Numerical Investigation of Slip Conditions in Nanofluid Flow Induced by a Nonlinearly Stretching Sheet: A bvp4c Approach

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Year : 2026 | Volume : 13 | Issue : 02 | Page :
By

Binaya Kumar Baral,

Lokendra Kumar,

  1. Research Scholar, Department of Mathematics, Jaypee Institute of Information Technology, Noida, Uttar Pradesh, India
  2. Professor, Department of Mathematics, Jaypee Institute of Information Technology, Noida, Uttar Pradesh, India

Abstract

The present work describes a numerical analysis of the steady, laminar flow over a nonlinear stretching sheet in a nanofluid medium. Slip conditions in terms of velocity, temperature, and concentration have been introduced into the mathematical model to capture the impact of interfacial mass transfer on the stretching surface. The problem is modeled to include nanoparticle transportation in terms of Brownian diffusion and thermophoresis, thereby affecting the temperature and concentration profiles. The linked set of ordinary differential equations has been obtained by applying appropriate similarity transformations. The subsequent boundary value problem is solved by a fourth–fifth order adaptive RK45-shooting scheme. The numerical results are then validated by the MATLAB bvp4c solver, which follows a collocation technique, and the similarity between the two results indicates the reliability of the computational technique. The impact of the velocity, thermal, and concentration slip factors, as well as the Prandtl number on the velocity, temperature, and nanoparticle concentration profiles is analyzed. An increase in velocity slip will result in the weakening of the momentum transfer between the stretching surface and the fluid; hence, the velocity in the boundary layer will be decreased. Similarly, both the temperature profile and the thickness of the thermal boundary layer will decrease as thermal slip increases. Furthermore, an increase in the concentration slips parameter results in a decrease in both the local Sherwood number and the thickness of the concentration boundary layer for a fixed Lewis number. In summary, the study reveals how the effects of different types of slips can greatly affect the momentum, heat, and mass transfer in nanofluids.

Keywords: Nanofluid; Boundary layer; Slip effect; Shooting method; Bvp4c solver

[This article belongs to Recent Trends in Fluid Mechanics ]

How to cite this article: Binaya Kumar Baral, Lokendra Kumar. Numerical Investigation of Slip Conditions in Nanofluid Flow Induced by a Nonlinearly Stretching Sheet: A bvp4c Approach. Recent Trends in Fluid Mechanics. 2026; 13(02):-.
How to cite this URL: Binaya Kumar Baral, Lokendra Kumar. Numerical Investigation of Slip Conditions in Nanofluid Flow Induced by a Nonlinearly Stretching Sheet: A bvp4c Approach. Recent Trends in Fluid Mechanics. 2026; 13(02):-. Available from: https://journals.stmjournals.com/rtfm/article=2026/view=255436

