Numerical Study for MHD Flow of an Oldroyd-B Fluid Over a Stretching Sheet in the Presence of Thermal Radiation with Soret and Dufour Effects

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Abdelmgid O.M. Sidahmed


This paper investigates the impact of Soret and Dufour's MHD flow of an Oldroyd-B fluid over a stretching sheet in the presence of thermal radiation. By a similarity transformation, the controlling partial differential equations are transformed into a system of nonlinear ordinary differential equations. Using the successive linearization method (SLM), the linear system is solved. A determination and discussion of the impacts of specific fluid parameters on the temperature, concentration distribution, and velocity are presented. As the magnetic field increases, we observe that the temperature and concentration profiles rise, while the velocity profile falls. In addition, increases in the Dufour and Soret levels will also result in an improvement in the temperature and concentration distribution. The validity of the acquired results is tested by comparing them to previously published works, with particular attention paid to the accuracy and convergence of the solution.

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  1. B. Shilpa, V. Leela, Galerkin Finite Element Analysis of Heat and Mass Transfer of Jeffrey, Maxwell and Oldroyd-B Nanofluids in a Vertical Annulus With an Induced Magnetic Field and a Non–Uniform Heat Source/Sink, Int. J. Ambient Energy. 44 (2023), 1887–1903.
  2. B.C. Prasannakumara, M. Gnaneswara Reddy, G.T. Thammanna, B.J. Gireesha, MHD Double-Diffusive Boundary-Layer Flow of a Maxwell Nanofluid Over a Bidirectional Stretching Sheet With Soret and Dufour Effects in the Presence of Radiation, Nonlinear Eng. 7 (2018), 195–205.
  3. K. Ghachem, A.K. Hussein, L. Kolsi, O. Younis, CNT–Water Nanofluid Magneto-Convective Heat Transfer in a Cubical Cavity Equipped With Perforated Partition, Eur. Phys. J. Plus. 136 (2021), 377.
  4. M. Bhuvaneswari, S. Eswaramoorthi, S. Sivasankaran, A.K. Hussein, Cross-Diffusion Effects on MHD Mixed Convection Over a Stretching Surface in a Porous Medium With Chemical Reaction and Convective Condition, Eng. Trans. 67 (2019), 3–19.
  5. B. Ali, S.A. Khan, A.K. Hussein, T. Thumma, S. Hussain, Hybrid Nanofluids: Significance of Gravity Modulation, Heat Source/Sink, and Magnetohydrodynamic on Dynamics of Micropolar Fluid Over an Inclined Surface via Finite Element Simulation, Appl. Math. Comput. 419 (2022), 126878.
  6. S.E. Ahmed, A.K. Hussein, M.A. Mansour, Z.A. Raizah, X. Zhang, MHD Mixed Convection in Trapezoidal Enclosures Filled With Micropolar Nanofluids, Nano Sci. Technol. Int. J. 9 (2018), 343–372.
  7. J. G. Oldroyd, On the Formulation of Rheological Equations of State, Proc. R. Soc. Lond. A. 200 (1950), 523–541.
  8. T. Hayat, T. Muhammad, S.A. Shehzad, A. Alsaedi, Temperature and Concentration Stratification Effects in Mixed Convection Flow of an Oldroyd-B Fluid with Thermal Radiation and Chemical Reaction, PLoS ONE. 10 (2015), e0127646.
  9. E.S.G. Shaqfeh, Purely Elastic Instabilities in Viscometric Flows, Annu. Rev. Fluid Mech. 28 (1996), 129–185.
  10. M. Laso, H.C. Öttinger, Calculation of Viscoelastic Flow Using Molecular Models: The Connffessit Approach, J. Non-Newtonian Fluid Mech. 47 (1993), 1–20.
  11. M. Sajid, Z. Abbas, T. Javed, N. Ali, Boundary Layer Flow of an Oldroyd-B Fluid in the Region of a Stagnation Point Over a Stretching Sheet, Can. J. Phys. 88 (2010), 635–640.
  12. N. Venkatesh, M.A. Kumar, R. Srinivasa Raju, Dufour and Soret Influence on MHD Boundary Layer Flow of a Maxwell Fluid Over a Stretching Sheet With Nanoparticles, Heat Transfer. 51 (2022), 5193–5205.
  13. S.S. Motsa, Z.G. Makukula, S. Shateyi, Numerical Investigation of the Effect of Unsteadiness on Three-Dimensional Flow of an Oldroyb-B Fluid, PLoS ONE. 10 (2015), e0133507.
  14. T. Hayat, M. Imtiaz, A. Alsaedi, S. Almezal, On Cattaneo–Christov Heat Flux in MHD Flow of Oldroyd-B Fluid With Homogeneous–Heterogeneous Reactions, J. Magnetism Magnetic Mater. 401 (2016), 296–303.
