Flow and heat transfer characteristics of jet-assisted non-Newtonian nanofluids in backward-facing step channels
Abstract
This study numerically investigates the thermal-hydraulic performance of a jet-assisted Backward-Facing Step (BFS)channel using a non-Newtonian Al₂O₃/Carboxymethyl Cellulose (CMC) nanofluid under steady-state, laminar, incompressible, and two-dimensional flow conditions. The governing equations of mass, momentum, and energy are solved using the finite volume method, while the rheological behavior of the CMC solution is modeled using the Power-Law model. The numerical model is validated against previously published experimental and numerical data, demonstrating good agreement with benchmark results. The effects of Reynolds number, nanoparticle volume fraction, fluid rheology, jet injection angle, and jet momentum ratio on the flow structure and thermal-hydraulic performance of the channel are systematically investigated. The results reveal that increasing the Reynolds number significantly enhances convective heat transfer by strengthening fluid mixing and reducing the thermal boundary layer thickness. The incorporation of Al₂O₃ nanoparticles improves the overall thermal performance owing to the enhanced effective thermal conductivity of the nanofluid. Furthermore, the shear-thinning behavior of the non-Newtonian CMC solution provides superior heat transfer characteristics compared with Newtonian water. The jet injection parameters are also found to play a critical role in controlling the flow structure and thermal performance of the system. Appropriate jet injection angles and momentum ratios improve fluid mixing and significantly enhance heat transfer while maintaining favorable thermal-hydraulic characteristics. The Performance Evaluation Criterion (PEC) confirms that the combined application of jet injection and non-Newtonian nanofluids offers considerable thermal enhancement with acceptable hydraulic penalties. The findings demonstrate the potential of jet-assisted non-Newtonian Al₂O₃/CMC nanofluids for advanced cooling and thermal management applications involving separated flow configurations.
Keywords:
Backward-facing step channel, Non-Newtonian nanofluid, Jet injection, Thermal-hydraulic performance, Heat transfer enhancement, Reynolds number, Jet momentum ratioReferences
- [1] Saldana, J. G. B., Anand, N. K., & Sarin, V. (2005). Forced convection over a three-dimensional horizontal backward facing step. International Journal for Computational Methods in Engineering Science and Mechanics, 6(4), 225–234. https://doi.org/10.1080/155022891009107
- [2] Schlichting, H., & Gersten, K. (2016). Boundary-layer theory. Springer. https://doi.org/10.1007/978-3-662-52919-5
- [3] Xuan, Y., & Li, Q. (2000). Heat transfer enhancement of nanofluids. International Journal of Heat and Fluid Flow, 21(1), 58–64. https://doi.org/10.1016/S0142-727X(99)00067-3
- [4] Choi, S. U. S., Zhang, Z. G., Yu, Wl., Lockwood, F. E., & Grulke, E. A. (2001). Anomalous thermal conductivity enhancement in nanotube suspensions. Applied Physics Letters, 79(14), 2252–2254. https://doi.org/10.1063/1.1408272
- [5] Paul, G., Philip, J., Raj, B., Das, P. K., & Manna, I. (2011). Synthesis, characterization, and thermal property measurement of nano-Al95Zn05 dispersed nanofluid prepared by a two-step process. International Journal of Heat and Mass Transfer, 54(15–16), 3783–3788. https://doi.org/10.1016/j.ijheatmasstransfer.2011.02.044
- [6] Yu, W., France, D. M., Routbort, J. L., & Choi, S. U. S. (2008). Review and comparison of nanofluid thermal conductivity and heat transfer enhancements. Heat Transfer Engineering, 29(5), 432–460. https://doi.org/10.1080/01457630701850851
- [7] Kakaç, S., & Pramuanjaroenkij, A. (2009). Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer, 52(13–14), 3187–3196. https://doi.org/10.1016/j.ijheatmasstransfer.2009.02.006
