Transient Flow Conjugated with Mixed Convection in a Vertical Channel

Abstract:

Transient laminar mixed convection of air (Pr = 0.71) in a vertical plane channel is numerically investigated for opposing buoyancy at Re=100. The channel walls include symmetric, discrete, isothermal heated sections applied on the external side of a central wall zone, resulting in a conjugate heat-transfer problem through the solid wall and the fluid domain. The two-dimensional unsteady Navier–Stokes and energy equations are solved using a finite-volume method on a staggered grid with SIMPLE pressure–velocity coupling. The Grashof number is varied over 10³ ≤ Gr ≤ 10⁵. Instability onset is identified using a quantitative criterion based on the growth and persistence of velocity/temperature fluctuations and a domain-integrated fluctuation energy. The effects of wall thickness Δ and heated length L_h on the critical Grashof number are reported. Increasing L_h lowers the instability threshold, whereas increasing Δ stabilizes the flow by damping thermal gradients transmitted to the fluid. The results provide a stability map and physical interpretation of the transition from steady to unsteady mixed convection at low Reynolds number.

• Periodical: Defect and Diffusion Forum (Volume 453)
• Pages: 301-316
• DOI: https://doi.org/10.4028/p-uhYb4s
• Online since: July 2026
• Authors: Sofiane Boulkroune*, Abdelfetah Belaid, Abdelkader Filali, Omar Kholai, Tawfiq Chekifi, Mawloud Guermoui, Reski Khelifi
• Keywords: Critical Grashof Number, Finite Volume Method, Heat Transfer, Transient Mixed Convection, Vertical Channel

References

[1] G. F. Scheele, E. M. Rosen and T. J. Hanratty, Effect of natural convection on transition to turbulence in vertical pipes, The Canadian Journal of Chemical Engineering 38 (1960) 67-73.

DOI: 10.1002/cjce.5450380302

[2] G. F. Scheele and T. J. Hanratty, Effect of natural convection on stability of flow in a vertical pipe, Journal of Fluid Mechanics 14 (1962) 244-256.

DOI: 10.1017/s0022112062001226

[3] M. Bernier and B. Baliga, Visualization of upward mixed-convection flows in vertical pipes using a thin semitransparent gold-film heater and dye injection, International Journal of Heat and Fluid Flow 13 (1992) 241-249.

DOI: 10.1016/0142-727x(92)90037-a

[4] A. Behzadmehr, A. Laneville and N. Galanis, Experimental study of onset of laminar–turbulent transition in mixed convection in a vertical heated tube, International Journal of Heat and Mass Transfer 51 (2008) 5895-5905.

DOI: 10.1016/j.ijheatmasstransfer.2008.04.005

[5] W. Yan, Transient laminar mixed convection heat in vertical pipe flows, Int. Commun. Heat Mass Transfer 19 (1992) 89-101.

DOI: 10.1016/0735-1933(92)90067-r

[6] T. Fusegi, Mixed convection in periodic open cavities with oscillatory throughflow, Numerical Heat Transfer Part A Applications 29 (1996) 33-47.

DOI: 10.1080/10407789608913777

[7] T. H. Mai, N. El Wakil and J. Padet, Mixed heat convection in vertical pipe flow submitted to variable flow rate, Revue Generale de Thermique 38 (1999).

DOI: 10.1615/ihtc10.3440

[8] A. Benahmed, K. Rakrak, T. Tayebi and M. A. Chohri, A numerical investigation of the impact of various parameters on the flow and heat transfer in a rectangular duct with inclined obstacles, Numerical Heat Transfer Part B Fundamentals 87 (2026) 2530676

DOI: 10.1080/10407790.2025.2530676

[9] S. Mihoub, B. Hani and A. Benahmed, Sustainable potential of concentrating solar power plants: A comparative study, Applied Solar Energy 58 (2022) 675-688.

DOI: 10.3103/s0003701x21101126

[10] F. Boufoudi, S. Mihoub, S. Zouaoui and A. Benahmed, Receiver parameter optimization for nanofluid-based parabolic trough concentrating plant: a case study, Energy Sources Part A Recovery Utilization and Environmental Effects 45 (2023) 5559-5576.

DOI: 10.1080/15567036.2023.2209036

[11] F. Boufoudi, S. Zouaoui, S. Mihoub, A. Benahmed and T. Tayebi, Numerical investigation of the (mono-hybrid) nanofluid thermophysical properties for concentrated solar power plant, Journal of Nanofluids 12 (2023) 1233-1241.