  15. K.R. Rajagopal, R.K. Bhatnagar, Exact Solutions for Some Simple Flows of an Oldroyd-B Fluid, Acta Mech. 113 (1995), 233–239.
  16. T. Hayat, S.A. Shehzad, A. Alsaedi, M.S. Alhothuali, Three-Dimensional Flow of Oldroyd-B Fluid Over Surface With Convective Boundary Conditions, Appl. Math. Mech.-Engl. Ed. 34 (2013), 489–500.
  17. T. Hayat, S.A. Shehzad, A. Alsaedi, Three-Dimensional Flow of an Oldroyd-B Fluid Over a Bidirectional Stretching Surface With Prescribed Surface Temperature and Prescribed Surface Heat Flux, J. Hydrol. Hydromech. 62 (2014), 117–125.
  18. F. Mabood, G. Bognár, A. Shafiq, Impact of Heat Generation/Absorption of Magnetohydrodynamics Oldroyd-B Fluid Impinging on an Inclined Stretching Sheet With Radiation, Sci. Rep. 10 (2020), 17688.
  19. B.M. Shankaralingappa, B.C. Prasannakumara, B.J. Gireesha, I.E. Sarris, 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 (2021), 95.
  20. M. Yasir, A. Ahmed, M. Khan, A.K. Alzahrani, Z.U. Malik, A.M. Alshehri, Mathematical Modelling of Unsteady Oldroyd-B Fluid Flow Due to Stretchable Cylindrical Surface With Energy Transport, Ain Shams Eng. J. 14 (2023), 101825.
  21. M. Arif, P. Kumam, T. Seangwattana, P. Suttiarporn, A Fractional Model Of Magnetohydrodynamics Oldroyd-B Fluid With Couple Stresses, Heat and Mass Transfer: A Comparison Among Non-Newtonian Fluid Models, Heliyon. 9 (2023), e17642.
  22. P.V. Satya Narayana, B. Venkateswarlu, Soret and Dufour Effects on Mhd Flow of a Maxwell Fluid Over a Stretching Sheet With Joule Heating, Front. Heat Mass Transfer. 9 (2017), 11.
  23. T. Hayat, S.A. Shehzad, A. Alsaedi, Soret and Dufour Effects on Magnetohydrodynamic (MHD) Flow of Casson Fluid, Appl. Math. Mech.-Engl. Ed. 33 (2012), 1301–1312.
  24. S.A. Khan, T. Hayat, A. Alsaedi, Simultaneous Features of Soret And Dufour in Entropy Optimized Flow of Reiner-Rivlin Fluid Considering Thermal Radiation, Int. Commun. Heat Mass Transfer. 137 (2022), 106297.
  25. M.M. Biswal, K. Swain, G.C. Dash, K. Ojha, Study of Radiative Magneto-Non-Newtonian Fluid Flow Over a Nonlinearly Elongating Sheet With Soret and Dufour Effects, Numer. Heat Transfer, Part A: Appl. 83 (2022), 331–342.
  26. N.K. Mishra, M. Sharma, B.K. Sharma, U. Khanduri, Soret and Dufour Effects on MHD Nanofluid Flow of Blood Through a Stenosed Artery With Variable Viscosity, Int. J. Mod. Phys. B. 37 (2023), 2350266.
  27. X. Yang, Y. Zhang, Lattice Boltzmann Study of the Double-Diffusive Convection in Porous Media With Soret and Dufour Effects, Comput. Geosci. (2023).
  28. N. Vijay, K. Sharma, Magnetohydrodynamic Hybrid Nanofluid Flow Over a Decelerating Rotating Disk With Soret and Dufour Effects, Multidiscip. Model. Mater. Struct. 19 (2023), 253–276.
  29. S.A. Khan, T. Hayat, A. Alsaedi, Numerical Study for Entropy Optimized Radiative Unsteady Flow of Prandtl Liquid, Fuel. 319 (2022), 123601.
  30. M. Jawad, A. Saeed, A. Khan, I. Ali, H. Alrabaiah, T. Gul, E. Bonyah, M. Zubair, Analytical Study of MHD Mixed Convection Flow for Maxwell Nanofluid With Variable Thermal Conductivity and Soret and Dufour Effects, AIP Adv. 11 (2021), 035215.
  31. M.V. Reddy, P. Lakshminarayana, K. Vajravelu, Magnetohydrodynamic Radiative Flow of a Maxwell Fluid on an Expanding Surface With the Effects of Dufour and Soret and Chemical Reaction, Comput. Therm. Sci. 12 (2020), 317–327.
  32. S. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Press, 2003.‏
  33. O.D. Makinde, Effect of Arbitrary Magnetic Reynolds Number on MHD Flows in Convergent‐Divergent Channels, Int. J. Numer. Methods Heat Fluid Flow. 18 (2008), 697–707.
  34. Z. Makukula, On a New Solution for the Viscoelastic Squeezing Flow between Two Parallel Plates, J. Adv. Res. Appl. Math. 2 (2010), 31–38.