- [8] Das, S. K., Choi, S. U., Yu, W., & Pradeep, T. (2007). Nanofluids: Science and technology. John Wiley & Sons. https://www.wiley.com/en-no/shop/nanotechnology-general/nanofluids-science-and-technology-p-9780470180693
- [9] Heyhat, M. M., Kowsary, F., Rashidi, A. M., Momenpour, M. H., & Amrollahi, A. (2013). Experimental investigation of laminar convective heat transfer and pressure drop of water-based Al2O3 nanofluids in fully developed flow regime. Experimental Thermal and Fluid Science, 44, 483–489. https://doi.org/10.1016/j.expthermflusci.2012.08.009
- [10] Nie, J. H., & Armaly, B. F. (2002). Three-dimensional convective flow adjacent to backward-facing step - effects of step height. International Journal of Heat and Mass Transfer, 45(12), 2431–2438. https://doi.org/10.1016/S0017-9310(01)00345-3
- [11] Armaly, B. F., Li, A., & Nie, J. H. (2003). Measurements in three-dimensional laminar separated flow. International Journal of Heat and Mass Transfer, 46(19), 3573–3582. https://doi.org/10.1016/S0017-9310(03)00153-4
- [12] Erturk, E. (2008). Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions. Computers & Fluids, 37(6), 633–655. https://doi.org/10.1016/j.compfluid.2007.09.003
- [13] Abdulrazzaq, T., Togun, H., Ariffin, M. K., Kazi, S. N., Badarudin, A., Adam, N. M., & Masuri, S. (2014). Heat transfer and turbulent fluid flow over vertical double forward-facing step. World Academy of Science, Engineering and Technology, 86, 722–726. file:///C:/Users/Administrator/Desktop/9997530.pdf
- [14] Moosavi, R., Moltafet, R., & Shekari, Y. (2021). Analysis of viscoelastic non-Newtonian fluid over a vertical forward-facing step using the Maxwell fractional model. Applied Mathematics and Computation, 401, 126119. https://doi.org/10.1016/j.amc.2021.126119
- [15] Danane, F., Boudiaf, A., Mahfoud, O., Ouyahia, S. E., Labsi, N., & Benkahla, Y. K. (2020). Effect of backward facing step shape on 3D mixed convection of Bingham fluid. International Journal of Thermal Sciences, 147, 106116. https://doi.org/10.1016/j.ijthermalsci.2019.106116
- [16] Poole, R. J., & Escudier, M. P. (2003). Turbulent flow of non-Newtonian liquids over a backward-facing step: Part II. Viscoelastic and shear-thinning liquids. Journal of Non-Newtonian Fluid Mechanics, 109((2-3)), 193–230. https://doi.org/10.1016/S0377-0257(02)00168-4
- [17] Ikegami, A., Tsukahara, T., & Kawaguchi, Y. (2015). Influence of viscoelasticity on turbulent flow over a backward-facing step. Fluids Engineering Division Summer Meeting (vol. 57213, p. v01at25a002). American Society of Mechanical Engineers. https://doi.org/10.1115/AJKFluids2015-25251
- [18] 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
- [19] Ahmed, H. E., & Yusoff, M. Z. (2014). Impact of delta-winglet pair of vortex generators on the thermal and hydraulic performance of a triangular channel using Al2O3–water nanofluid. Journal of Heat Transfer, 136(2), 021901. https://doi.org/10.1115/1.4025434
- [20] Pour, M. S., & Nassab, S. G. (2012). Numerical investigation of forced laminar convection flow of nanofluids over a backward facing step under bleeding condition. Journal of Mechanics, 28(2), N7–N12. https://doi.org/10.1017/jmech.2012.45
- [21] Togun, H., Safaei, M. R., Sadri, R., Kazi, S. N., Badarudin, A., Hooman, K., & Sadeghinezhad, E. (2014). Numerical simulation of laminar to turbulent nanofluid flow and heat transfer over a backward-facing step. Applied Mathematics and Computation, 239, 153–170. https://doi.org/10.1016/j.amc.2014.04.051
- [22] Soltani, S., Etemad, S. G., & Thibault, J. (2010). Pool boiling heat transfer of non-Newtonian nanofluids. International Communications in Heat and Mass Transfer, 37(1), 29–33. https://doi.org/10.1016/j.icheatmasstransfer.2009.08.005
