Effect of an Inclined Elastic Fin on Heat Transfer in a Backward-Facing Step Channel

Abstract

The current study investigates heat transfer improvement in backward-facing step configuration using a inclined flexible fin through numerical simulation based on the Finite Element Method (FEM). Investigating the influence of the position of the flexible fin, on thermal and fluid dynamic performance using forced convection air as fluid. The heat transfer characteristics are studied for different Reynolds numbers (Re between 50 and 200), Cauchy numbers (Ca from10-8, to 10-4) at three positions (P1, P2, P3) in the channel, and a constant Prandtl number of Pr=0.71. The results show an enhancement in heat transfer, with best performance occurring at a Reynolds number of 200 and a Cauchy number of Ca=10-8 (more flexible fin). Specifically, when the fin located closer the step, a remarkable 40% increase in the Nusselt number was observed compared to the case of without fin. Also, the paper shows the influence of flow separation and recirculation zones interaction with the elastic character of the fin on affecting convective heat transfer. These findings highlight the potential of elastic fins as an effective strategy for passive heat transfer enhancement in compact thermal systems.

Keywords

• Backward- facing step (BFS)
• Heat transfer
• Fluid-structure interaction (FSI)
• Flexible fin
• Forced convection

Effect of an Inclined Elastic Fin on Heat Transfer in a Backward-Facing Step Channel

Abstract

The current study investigates heat transfer improvement in a backward-facing step configuration using an inclined flexible fin, through numerical simulation based on the Finite Element Method (FEM). The influence of the position of the flexible fin on thermal and fluid dynamic performance is examined using forced convection of air as the working fluid. The heat transfer characteristics are studied for different Reynolds numbers (Re between 50 and 200) and Cauchy numbers (Ca from 10−8 to 10−4) at three positions (P1, P2, P3) in the channel, with a constant Prandtl number of Pr = 0.71. The results show an enhancement in heat transfer, with the best performance occurring at a Reynolds number of 200 and a Cauchy number of Ca = 10−8, corresponding to the most rigid fin. Specifically, when the fin is located closer to the step, a remarkable 40% increase in the Nusselt number is observed compared to the case without a fin. Additionally, the paper highlights the influence of flow separation and the interaction of recirculation zones with the elastic characteristics of the fin on convective heat transfer. These findings demonstrate the potential of elastic fins as an effective strategy for passive heat transfer enhancement in compact thermal systems.

Keywords

• Backward- facing step (BFS)
• Heat transfer
• Fluid-structure interaction (FSI)
• Flexible fin
• Forced convection

References

1. Al-aswadi, A. A., Mohammed, H. A., Shuaib, N. H., & Campo, A. (2010). Laminar forced convection flow over a backward facing step using nanofluids. International Communications in Heat and Mass Transfer, 37(8), 950–957. https://doi.org/10.1016/j.icheatmasstransfer.2010.06.007
2. Alhasan, M., Hamzah, H., Koprulu, A., & Sahin, B. (2024). Couette-Poiseuille flow over a backward-facing step: Investigating hydrothermal performance and irreversibility analysis. Case Studies in Thermal Engineering, 53, 103954. https://doi.org/10.1016/j.csite.2023.103954
3. Amiri, A., Arzani, H. K., Kazi, S. N., Chew, B. T., & Badarudin, A. (2016). Backward-facing step heat transfer of the turbulent regime for functionalized graphene nanoplatelets based water–ethylene glycol nanofluids. International Journal of Heat and Mass Transfer, 97, 538–546. https://doi.org/10.1016/j.ijheatmasstransfer.2016.02.042
4. Aubrun, S., Kao, P. L., & Boisson, H. C. (2000). Experimental coherent structures extraction and numerical semi- deterministic modelling in the turbulent flow behind a backward-facing step. Experimental Thermal and Fluid Science, 22, 93-101. https://doi.org/10.1016/S0894-1777(00)00015-7
5. Boruah, M. P., Pati, S., & Randive, P. R. (2019). Implication of fluid rheology on the hydrothermal and entropy generation characteristics for mixed convective flow in a backward facing step channel with baffle. International Journal of Heat and Mass Transfer, 137, 138–160. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.094
6. Chen, L., Asai, K., Nonomura, T., Xi, G., & Liu, T. (2018). A review of backward-facing step (BFS) flow mechanisms, heat transfer and control. Thermal Science and Engineering Progress, 6, 194–216. https://doi.org/10.1016/j.tsep.2018.04.004
7. Das, A., Mahmood, F. T., Smriti, R. B., Saha, S., & Hasan, M. N. (2023). CFD analysis of heat transfer enhancement by wall mounted flexible flow modulators in a channel with pulsatile flow. Heliyon, 9(6), e16741. https://doi.org/10.1016/j.heliyon.2023.e16741
8. Hara, S., Ii, R., Onishi, S., Tsukahara, T., & Kawaguchi, Y. (2025). Inertia-viscoelastic meandering motion in a backward-facing step flow. International Journal of Heat and Mass Transfer, 242, 126793. https://doi.org/10.1016/j.ijheatmasstransfer.2025.126793