  35. Z.G. Makukula, P. Sibanda, S.S. Motsa, A Novel Numerical Technique for Two-Dimensional Laminar Flow between Two Moving Porous Walls, Math. Probl. Eng. 2010 (2010), 528956.
  36. M. Narayana, P. Sibanda, On the Solution of Double-Diffusive Convective Flow due to a Cone by a Linearization Method, J. Appl. Math. 2012 (2012), 587357.
  37. S. Shateyi, S. Motsa, Variable Viscosity on Magnetohydrodynamic Fluid Flow and Heat Transfer over an Unsteady Stretching Surface with Hall Effect, Bound Value Probl. 2010 (2010), 257568.
  38. M. A. Mohammed Ahmed, M.E. Mohammed, A.A. Khidir, On Linearization Method to MHD Boundary Layer Convective Heat Transfer With Low Pressure Gradient, Propuls. Power Res. 4 (2015), 105–113.
  39. A.A. Khidir, Application of Successive Linearisation Method on Mixed Convection Boundary Layer Flow of Nanofluid from an Exponentially Stretching Surface with Magnetic Field Effect, J. Nanofluids. 12 (2023), 465–475.
  40. Y. Daoud, M. Abdalbagi, A.A. Khidir, On the Solution of Magneto-Hydrodynamics Three-Dimensional Flow Due to a Stretching Sheet in a Porous Medium Using the Successive Linearization Method, Chinese J. Phys. 73 (2021), 232–238.
  41. F. Salah, A.K. Alzahrani, A. O. Sidahmed, K.K. Viswanathan, A Note on Thin-Film Flow of Eyring-Powell Fluid on the Vertically Moving Belt Using Successive Linearization Method, Int. J. Adv. Appl. Sci. 6 (2019), 17–22.
  42. A.A. Khidir, S.L. Alsharari, Application of Successive Linearisation Method on the Boundary Layer Flow Problem of Heat and Mass Transfer with Radiation Effect, Int. J. Anal. Appl. 19 (5) (2021), 725-742.‏
  43. R. Cortell, A Note on Flow And Heat Transfer of a Viscoelastic Fluid Over a Stretching Sheet, Int. J. Non-Linear Mech. 41 (2006), 78–85.
  44. F. Salah, Numerical Solution for Heat Transfer of Oldroyd–B Fluid Over a Stretching Sheet Using Successive Linearization Method, Int. J. Adv. Appl. Sci. 7 (2020), 40–47.
  45. Z. Makukula, P. Sibanda, S. Motsa, A Note on the Solution of the Von Kármán Equations Using Series and Chebyshev Spectral Methods, Bound Value Probl. 2010 (2010), 471793.
  46. M.A. Mohammed Ahmed, M.E. Mohammed, A.A. Khidir, 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, Propuls. Power Res. 5 (2016), 149–163.
  47. A. Sidahmed, F. Salah, Radiation Effects on MHD Flow of Second Grade Fluid Through Porous Medium Past an Exponentially Stretching Sheet With Chemical Reaction, J. Adv. Res. Fluid Mech. Therm. Sci. 99 (2022), 1–16.
  48. F. Salah, M.H. Elhafian, Numerical Solution for Heat Transfer of Non-Newtonian Second-Grade Fluid Flow over Stretching Sheet via Successive Linearization Method, IAENG Int. J. Appl. Math. 49 (2019), 505.
  49. M.Y. Hussaini, T.A. Zang, Spectral Methods in Fluid Dynamics, Ann. Rev. Fluid Mech. 19 (1987), 339–367.
  50. K. Sadeghy, H. Hajibeygi, S.-M. Taghavi, Stagnation-Point Flow of Upper-Convected Maxwell Fluids, Int. J. Non-Linear Mech. 41 (2006), 1242–1247.
  51. M. Subhas Abel, J.V. Tawade, M.M. Nandeppanavar, MHD Flow and Heat Transfer for the Upper-Convected Maxwell Fluid Over a Stretching Sheet, Meccanica. 47 (2011), 385–393.
  52. M.S. Mandal, S. Mukhopadhyay, The Flow of MHD Maxwell Liquid Over an Extending Surface With Variable Free Stream Temperature, Heat Trans. 51 (2022), 6801–6814.
  53. M. Waqas, T. Hayat, S.A. Shehzad, A. Alsaedi, Transport of Magnetohydrodynamic Nanomaterial in a Stratified Medium Considering Gyrotactic Microorganisms, Physica B: Condensed Matter. 529 (2018), 33–40.
  54. S.S. Ghadikolaei, Kh. Hosseinzadeh, M. Yassari, H. Sadeghi, D.D. Ganji, Analytical and Numerical Solution of Non-Newtonian Second-Grade Fluid Flow on a Stretching Sheet, Therm. Sci. Eng. Progress. 5 (2018), 309–316.