- [23] Hojjat, M., Etemad, S. G., & Bagheri, R. (2010). Laminar heat transfer of non-Newtonian nanofluids in a circular tube. Korean Journal of Chemical Engineering, 27(5), 1391–1396. https://doi.org/10.1007/s11814-010-0250-3
- [24] Hojjat, M., Etemad, S. G., Bagheri, R., & Thibault, J. (2011). Rheological characteristics of non-Newtonian nanofluids: Experimental investigation. International Communications in Heat and Mass Transfer, 38(2), 144–148. https://doi.org/10.1016/j.icheatmasstransfer.2010.11.019
- [25] Chamkha, A. J., & Selimefendigil, F. (2018). Forced convection of pulsating nanofluid flow over a backward facing step with various particle shapes. Energies, 11(11), 3068. https://doi.org/10.3390/en11113068
- [26] 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
- [27] Nath, R., & Krishnan, M. (2019). Numerical study of double diffusive mixed convection in a backward facing step channel filled with Cu-water nanofluid. International Journal of Mechanical Sciences, 153–154, 48–63. https://doi.org/10.1016/j.ijmecsci.2019.01.035
- [28] Bobaru, F., & Rachakonda, S. (2004). Optimal shape profiles for cooling fins of high and low conductivity. International Journal of Heat and Mass Transfer, 47(23), 4953–4966. https://doi.org/10.1016/j.ijheatmasstransfer.2004.06.013
- [29] Wang, Q. W., Lin, M., & Zeng, M. (2009). Effect of lateral fin profiles on turbulent flow and heat transfer performance of internally finned tubes. Applied Thermal Engineering, 29(14–15), 3006–3013. https://doi.org/10.1016/j.applthermaleng.2009.03.016
- [30] Tang, L. H., Zeng, M., & Wang, Q. W. (2009). Experimental and numerical investigation on air-side performance of fin-and-tube heat exchangers with various fin patterns. Experimental Thermal and Fluid Science, 33(5), 818–827. https://doi.org/10.1016/j.expthermflusci.2009.02.008
- [31] Yang, M. H., Yeh, R. H., & Hwang, J. J. (2010). Mixed convective cooling of a fin in a channel. International Journal of Heat and Mass Transfer, 53(4), 760–771. https://doi.org/10.1016/j.ijheatmasstransfer.2009.10.012
- [32] Mushatet, K. S. (2011). Simulation of turbulent flow and heat transfer over a backward facing step with ribs turbulators. Thermal Science, 15(1), 245–255. https://thermalscience.rs/pdfs/papers/TSCI090926044M.pdf
- [33] 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
- [34] Alawi, O. A., Mohammed, H. A., & Sidik, N. C. (2016). Mixed convective nanofluids flow in a channel having forward-facing step with baffle. Journal of Advanced Research in Applied Mechanics, 24(1), 1–21. https://www.akademiabaru.com/submit/index.php/aram/article/view/1759
- [35] 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
- [36] Heshmati, A., Mohammed, H. A., & Darus, A. N. (2014). Mixed convection heat transfer of nanofluids over backward facing step having a slotted baffle. Applied Mathematics and Computation, 240, 368–386. https://doi.org/10.1016/j.amc.2014.04.058
- [37] 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
- [38] Patankar, S. (2018). Numerical heat transfer and fluid flow. CRC press. https://doi.org/10.1201/9781482234213
- [39] Abu-Nada, E. (2008). Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. International Journal of Heat and Fluid Flow, 29(1), 242–249. https://doi.org/10.1016/j.ijheatfluidflow.2007.07.001
- [40] Mosavi, A., Hekmatifar, M., Alizadeh, A. ad, Toghraie, D., Sabetvand, R., & Karimipour, A. (2020). RETRACTED: The molecular dynamics simulation of thermal manner of Ar/Cu nanofluid flow: The effects of spherical barriers size. Journal of Molecular Liquids, 319, 114183. https://doi.org/10.1016/j.molliq.2020.114183
- [41] Santra, A. K., Sen, S., & Chakraborty, N. (2008). Study of heat transfer augmentation in a differentially heated square cavity using copper--water nanofluid. International Journal of Thermal Sciences, 47(9), 1113–1122. https://doi.org/10.1016/j.ijthermalsci.2007.10.005