International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

Frequency: 12

line decor
  
line decor

 Volume 10, Issue 12 (December 2023), Pages: 121-131

----------------------------------------------

 Original Research Paper

Numerical solution for MHD Flow of an Oldroyd–B fluid over a stretching sheet in the presence of thermophoresis with chemical reaction effects

 Author(s): 

 Abdelmgid O. M. Sidahmed *

 Affiliation(s):

 Department of Mathematics, College of Science and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia

 Full text

  Full Text - PDF

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-1926-6162

 Digital Object Identifier (DOI)

 https://doi.org/10.21833/ijaas.2023.12.014

 Abstract

The magnetohydrodynamic flow of an Oldroyd-B fluid across a vertical stretching sheet through a porous medium is investigated. Using a similarity transformation, the boundary layer equations for momentum, thermal energy, and concentration can be simplified into a set of linked ordinary differential equations. The successive linearization method is then used to numerically solve the system of ordinary differential equations. Graphical and tabular representations of the physical parameter effects on velocity, temperature, concentration profiles, the local skin friction coefficient, and heat and mass transfer rates are provided. Deborah's number in terms of relaxation time has been reported to resist and slow down the motion of fluid particles at different time instants in terms of relaxation time. By raising Deborah's numbers in terms of relaxation time, the temperature profile rises. Additionally, excellent agreement was found after the current results were examined and contrasted with the published results.

 © 2023 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 MHD, Oldroyd-B fluid, Chemical reaction, SLM

 Article history

 Received 23 July 2023, Received in revised form 25 November 2023, Accepted 27 November 2023

 Acknowledgment 

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Sidahmed AOM (2023). Numerical solution for MHD Flow of an Oldroyd–B fluid over a stretching sheet in the presence of thermophoresis with chemical reaction effects. International Journal of Advanced and Applied Sciences, 10(12): 121-131

 Permanent Link to this page

 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 

 Tables

 Table 1 Table 2 Table 3 Table 4 Table 5 

----------------------------------------------   

 References (42)

