Mechanical Engineering and Technology, 10(6), 266-277.

  • Projahn, U., Rieger, H., & Beer, H. (1981). Numerical analysis of laminar natural convection between concentric and eccentric cylinders. Numerical Heat Transfer, 4(2), 131-146. https://doi.org/10.1080/01495728108961783

  • Sarhan, A. R., Karim, M. R., Kadhim, Z. K., & Naser, J. (2019). Experimental investigation on the effect of vertical vibration on thermal performances of rectangular flat plate. Experimental Thermal and Fluid Science, 101, 231-240. https://doi.org/10.1016/j.expthermflusci.2018.10.024

  • Shahsavar, A., Moradi, M., & Bahiraei, M. (2018). Heat transfer and entropy generation optimization for flow of a non-Newtonian hybrid nanofluid containing coated CNT/Fe3O4 nanoparticles in a concentric annulus. Journal of the Taiwan Institute of Chemical Engineers, 84, 28-40. https://doi.org/10.1016/j.jtice.2017.12.029

  • Shokouhmand, H., Abadi, S. M. A. N. R., & Jafari, A. (2011). The effect of the horizontal vibrations on natural heat transfer from an isothermal array of cylinders. International Journal of Mechanics and Materials in Design, 7(4), 313-326. https://doi.org/10.1007/s10999-011-9170-6

  • Tayebi, T., & Chamkha, A. J. (2021). Analysis of the effects of local thermal non-equilibrium (LTNE) on thermo-natural convection in an elliptical annular space separated by a nanofluid-saturated porous sleeve. International Communications in Heat and Mass Transfer, 129, Article 105725. https://doi.org/10.1016/j.icheatmasstransfer.2021.105725

  • Tayebi, T., Chamkha, A. J., Melaibari, A. A., & Raouache, E. (2021). Effect of internal heat generation or absorption on conjugate thermal-free convection of a suspension of hybrid nanofluid in a partitioned circular annulus. Communications in Heat and Mass Transfer, 126, Article 105397. https://doi.org/10.1016/j.icheatmasstransfer.2021.105397

  • Tayebi, T., Chamkha, A. J., Öztop, H. F., & Bouzeroura, L. (2022). Local thermal non-equilibrium (LTNE) effects on thermal-free convection in a nanofluid-saturated horizontal elliptical non-Darcian porous annulus. Mathematics and Computers in Simulation, 194, 124-140. https://doi.org/10.1016/j.matcom.2021.11.011

  • Tayebi, T., Djezzar, M., Bouzerzour, A., Azzouz, K., & Khan, Z. H. (2016). Numerical Simulation of Natural Convection of Water Based Nanofluids in Horizontal Eccentric Cylindrical Annuli. Journal of Nanofluids, 5(2), 253-263. https://doi.org/10.1166/jon.2016.1211

  • Tayebi, T., Öztop, H. F., & Chamkha, A. J. (2021). MHD natural convection of a CNT-based nanofluid-filled annular circular enclosure with inner heat-generating solid cylinder. The European Physical Journal Plus, 136(2), Article 150. https://doi.org/10.1140/epjp/s13360-021-01106-7

  • Thompson, J., F., Thames, F. C., & Mastin, C. W. (1974). Automatic numerical generation of body-fitted curvilinear coordinate system for fields containing any number of arbitrary two-dimensional bodies. Journal of Computational Physics, 15(3), 299-319.

  • Wang, B. F., Zhou, Q., & Sun, C. (2020). Vibration-Induced Boundary-Layer Destabilization Achieves Massive Heat-Transport Enhancement. Science Advances, 6(21). https://doi.org/10.1126/sciadv.aaz8239