Three-dimensional rotating viscous flow past a permeable stretching/shrinking sheet with convective boundary condition

2023;
: pp. 1206–1214
https://doi.org/10.23939/mmc2023.04.1206
Received: September 26, 2023
Revised: November 15, 2023
Accepted: November 16, 2023

Mathematical Modeling and Computing, Vol. 10, No. 4, pp. 1206–1214 (2023)

1
Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia
2
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia
3
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia
4
Department of Mathematics, Babes-Bolyai University

The study of three-dimensional rotating boundary layer flow approaching a stretching or shrinking surface under convective boundary conditions is presented in this paper.  This study expands the scope of previous researchers' work to encompass broader scenarios, including situations involving mass transfer (suction) on the wall, the Biot number and cases featuring a shrinking surface.  It is found that the increase of suction and rotating parameters leads to a noticeable rise in both the local skin friction coefficients and the local Nusselt number, and the solutions to the governing ordinary differential equations exhibit a dual-branch nature, comprising both upper and lower branch solutions, within a specific range of the governing parameters.

  1. Wang C. Y.  Stretching a surface in a rotating fluid.  Zeitschrift für angewandte Mathematik und Physik ZAMP.  39 (2), 177–185 (1988).
  2. Ali F. M., Nazar R., Arifin N. M., Pop I.  Unsteady shrinking sheet with mass transfer in a rotating fluid.  International Journal for Numerical Methods in Fluids.  66 (11), 1465–1474 (2011).
  3. Javed T., Sajid M., Abbas Z., Ali N.  Non-similar solution for rotating flow over an exponentially stretching surface.  International Journal of Numerical Methods for Heat & Fluid Flow.  21 (7), 903–908 (2011).
  4. Rosali H., Ishak A., Nazar R., Pop I.  Rotating flow over an exponentially shrinking sheet with suction.  Journal of Molecular Liquids.  211, 965–969 (2015).
  5. Mustafa M., Mushtaq A., Hayat T., Alsaedi A.  Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation.  PLOS ONE.  11 (2), e0149304 (2016).
  6. Hayat T., Nadeem S.  Heat transfer enhancement with Ag-CuO/water hybrid nanofluid.  Results in Physics.  7, 2317–2324 (2017).
  7. Asghar A., Vrinceanu N., Yuan Ying T., Ali Lund L., Shah Z., Tirth V.  Dual solutions of convective rotating flow of three-dimensional hybrid nanofluid across the linear stretching/shrinking sheet.  Alexandria Engineering Journal.  75, 297–312 (2023).
  8. Bataller R. C.  Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition.  Applied Mathematics and Computation.  206 (12), 832–840 (2008).
  9. Aziz A.  A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition.  Communications in Nonlinear Science and Numerical Simulation.  14 (4), 1064–1068 (2009).
  10. Magyari E.  Comment on "A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition" by A. Aziz, Comm. Nonlinear Sci. Numer. Simul.  14, 1064-8 (2009).  Communications in Nonlinear Science and Numerical Simulation.  16 (1), 599–601 (2011).
  11. Akbar N. S., Nadeem S., Haq R. U., Khan Z.  Radiation effects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition.  Chinese Journal of Aeronautics.  26 (6), 1389–1397 (2013).
  12. Shafiq A., Rasool G., Khalique C.  Significance of Thermal Slip and Convective Boundary Conditions in Three Dimensional Rotating Darcy-Forchheimer Nanofluid Flow.  Symmetry.  12 (5), 741 (2020).
  13. Khashi'ie N. S., Arifin N. M., Pop I., Nazar R., Hafidzuddin E. H., Wahi N.  Three-Dimensional Hybrid Nanofluid Flow and Heat Transfer past a Permeable Stretching/Shrinking Sheet with Velocity Slip and Convective Condition.  Chinese Journal of Physics.  66, 157–171 (2020).
  14. Hafidzuddin M. E. H., Alias N. S.  Effect of suction and MHD induced Navier slip flow due to a non-linear stretching/shrinking sheet.  Mathematical Modeling and Computing.  9 (1), 83–91 (2022).
  15. Wahid N. S, Arifin N. M., Khashi'ie N. S., Pop I., Bachok N., Hafidzuddin M. E. H.  Radiative flow of magnetic nanofluids over a moving surface with convective boundary condition.  Mathematical Modeling and Computing.  9 (4), 791–804 (2022).
  16. Raju G., Hari Babu B., Rama Mohan Reddy L., Varma S.  MHD convective rotating flow of viscoelastic fluid past an infinite vertical oscillating porous plate with Hall effects.  Heat Transfer.  52, 2277–2294 (2023).
  17. Surma Devi C., Takhar H., Nath G.  Unsteady, three-dimensional, boundary-layer flow due to a stretching surface.  International Journal of Heat and Mass Transfer.  29 (12), 1996–1999 (1986).
  18. Kierzenka J., Shampine L.  A BVP Solver that Controls Residual and Error.  Journal of Numerical Analysis, Industrial and Applied Mathematics.  3 (1–2), 27–41 (2008).
  19. Merkin J.  On dual solutions occurring in mixed convection in a porous medium.  Journal of Engineering Mathematics.  20, 171–179 (1986).
  20. Weidman P., Kubitschek D., Davis A.  The effect of transpiration on self-similar boundary layer flow over moving surfaces.  International Journal of Engineering Science.  44 (11–12), 730–737 (2006).
  21. Rosca A. V., Pop I.  Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip.  International Journal of Heat and Mass Transfer.  60, 355–364 (2013).
  22. Miklavčič M., Wang C.  Viscous flow due to a shrinking sheet.  Quarterly of Applied Mathematics.  64 (2), 283–290 (2006).