9. Hilo, A. K., Talib, A. R. A., Iborra, A. A., Sultan, M. T. H., & Hamid, M. F. A. (2020). Experimental study of nanofluids flow and heat transfer over a backward-facing step channel. Powder Technology, 372, 497–505. https://doi.org/10.1016/j.powtec.2020.06.013
10. Hussain, S., & Ahmed, S. E. (2019). Unsteady MHD forced convection over a backward facing step including a rotating cylinder utilizing Fe3O4-water ferrofluid. Journal of Magnetism and Magnetic Materials, 484, 356–366. https://doi.org/10.1016/j.jmmm.2019.04.040
11. Jahin, A. S., Samin, J. H., Chhoa, M. F., Faisal, F., Nokib, M. H. I., & Rabby, M. I. I. (2025). Computational study of thermofluidic characteristics of Al2O3-Cu hybrid nanofluids in backward facing step channel with varying step angles. Heliyon, 11(4), e42638. https://doi.org/10.1016/j.heliyon.2025.e42638
12. Jin, Y., Zhao, P., Lei, M., Li, Y., & Wan, Y. (2024). DNS investigation of flow and heat transfer characteristics of supercritical carbon dioxide over a backward-facing step. International Journal of Heat and Mass Transfer, 219, 124897. https://doi.org/10.1016/j.ijheatmasstransfer.2023.124897
13. Kherbeet, A. Sh., Mohammed, H. A., Salman, B. H., Ahmed, H. E., & Alawi, O. A. (2014). Experimental and numerical study of nanofluid flow and heat transfer over microscale backward-facing step. International Journal of Heat and Mass Transfer, 79, 858–867. https://doi.org/10.1016/j.ijheatmasstransfer.2014.08.074
14. Klazly, M., & Bognar, G. (2022). Heat transfer enhancement for nanofluid flows over a microscale backward-facing step. Alexandria Engineering Journal, 61(10),8161–8176. https://doi.org/10.1016/j.aej.2022.01.008
15. Kumar, A., & Dhiman, A. K. (2012). Effect of a circular cylinder on separated forced convection at a backward-facing step. International Journal of Thermal Sciences, 52, 176–185. https://doi.org/10.1016/j.ijthermalsci.2011.09.014
16. Kumar, S., Boruah, M. P., & Pati, S. (2023). Hydrothermal performance for forced convective flow of viscoplastic fluid through a backward facing step channel. International Communications in Heat and Mass Transfer, 143, 106660. https://doi.org/10.1016/j.icheatmasstransfer.2023.106660
17. Kumar, S., & Vengadesan, S. (2019). The effect of fin oscillation in heat transfer enhancement in separated flow over a backward facing step. International Journal of Heat and Mass Transfer, 128, 954–963. https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.001
18. Lan, H., Armaly, B. F., & Drallmeier, J. A. (2009). Three- dimensional simulation of turbulent forced convection in a duct with backward-facing step. International Journal of Heat and Mass Transfer, 52(7–8), 1690–1700. https://doi.org/10.1016/j.ijheatmasstransfer.2008.09.022
19. Lancial, N., Beaubert, F., Harmand, S., & Rolland, G. (2013). Effects of a turbulent wall jet on heat transfer over a non- confined backward-facing step. International Journal of Heat and Fluid Flow, 44, 336–347. https://doi.org/10.1016/j.ijheatfluidflow.2013.07.003
20. Luo, Q., Dolcetti, G., Stoesser, T., & Tait, S. (2023). Water surface response to turbulent flow over a backward- facing step. Journal of Fluid Mechanics, 966, A18. https://doi.org/10.1017/jfm.2023.350
21. Lv, J., Hu, C., Bai, M., Li, L., Shi, L., & Gao, D. (2019). Visualization of SiO2-water nanofluid flow characteristics in backward-facing step using PIV. Experimental Thermal and Fluid Science, 101, 151–159. https://doi.org/10.1016/j.expthermflusci.2018.10.013
22. Ma, Y., Mohebbi, R., Rashidi, M. M., Yang, Z., & Fang, Y. (2020). Baffle and geometry effects on nanofluid forced convection over forward- and backward-facing steps channel by means of lattice Boltzmann method. Physica A: Statistical Mechanics and Its Applications, 554, 124696. https://doi.org/10.1016/j.physa.2020.124696
23. Mahmood, F. T., Das, A., Smriti, R. B., Hakim, Md. A., Saha, S., & Hasan, M. N. (2023). Role of wall-mounted flexible flow modulator on thermo-hydraulic characteristics of pulsating channel flow. Results in Engineering, 17, 100941. https://doi.org/10.1016/j.rineng.2023.100941
24. Mohammed, H. A., Alawi, O. A., & Wahid, M. A. (2015). Mixed convective nanofluid flow in a channel having backward- facing step with a baffle. Powder Technology, 275,329–343. https://doi.org/10.1016/j.powtec.2014.09.046