References

  1. Crane LJ. Flow past a stretching plate. Zeitschrift für angewandte Mathematik und Physik ZAMP. 1970 Jul;21(4):645-7.
  2. Choi SU. Enhancing thermal conductivity of fluids with nanoparticles. InASME international mechanical engineering congress and exposition 1995 Nov 12 (Vol. 17421, pp. 99-105). American Society of Mechanical Engineers.
  3. Daungthongsuk W, Wongwises S. A critical review of convective heat transfer of nanofluids. Renewable and sustainable energy reviews. 2007 Jun 1;11(5):797-817.
  4. Kuznetsov AV, Nield DA. Natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences. 2010 Feb 1;49(2):243-7.
  5. Jou RY, Tzeng SC. Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures. International Communications in Heat and Mass Transfer. 2006 Jul 1;33(6):727-36.
  6. Jou RY, Tzeng SC. Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures. International Communications in Heat and Mass Transfer. 2006 Jul 1;33(6):727-36.
  7. Ghasemi B, Aminossadati SM. Natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Numerical Heat Transfer, Part A: Applications. 2009 Apr 16;55(8):807-23.
  8. Khan WA, Aziz A. Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux. International Journal of Thermal Sciences. 2011 Jul 1;50(7):1207-14.
  9. Sakiadis BC. Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow. AIChE Journal. 1961 Mar;7(1):26- 8.
  10. Bhargava R, Kumar L, Takhar HS. Finite element solution of mixed convection micropolar flow driven by a porous stretching sheet. International journal of engineering science. 2003 Nov 1;41(18):2161-78.
  11. Desseaux A, Kelson NA. Flow of a micropolar fluid bounded by a stretching sheet. Anziam J. 2000 Aug;42:536-60.
  12. Bhargava R, Sharma S, Takhar HS, Bég OA, Bhargava P. Numerical solutions for micropolar transport phenomena over a nonlinear stretching sheet. Nonlinear Analysis: Modelling and Control. 2007 Jan 25;12(1):45-63.
  13. Parida C, Mahanta G, Shaw S. Marangoni and interfacial mechanisms in dihydrogen oxide–based nanofluid flow over a stretched surface: comparative machine- learning approaches. International Journal of Hydrogen Energy. 2025 Dec 8;196:152528.
  14. Parida C, Mahanta G, Shaw S. Nonlinear hemodynamics modeling of fractional Jeffery ternary hybrid nanofluid flow in multi-stenosed arteries with ANN-based simulation: C. Parida et al. Nonlinear Dynamics. 2025 Dec;113(25):34873-904..
  15. Vajravelu K. Viscous flow over a nonlinearly stretching sheet. Applied mathematics and computation. 2001 Dec 15;124(3):281-8.
  16. Parida C, Mohanty D, Mahanta G, Shaw S. Thermo-solutal impact of MHD hybrid nanofluid flow containing gyrotactic microorganisms over an inclined cylinder. Numerical Heat Transfer, Part A: Applications. 2026 Dec 31;87(1):2541813.
  17. Cortell R. Viscous flow and heat transfer over a nonlinearly stretching sheet. Applied Mathematics and Computation. 2007 Jan 15;184(2):864-73.
  18. Al-Mdallal QM, Syam MI, Anwar MN. A collocation-shooting method for solving fractional boundary value problems. Communications in Nonlinear Science and Numerical Simulation. 2010 Dec 1;15(12):3814-22.
  19. Mohanty A, Parida C, Mahanta G, Shaw S, Panigrahi L. ANN model for heat and mass transfer of Cu–Al2O3–TiO2–SiO2–MWCNT hybrid nanofluid for solar applications. International Journal of Ambient Energy. 2026 Dec 31;47(1):2691199.
  20. Parida C, Ratha SP, Mahanta G, Parija S, Shaw S. Multilayer neural network analysis of penta-hybrid nanofluid flow with entropy optimization: Application to rocket engine nozzle cooling. Engineering Applications of Artificial Intelligence. 2025 Sep 15;156:111106.
  21. Jumri NJ, Shab NF. A non-linear shooting method for two-point boundary value problems. Enhanced Knowledge in Sciences and Technology. 2021 Jul 29;1(2):124-31.
  22. Bhatti MM, Bég OA, Abdelsalam SI. Computational framework of magnetized MgO–Ni/water-based stagnation nanoflow past an elastic stretching surface: Application in solar energy coatings. Nanomaterials. 2022 Mar 23;12(7):1049.
  23. Bachok N, Ishak A, Pop I. Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. International Journal of Thermal Sciences. 2010 Sep 1;49(9):1663-8.
  24. Rana P, Bhargava R. Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study. Communications in Nonlinear Science and Numerical Simulation. 2012 Jan 1;17(1):212-26.
  25. Awais M, Hayat T, Ali A, Irum S. Velocity, thermal and concentration slip effects on a magneto-hydrodynamic nanofluid flow. Alexandria Engineering Journal. 2016 Sep 1;55(3):2107-14.
  26. Alinejad J, Samarbakhsh S. Viscous flow over nonlinearly stretching sheet with effects of viscous dissipation. Journal of applied mathematics. 2012;2012(1):587834.
  27. Ramya D, Srinivasa Raju R, Anand Rao J, Rashidi MM. Boundary layer viscous flow of nanofluids and heat transfer over a nonlinearly isothermal stretching sheet in the presence of heat generation/absorption and slip boundary conditions. International Journal of Nanoscience and Nanotechnology. 2016 Nov 1;12(4):251- 68.
  28. Arefin MA, Nishu MA, Dhali MN, Uddin MH. Analysis of reliable solutions to the boundary value problems by using shooting method. Mathematical Problems in Engineering. 2022;2022(1):2895023.
  29. Edun IF, Akinlabi GO. Application of the shooting method for the solution of second order boundary value problems. InJournal of Physics: Conference Series 2021 Jan 1 (Vol. 1734, No. 1, p. 012020). IOP Publishing.
  30. Sharma PR, Sinha S, Yadav RS, Filippov AN. MHD mixed convective stagnation point flow along a vertical stretching sheet with heat source/sink. International Journal of Heat and Mass Transfer. 2018 Feb 1;117:780-6.
  31. Etwire CJ, Seini IY, Musah R, Makinde OD. On the flow of oil-based nanofluid on a stretching permeable surface with radiative heat transfer and dissipative energy. InDefect and Diffusion Forum 2021 Jun 18 (Vol. 409, pp. 1-16). Trans Tech Publications Ltd.
  32. Baral BK, Kumar L. Numerical investigation of Sisko nanofluid flow and heat transfer with velocity slip effect over a nonlinearly stretching sheet: BK Baral, L. Kumar. Journal of the Korean Physical Society. 2026 Feb;88(4):470-82.
  33. Adem GA, Kishan N. Slip effects in a flow and heat transfer of a nanofluid over a nonlinearly stretching sheet using optimal homotopy asymptotic method. Int. J. Eng. Manuf. Sci. 2018;8(1):25-46.
Regular Issue Subscription Original Research
Volume 13
Issue 02
Received 05/09/2026
Accepted 09/09/2026
Published 12/09/2026
Publication Time 7 Days

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