  1. Ahmed MAM, Mohammed ME, and Khidir AA (2015). On linearization method to MHD boundary layer convective heat transfer with low pressure gradient. Propulsion and Power Research, 4(2): 105-113. https://doi.org/10.1016/j.jppr.2015.04.001   [Google Scholar]
  2. Ahmed MAM, Mohammed ME, and Khidir AA (2016). The effects of cross-diffusion and radiation on mixed convection from a vertical flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation. Propulsion and Power Research, 5(2): 149-163. https://doi.org/10.1016/j.jppr.2016.05.001   [Google Scholar]
  3. Azeem KW, Khan M, and Malik R (2014). Three-dimensional flow of an Oldroyd-B nanofluid towards stretching surface with heat generation/absorption. PLOS ONE, 9(8): e105107. https://doi.org/10.1371/journal.pone.0105107   [Google Scholar] PMid:25170945 PMCid:PMC4149422
  4. Cortell R. (2006). A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet. International Journal of Non-Linear Mechanics, 41(1): 78-85. https://doi.org/10.1016/j.ijnonlinmec.2005.04.008   [Google Scholar]
  5. Daoud Y, Abdalbagi M, and Khidir AA (2021). On the solution of magneto-hydrodynamics three-dimensional flow due to a stretching sheet in a porous medium using the successive linearization method. Chinese Journal of Physics, 73: 232-238. https://doi.org/10.1016/j.cjph.2021.06.011   [Google Scholar]
  6. Ghadikolaei SS, Hosseinzadeh K, Yassari M, Sadeghi H, and Ganji DD (2018). Analytical and numerical solution of non-Newtonian second-grade fluid flow on a stretching sheet. Thermal Science and Engineering Progress, 5: 309-316. https://doi.org/10.1016/j.tsep.2017.12.010   [Google Scholar]
  7. Gireesha BJ, Kumar KG, Ramesh GK, and Prasannakumara BC (2018). Nonlinear convective heat and mass transfer of Oldroyd-B nanofluid over a stretching sheet in the presence of uniform heat source/sink. Results in Physics, 9: 1555-1563. https://doi.org/10.1016/j.rinp.2018.04.006   [Google Scholar]
  8. Hayat T, Imtiaz M, Alsaedi A, and Almezal S (2016). On Cattaneo–Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous–heterogeneous reactions. Journal of Magnetism and Magnetic Materials, 401: 296-303. https://doi.org/10.1016/j.jmmm.2015.10.039   [Google Scholar]
  9. Hayat T, Muhammad T, Shehzad SA, and Alsaedi A (2015). Temperature and concentration stratification effects in mixed convection flow of an Oldroyd-B fluid with thermal radiation and chemical reaction. PLOS ONE, 10(6): e0127646. https://doi.org/10.1371/journal.pone.0127646   [Google Scholar] PMid:26102200 PMCid:PMC4478041
  10. Hayat T, Shehzad SA, Al-Mezel S, and Alsaedi A (2014). Three-dimensional flow of an Oldroyd-B fluid over a bidirectional stretching surface with prescribed surface temperature and prescribed surface heat flux. Journal of Hydrology and Hydromechanics, 62(2): 117-125. https://doi.org/10.2478/johh-2014-0016   [Google Scholar]
  11. Hayat T, Shehzad SA, Alsaedi A, and Alhothuali MS (2013). Three-dimensional flow of Oldroyd-B fluid over surface with convective boundary conditions. Applied Mathematics and Mechanics, 34(4): 489-500. https://doi.org/10.1007/s10483-013-1685-9   [Google Scholar]
  12. Hussaini MY and Zang TA (1987). Spectral methods in fluid dynamics. Annual Review of Fluid Mechanics, 19(1): 339-367. https://doi.org/10.1146/annurev.fl.19.010187.002011   [Google Scholar]
  13. Khan M, Yasir M, Alshomrani AS, Sivasankaran S, Aladwani YR, and Ahmed A (2022). Variable heat source in stagnation-point unsteady flow of magnetized Oldroyd-B fluid with cubic autocatalysis chemical reaction. Ain Shams Engineering Journal, 13(3): 101610. https://doi.org/10.1016/j.asej.2021.10.005   [Google Scholar]
  14. Khidir AA (2023). Application of successive linearisation method on mixed convection boundary layer flow of nanofluid from an exponentially stretching surface with magnetic field effect. Journal of Nanofluids, 12(2): 465-475. https://doi.org/10.1166/jon.2023.1961   [Google Scholar]
  15. Liao S (2003). Beyond perturbation: Introduction to the homotopy analysis method. CRC Press, Boca Raton, USA.   [Google Scholar]
  16. Mabood F, Bognár G, and Shafiq A (2020). Impact of heat generation/absorption of magnetohydrodynamics Oldroyd-B fluid impinging on an inclined stretching sheet with radiation. Scientific Reports, 10: 17688. https://doi.org/10.1038/s41598-020-74787-2   [Google Scholar] PMid:33077753 PMCid:PMC7572406
  17. Makinde OD (2008). Effect of arbitrary magnetic Reynolds number on MHD flows in convergent‐divergent channels. International Journal of Numerical Methods for Heat and Fluid Flow, 18(6): 697-707. https://doi.org/10.1108/09615530810885524   [Google Scholar]
  18. Makukula Z, Motsa SS, and Sibanda P (2010a). On a new solution for the viscoelastic squeezing flow between two parallel plates. Journal of Advanced Research in Applied Mathematics, 2(4): 31-38. https://doi.org/10.5373/jaram.455.060310   [Google Scholar]
  19. Makukula ZG, Sibanda P, and Motsa SS (2010b). A novel numerical technique for two-dimensional laminar flow between two moving porous walls. Mathematical Problems in Engineering, 2010: 528956. https://doi.org/10.1155/2010/528956   [Google Scholar]
  20. Motsa SS, Makukula ZG, and Shateyi S (2015). Numerical investigation of the effect of unsteadiness on three-dimensional flow of an Oldroyb-B fluid. PLOS ONE, 10(7): e0133507. https://doi.org/10.1371/journal.pone.0133507   [Google Scholar] PMid:26196291 PMCid:PMC4510369
  21. Narayana M and Sibanda P (2012). On the solution of double-diffusive convective flow due to a cone by a linearization method. Journal of Applied Mathematics, 2012: 587357. https://doi.org/10.1155/2012/587357   [Google Scholar]
