Elastico–Viscous Boundary Layer Flow Over A Wedge Incorporating Nanofluid Interaction Effects

  • Authors

    • Bikash Koli Saha Independent Researcher, Mathematics, Guwahati, Kamrup Metropolitan, Assam, Pin:781018, India
    https://doi.org/10.14419/4bv4wg35
  • Boundary Layer; Elastico-Viscous Fluid; Nanofluid; Shrinking Wedge; Stretching Wedge

  • Abstract

    The present discourse delineates a rigorous examination of steady elastico–viscous boundary layer flow past a wedge embedded within a ‎nanofluid environment under a uniform free-stream velocity. The framework imposes isothermal boundary conditions alongside a pre-‎scribed homogeneous quantifiable measure of nanoparticle occupancy relative to the total fluidic domain at the stretching interface. The governing relations for the coupled mechanisms of momentum transfer, thermo-energetic diffusion, and nanoparticle volumetric stratification are ‎constructed via Walter’s liquid model B/ synergistically coupled with the Kuznetsov–Nield nanofluid formulation [27-28]. Through the ‎application of similarity transformations, augmented by appropriate boundary constraints, the system is reformulated as a nonlinear system ‎of ordinary differential relations, subsequently addressed via the bvp4c numerical integrator embedded within MATLAB. The outcomes ‎underscore the decisive role of the elastico–viscous parameter in modulating velocity, thermal, and concentration distributions, while simultaneously elucidating the coupled dynamics of the conjoint modulation of hydrodynamic, thermo-diffusive, and concentration stratified layers ‎in shaping the overall transport phenomena of the system‎.