DOI: 10.1166/jon.2023.2015

[12] G. Laplante and M. Bernier, Convection mixte défavorable et conjuguée dans un tube vertical, International Journal of Heat and Mass Transfer 40 (1997) 3527-3536.

DOI: 10.1016/s0017-9310(97)00028-8

[13] A. Omara and S. Abboudi, Transient heat transfer analysis laminar flow, Numerical Heat Transfer (2006) 1-24.

DOI: 10.1615/ichmt.1996.transientconvheattransf.440

[14] H. Su et al., Fast simulation of a vertical U-tube ground heat exchanger by using a one-dimensional transient numerical model, Numerical Heat Transfer Part A Applications 60 (2011) 328-346.

DOI: 10.1080/10407782.2011.600600

[15] M. Wang, T. Tsuji and Y. Nagano, Mixed convection with flow reversal in the thermal entrance region of horizontal and vertical pipes, International Journal of Heat and Mass Transfer 37 (1994) 2305-2319.

DOI: 10.1016/0017-9310(94)90372-7

[16] M. Boumaza and A. Omara, Numerical investigation of transport phenomena properties on transient heat transfer in a vertical pipe flow, Journal of King Saud University Engineering Sciences 27 (2015) 119-129.

DOI: 10.1016/j.jksues.2013.06.004

[17] H. Benhacine, B. Mahfoud and M. Salmi, Stability of an electrically conducting fluid flow between coaxial cylinders under magnetic field, Journal of Applied Fluid Mechanics 15 (2022) 563-577.

DOI: 10.47176/jafm.15.02.33050

[18] H. Benhacine, B. Mahfoud and M. Salmi, Stability of conducting fluid flow between coaxial cylinders under thermal gradient and axial magnetic field, International Journal of Thermofluid Science and Technology 9 (2022) 090202.

DOI: 10.36963/ijtst.2022090202

[19] B. Mahfoud and M. Moussaoui, Buoyancy force and magnetic field effects on laminar vortex breakdown and fluid layers, Journal of Thermal Engineering 9 (2023) 12-23.

DOI: 10.18186/thermal.1232431

[20] B. Mahfoud, Enhancement heat transfer of swirling nanofluid using an electrical conducting lid, Journal of Thermophysics and Heat Transfer 37 (2023) 263-271.

DOI: 10.2514/1.t6550

[21] B. Mahfoud, Effect of wall electrical conductivity on heat transfer enhancement of swirling nanofluid-flow, Journal of Nanofluids 12 (2023) 418-428.

DOI: 10.1166/jon.2023.1932

[22] S. Boulkroune, O. Kholai and B. Mahfoud, Effects of Important Parameters on the Transition from Forced to Mixed Convection Flow in a Square Cavity, Defect and Diffusion Forum 406 (2021) 36-52.

DOI: 10.4028/www.scientific.net/ddf.406.36

[23] A. Kumar and R. Sharma, Experimental investigation of mixed convection in vertically heated tubes under buoyancy-assisted and opposing-flow conditions, Int. J. Heat Mass Transfer 230 (2024) 125012.

[24] C.J. Howland, G.S. Yerragolam, R. Verzicco and D. Lohse, Turbulent mixed convection in vertical and horizontal channels, J. Fluid Mech. 998 (2024) A48.

DOI: 10.1017/jfm.2024.598

[25] A. Xu, R.Q. Li and H.D. Xi, Temporal modulation on mixed convection in turbulent channels, J. Fluid Mech. 1003 (2025) A22.

[26] S. Patankar, Numerical Heat Transfer and Fluid Flow, CRC Press, 2018.

[27] S. Kakac, Y. Yener and A. Pramuanjaroenkij, Convective Heat Transfer, CRC Press, 2013.

DOI: 10.1201/b16194

[28] M. Zghal, N. Galanis and C. T. Nguyen, Developing mixed convection with aiding buoyancy in vertical tubes: a numerical investigation of different flow regimes, International Journal of Thermal Sciences 40 (2001) 816-824.

DOI: 10.1016/s1290-0729(01)01268-6

[29] B. Zeldin and F. W. Schmidt, Developing flow with combined forced–free convection in an isothermal vertical tube, 1972.

DOI: 10.1115/1.3449899

[30] W. Marner and H. McMillan, Combined free and forced laminar convection in a vertical tube with constant wall temperature, 1970.

DOI: 10.1115/1.3449722