25. Mohammed, H. A., Fathinia, F., Vuthaluru, H. B., & Liu, S. (2019). CFD based investigations on the effects of blockage shapes on transient mixed convective nanofluid flow over a backward facing step. Powder Technology, 346,441–451. https://doi.org/10.1016/j.powtec.2019.02.002
26. Nguyen, T. D., & Souad, H. (2015). PIV measurements in a turbulent wall jet over a backward-facing step in a three- dimensional, non-confined channel. Flow Measurement and Instrumentation, 42, 26–39. https://doi.org/10.1016/j.flowmeasinst.2015.01.002
27. Rashid, F. L., Eleiwi, M. A., Tahseen, T. A., Mohammed, H. I., Tuama, S. A., Ameen, A., & Agyekum, E. B. (2025). Influence of adiabatic semi-circular grooved in backward-facing step on thermal-hydraulic characteristics of nanofluid. International Journal of Thermofluids, 26, 101052. https://doi.org/10.1016/j.ijft.2024.101052
28. Saleh, H., Hashim, I., Jamesahar, E., & Ghalambaz, M. (2020). Effects of flexible fin on natural convection in enclosure partially-filled with porous medium. Alexandria Engineering Journal, 59(5), 3515–3529. https://doi.org/10.1016/j.aej.2020.05.034
29. Selimefendigil, F., & Öztop, H. F. (2013). Numerical analysis of laminar pulsating flow at a backward facing step with an upper wall mounted adiabatic thin fin. Computers & Fluids, 88, 93–107. https://doi.org/10.1016/j.compfluid.2013.08.013
30. Selimefendigil, F., & Öztop, H. F. (2017). Forced convection and thermal predictions of pulsating nanofluid flow over a backward facing step with a corrugated bottom wall. International Journal of Heat and Mass Transfer, 110, 231–247. https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.010
31. Toumi, M., Bouzit, M., Bouzit, F., & Mokhefi, A. (2022). MHD forced convection using ferrofluid over a backward facing step containing a finned cylinder. Acta Mechanica et Automatica, 16(1), 70–81. https://doi.org/10.2478/ama-2022-0009
32. Wang, F., Wu, S., & Zhu, S. (2019). Numerical simulation of flow separation over a backward-facing step with high Reynolds number. Water Science and Engineering, 12(2), 145–154. https://doi.org/10.1016/j.wse.2019.05.003
33. Wu, Y., Ren, H., & Tang, H. (2013). Turbulent flow over a rough backward-facing step. International Journal of Heat and Fluid Flow, 44, 155–169. https://doi.org/10.1016/j.ijheatfluidflow.2013.05.014
34. Xu, F., Gao, Z., Ming, X., Xia, L., Wang, Y., Sun, W., & Ma, R. (2015). The optimization for the backward-facing step flow control with synthetic jet based on experiment. Experimental Thermal and Fluid Science, 64, 94–107. https://doi.org/10.1016/j.expthermflusci.2015.02.014
35. Xu, J. H., Zou, S., Inaoka, K., & Xi, G. N. (2017). Effect of Reynolds number on flow and heat transfer in incompressible forced convection over a 3D backward-facing step. International Journal of Refrigeration, 79, 164–175. https://doi.org/10.1016/j.ijrefrig.2017.04.012
36. Yamada, S., & Nakamura, H. (2016). Construction of 2D-3C PIV and high-speed infrared thermography combined system for simultaneous measurement of flow and thermal fluctuations over a backward facing step. International Journal of Heat and Fluid Flow, 61, 174–182. https://doi.org/10.1016/j.ijheatfluidflow.2016.04.010
37. Yang, D., Sun, B., Xu, T., Liu, B., & Li, H. (2021). Experimental and numerical study on the flow and heat transfer characteristic of nanofluid in the recirculation zone of backward-facing step microchannels. Applied Thermal Engineering, 199, 117527. https://doi.org/10.1016/j.applthermaleng.2021.117527
38. Yousefi, S., Mahdavi, M., Soheil Mousavi Ajarostaghi, S., & Sharifpur, M. (2023). Hydrothermal behavior of nanofluid flow in a microscale backward-facing step equipped with dimples and ribs; lattice Boltzmann method approach. Thermal Science and Engineering Progress, 43, 101987. https://doi.org/10.1016/j.tsep.2023.101987
39. Zhang, Y., Rabczuk, T., Lin, J., Lu, J., & Chen, C. S. (2024). Numerical simulations of two-dimensional incompressible Navier-Stokes equations by the backward substitution projection method. Applied Mathematics and Computation, 466, 128472. https://doi.org/10.1016/j.amc.2023.128472
40. Zhu, Y., Yi, S., Ding, H., Nie, W., & Zhang, Z. (2019). Structures and aero-optical effects of supersonic flow over a backward facing step with vortex generators. European Journal of Mechanics - B/Fluids, 74, 302–311. https://doi.org/10.1016/j.euromechflu.2018.09.003