  22. Noor NFM (2012). Analysis for MHD flow of a Maxwell fluid past a vertical stretching sheet in the presence of thermophoresis and chemical reaction. World Academy of Science, Engineering and Technology, 64: 1019-1023.   [Google Scholar]
  23. Paul A and Das TK (2023). Thermal and mass transfer aspects of MHD flow across an exponentially stretched sheet with chemical reaction. International Journal of Ambient Energy, 44(1): 1563-1574. https://doi.org/10.1080/01430750.2023.2179110   [Google Scholar]
  24. Pires M and Sequeira A (2011). Flows of generalized Oldroyd-B fluids in curved pipes. In: Escher J, Guidotti P, Hieber M, and Zajaczkowski W (Eds.), Parabolic problems: The Herbert Amann festschrift: 21-43. Volume 80, Springer, Basel, Switzerland. https://doi.org/10.1007/978-3-0348-0075-4_2   [Google Scholar]
  25. Raptis A (1998). Flow of a micropolar fluid past a continuously moving plate by the presence of radiation. International Journal of Heat and Mass Transfer, 18(41): 2865-2866. https://doi.org/10.1016/S0017-9310(98)00006-4   [Google Scholar]
  26. Reddy NN, Rao VS, and Reddy BR (2021). Chemical reaction impact on MHD natural convection flow through porous medium past an exponentially stretching sheet in presence of heat source/sink and viscous dissipation. Case Studies in Thermal Engineering, 25: 100879. https://doi.org/10.1016/j.csite.2021.100879   [Google Scholar]
  27. Rubbab Q, Husnine SM, and Mahmood AMIR (2009). Exact solutions of generalized Oldroyd-B fluid subject to a time-dependent shear stress in a pipe. Journal of Prime Research in Mathematics, 5: 139-148.   [Google Scholar]
  28. Sajid M, Abbas Z, Javed T, and Ali N (2010). Boundary layer flow of an Oldroyd-B fluid in the region of a stagnation point over a stretching sheet. Canadian Journal of Physics, 88(9): 635-640. https://doi.org/10.1139/P10-049   [Google Scholar]
  29. Salah F (2022). Chemical reaction and generalized heat flux model for Powell–Eyring model with radiation effects. International Journal of Mathematics and Mathematical Sciences, 2022: 4076426. https://doi.org/10.1155/2022/4076426   [Google Scholar]
  30. Salah F and Elhafian MH (2019). Numerical solution for heat transfer of non-Newtonian second-grade fluid flow over stretching sheet via successive linearization method. IAENG International Journal of Applied Mathematics, 49(4): 505-512.   [Google Scholar]
  31. Salah F and Sidahmed AO (2022). Chemical reaction and radiation effects on MHD flow of Oldroyd-B fluid through porous medium past an exponentially stretching sheet with heat sink. Journal of Applied Mathematics, 2022: 6582295. https://doi.org/10.1155/2022/6582295   [Google Scholar]
  32. Salah F, Alzahrani A, Sidahmed AO, and Viswanathan KK (2019). A note on thin-film flow of Eyring-Powell fluid on the vertically moving belt using successive linearization method. International Journal of Advanced and Applied Sciences, 6(2): 17-22. https://doi.org/10.21833/ijaas.2019.02.004   [Google Scholar]
  33. Salah F, Sidahmed AO, and Viswanathan KK (2023). Chemical MHD Hiemenz flow over a nonlinear stretching sheet and Brownian motion effects of nanoparticles through a porous medium with radiation effect. Mathematical and Computational Applications, 28(1): 21. https://doi.org/10.3390/mca28010021   [Google Scholar]
  34. Seini YI and Makinde OD (2013). MHD boundary layer flow due to exponential stretching surface with radiation and chemical reaction. Mathematical Problems in Engineering, 2013: 163614. https://doi.org/10.1155/2013/163614   [Google Scholar]
  35. Shankaralingappa BM, Prasannakumara BC, Gireesha BJ, and Sarris IE (2021). The impact of Cattaneo–Christov double diffusion on Oldroyd-B Fluid flow over a stretching sheet with thermophoretic particle deposition and relaxation chemical reaction. Inventions, 6(4): 95. https://doi.org/10.3390/inventions6040095   [Google Scholar]
  36. Shateyi S (2013). A new numerical approach to MHD flow of a Maxwell fluid past a vertical stretching sheet in the presence of thermophoresis and chemical reaction. Boundary Value Problems, 2013: 196. https://doi.org/10.1186/1687-2770-2013-196   [Google Scholar]
  37. Shateyi S and Motsa SS (2010). Variable viscosity on magnetohydrodynamic fluid flow and heat transfer over an unsteady stretching surface with Hall effect. Boundary Value Problems, 2010: 257568. https://doi.org/10.1155/2010/257568   [Google Scholar]
  38. Sidahmed A and Salah F (2022). Radiation effects on MHD flow of second grade fluid through porous medium past an exponentially stretching sheet with chemical reaction. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 99(2): 1-16. https://doi.org/10.37934/arfmts.99.2.116   [Google Scholar]
  39. Waqas M, Hayat T, Shehzad SA, and Alsaedi A (2018). Transport of magnetohydrodynamic nanomaterial in a stratified medium considering gyrotactic microorganisms. Physica B: Condensed Matter, 529: 33-40. https://doi.org/10.1016/j.physb.2017.09.128   [Google Scholar]
  40. Yasir M and Khan M (2023). Dynamics of unsteady axisymmetric of Oldroyd-B material with homogeneous-heterogeneous reactions subject to Cattaneo-Christov heat transfer. Alexandria Engineering Journal, 74: 665-674. https://doi.org/10.1016/j.aej.2023.05.065   [Google Scholar]
  41. Yasir M, Ahmed A, Khan M, Alzahrani AK, Malik ZU, and Alshehri AM (2023). Mathematical modelling of unsteady Oldroyd-B fluid flow due to stretchable cylindrical surface with energy transport. Ain Shams Engineering Journal, 14(1): 101825. https://doi.org/10.1016/j.asej.2022.101825   [Google Scholar]
  42. Yasir M, Ahmed A, Khan M, and Ullah MZ (2021). Convective transport of thermal and solutal energy in unsteady MHD Oldroyd-B nanofluid flow. Physica Scripta, 96(12): 125266. https://doi.org/10.1088/1402-4896/ac3b67   [Google Scholar]