  • References

    1. Falkner, V. M., & Skan, S. W. (1931). Some approximate solutions of the boundary-layer equations. Philosophical Magazine, 12, 865–896. https://doi.org/10.1080/14786443109461870.
    2. Saidur, R., Kazi, S. N., Hossain, M. S., Rahman, M. M., & Mohamed, H. A. (2011). A review of the performance of nanoparticles suspended with refrigerants and lubricating oils in refrigeration systems. Renewable and Sustainable Energy Reviews, 15(1), 310–323. https://doi.org/10.1016/j.rser.2010.08.018.
    3. Mahian, O., Kianifar, A., Kalogirou, S. A., Pop, I., & Wongwises, S. (2013). A review of the applications of nanofluids in solar energy. Interna-tional Journal of Heat and Mass Transfer, 57(2), 582–594. https://doi.org/10.1016/j.ijheatmasstransfer.2012.10.037.
    4. Behar, O., Khellaf, A., & Mohammedi, K. (2013). A review of studies on central receiver solar thermal power plants. Renewable and Sustainable Energy Reviews, 23, 12–39. https://doi.org/10.1016/j.rser.2013.02.017.
    5. Bondareva, N. S., Sheremet, M. A., Oztop, H. F., & Abu-Hamdeh, N. (2017). Heatline visualization of natural convection in a thick-walled open cavity filled with a nanofluid. International Journal of Heat and Mass Transfer, 109, 175–186. https://doi.org/10.1016/j.ijheatmasstransfer.2017.01.013.
    6. Saidur, R., Leong, K. Y., & Mohammad, H. A. (2011). A review on applications and challenges of nanofluids. Renewable and Sustainable Energy Reviews, 15, 1646–1668. https://doi.org/10.1016/j.rser.2010.11.035.
    7. Das, S. K., Choi, S. U. S., Yu, W., & Pradeep, T. (2008). Nanofluids: Science and technology. Hoboken, NJ: Wiley. https://doi.org/10.1002/9780470180693.
    8. Nield, D. A., & Bejan, A. (2013). Convection in porous media (4th ed.). New York, NY: Springer. https://doi.org/10.1007/978-1-4614-5541-7.
    9. Minkowycz, W. J., Sparrow, E. M., & Abraham, J. P. (2013). Nanoparticle heat transfer and fluid flow (Vol. IV). CRC Press, Taylor & Francis Group.
    10. Shenoy, A., Sheremet, M., & Pop, I. (2016). Convective flow and heat transfer from wavy surfaces: Viscous fluids, porous media and nanofluids. CRC Press, Taylor & Francis Group. https://doi.org/10.1201/9781315367637.
    11. Buongiorno, J., Venerus, D. C., Prabhat, N., McKrell, T., Townsend, J., Christianson, R., Tolmachev, Y. V., Keblinski, P., Hu, L., Alvarado, J. L., et al. (2009). A benchmark study on the thermal conductivity of nanofluids. Journal of Applied Physics, 106(9), 094312. https://doi.org/10.1063/1.3245330.
    12. Kakac, 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.
    13. Manca, O., Jaluria, Y., & Poulikakos, D. (2010). Heat transfer in nanofluids. Advances in Mechanical Engineering, 2010, 380826. https://doi.org/10.1155/2010/380826.
    14. Fan, J., & Wang, L. (2011). Review of heat conduction in nanofluids. ASME Journal of Heat Transfer, 133(4), 040801. https://doi.org/10.1115/1.4002633.
    15. Mahian, O., Kianifar, A., Kalogirou, S. A., Pop, I., & Wongwises, S. (2013). A review of the applications of nanofluids in solar energy. Interna-tional Journal of Heat and Mass Transfer, 57(2), 582–594. https://doi.org/10.1016/j.ijheatmasstransfer.2012.10.037
    16. Sheikholeslami, M., & Ganji, D. D. (2016). Nanofluid convective heat transfer using semi-analytical and numerical approaches: A review. Journal of the Taiwan Institute of Chemical Engineers, 65, 43–77. https://doi.org/10.1016/j.jtice.2016.05.014.
    17. Myers, T. G., Ribera, H., & Cregan, V. (2017). Does mathematics contribute to the nanofluid debate? International Journal of Heat and Mass Transfer, 111, 279–288. https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.118.
    18. Sheikholeslami, M., Mehryan, S. A. M., Shafee, A., & Sheremet, M. A. (2019). Variable magnetic forces impact on magnetizable hybrid nanofluid heat transfer through a circular cavity. Journal of Molecular Liquids, 277, 388–396. https://doi.org/10.1016/j.molliq.2018.12.104.
    19. Maatoug, S., Khan, S. U., Abbas, T., Ul Haq, E., Ghachem, K., Kolsi, L., et al. (2023). A lubricated stagnation point flow of nanofluid with heat and mass transfer phenomenon: Significance to hydraulic systems. Journal of the Indian Chemical Society, 100(6), 100825. https://doi.org/10.1016/j.jics.2022.100825
    20. Zhang, K., Li, Z., Wang, S., Wang, P., Zhang, Y., & Guo, X. (2023). Study on the cooling and lubrication mechanism of magnetic field-assisted Fe₃O₄@CNTs nanofluid in micro-textured tool cutting. Journal of Manufacturing Processes, 85, 556–568. https://doi.org/10.1016/j.jmapro.2022.11.081.
    21. Gupta, S. K. (2023). A short and updated review of nanofluids utilization in solar parabolic trough collector. Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2022.12.278.
    22. Hisham, S., Kadirgama, K., Alotaibi, J. G., Alajmi, A. E., Ramasamy, D., Sazali, N., et al. (2024). Enhancing stability and tribological applications using hybrid nanocellulose–copper (II) oxide (CNC–CuO) nanolubricant: An approach towards environmental sustainability. Tribology Internation-al, 2024, 109506. https://doi.org/10.1016/j.triboint.2024.109506
    23. Zawawi, N. N. M., Azmi, W. H., Hamisa, A. H., Hendrawati, T. Y., & Aminullah, A. R. M. (2024). Experimental investigation of air-conditioning electrical compressor using binary TiO₂–SiO₂ polyol-ester nanolubricants. Case Studies in Thermal Engineering, 54, 104045. https://doi.org/10.1016/j.csite.2024.104045.
    24. Khan, W. A., & Pop, I. (2013). Boundary layer flow past a wedge moving in a nanofluid. Mathematical Problems in Engineering, 2013, Article 637285. https://doi.org/10.1155/2013/637285.
    25. Nield, D. A., & Kuznetsov, A. V. (2011). The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid. International Journal of Heat and Mass Transfer, 54(1–3), 374–378. https://doi.org/10.1016/j.ijheatmasstransfer.2010.09.009.
    26. Kuznetsov, A. V., & Nield, D. A. (2010). Natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences, 49(2), 243–247. https://doi.org/10.1016/j.ijthermalsci.2009.07.015.
    27. Kuznetsov, A. V., & Nield, D. A. (2006). Boundary layer treatment of forced convection over a wedge with an attached porous substrate. Journal of Porous Media, 9(7), 683–694. https://doi.org/10.1615/JPorMedia.v9.i7.20.
    28. Nield, D. A., & Kuznetsov, A. V. (2009). The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturat-ed by a nanofluid. International Journal of Heat and Mass Transfer, 52(25–26), 5792–5795. https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.024.
    29. Yih, K. A. (1998). Uniform suction/blowing effect on forced convection about a wedge: Uniform heat flux. Acta Mechanica, 128(3–4), 173–181. https://doi.org/10.1007/BF01182648.
    30. Yacob, N. A., Ishak, A., & Pop, I. (2011). Falkner–Skan problem for a static or moving wedge in nanofluids. International Journal of Thermal Sci-ences, 50(2), 133–139. https://doi.org/10.1016/j.ijthermalsci.2010.11.009
    31. White, F. M. (1991). Viscous fluid flow (2nd ed.). McGraw-Hill.
    32. Kuo, B. L. (2005). Heat transfer analysis for the Falkner–Skan wedge flow by the differential transformation method. International Journal of Heat and Mass Transfer, 48(23–24), 5036–5046. https://doi.org/10.1016/j.ijheatmasstransfer.2005.06.021.
    33. Blasius, H. (1908). Grenzschichten in Flüssigkeiten mit kleiner Reibung. Zentralblatt für Mathematische Physik, 56, 1–37.

  • Downloads

  • How to Cite

    Saha , B. K. . (2026). Elastico–Viscous Boundary Layer Flow Over A Wedge Incorporating Nanofluid Interaction Effects. International Journal of Advanced Mathematical Sciences, 12(1), 68-78. https://doi.org/10.14419/4bv4wg35