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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Multiple Slip Effects on Unsteady MHD Casson Nanofluid Flow over a Porous Stretching Sheet

Journal of Applied Nonlinear Dynamics 11(3) (2022) 651--666 | DOI:10.5890/JAND.2022.09.009

G. Venkata Ramana Reddy$^1$, K.V.Chandra Sekhar$^1$, Bidemi Olumide Falodun$^2$

$^{1}$ Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, India-522502

$^{3}$ Department of Mathematics, University of Ilorin, Ilorin, Kwara State, Nigeria

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A speculative investigation has been presented on explore the salient features of multiple slip effects on MHD Casson nanofluid flow over a porous stretching sheet in the presence of Soret effect, thermal radiation and chemical reaction are numerically examined. We consider an applied magnetic field and stretching sheet time-dependent, which moves with non-uniform velocity. For the transformation of governing partial differential equations into a system of coupled nonlinear ordinary differential equations, suitable similarity variables are used. The transformed equations are then solved numerically by applying Runge-Kutta Fehlberg method with shooting technique. The influences of the various physical parameters on the velocity, temperature, and concentration profiles as well as on the skin friction coefficient, Nusselt and Sherwood numbers are discussed by the aid of graphs and tables. The imposed magnetic field produces a Lorentz force which drags the velocity of an electrically conducting Casson fluid. Due to the magnetic field strength (B$_{0}$), a higher value of Casson parameter decelerates the velocity field. Also, increase in thermal radiation parameter enhances the temperature distribution when the plate is hot.


  1. [1]  Mahanthesh, B., Mabood, F., Gireesha, B.J., and Gorla, R.S.R. (2017), Effects of chemical reaction and partial slip on the three dimensional flow of a nanofluid impinging on an exponentially stretching surface, European Physical Journal Plus, 132(3).
  2. [2]  Chamkha, A.J., Aly, A.M., and Mansour, M.A. (2010), Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and chemical reaction effects, Chemical Engineering Communications, 197(6), 846-858.
  3. [3]  Hayat, T., Hina, S., and Ali, N. (2010), Simultaneous effects of slip and heat transfer on the peristaltic flow, Communications in Nonlinear Science and Numerical Simulation, 15(6), 1526-1537.
  4. [4]  Motsa, S.S. and Shateyi, S. (2012), Successive linearization analysis of the effects of partial slip, thermal diffusion, and diffusion thermo on steady MHD convective flow due to a rotating disk, Mathematical Problems in Engineering, 2012, Article ID 397637, 15 pages.
  5. [5]  Shateyi, S. and Mabood, F. (2017), MHD mixed convection slip flow near a stagnation-point on a non-linearly vertical stretching sheet in the presence of viscous dissipation, thermal Science, 21(6), 2731-2745.
  6. [6]  Prasannakumara, B.C., Krishnamurthy, M.R., Gireesha, B.J., and Gorla, R.S.R. (2016), Effect of multiple slips and thermal radiation on MHD flow of jeffery nanofluid with heat transfer, Journal of Nanofluids, 5(1), 82-93.
  7. [7]  Mabood, F., Shafiq, A., Hayat, T., and Abelman, S. (2017), Radiation effects on stagnation point flow with melting heat transfer and second order slip, Results in Physics, 7, 31-42.
  8. [8]  Mabood, F. and Shateyi, S. (2019), Multiple slip effects on MHD unsteady flow heat and mass transfer impinging on permeable stretching sheet with radiation, Model. Simul. Eng. 2019, 3052790.
  9. [9]  Sharidan, S., Mahmood, T., and Pop, I. (2006), Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet, Int. J. Appl. Mech. Eng., 11, 647-654.
  10. [10]  Elbashbeshy, E.M.A. and Bazid, M.A.A. (2004), Heat transfer over an unsteady stretching surface, Heat Mass Transfer, 41, 1-4.
  11. [11]  Grubka, L.J. and Bobba, K.M. (1985), Heat transfer characteristic of a continuous stretching surface with variable temperature, J. Heat Transfer, 107, 248-250.
  12. [12]  Magyari, E. and Kellerm B. (1999), Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface, J. Phys. D: Appl. Phys., 32, 577-585.
  13. [13]  Nazar, R., Amin, N., Filip, D., and Pop, I. (2004), Unsteady boundary layer flow in the region of the stagnation point on the stretching sheet, Int. J. Eng. Sci., 42, 1241-1253.
  14. [14]  Magyari, E. and Keller, B. (2000), Exact solutions for self-similar boundary-layer flows induced by permeable stretching surfaces, Eur. J. Mech. B-Fluids, 19, pp.109-122.
  15. [15]  Ibrahim, S.M., Mabood, F., Suneetha, K., and Lorenzini, G. (2017), Effects of chemical reaction on combined heat and mass transfer by laminar mixed convection flow from vertical surface with induced magnetic field and radiation, Journal of Engineering Thermophysics, 26(2), 234-255.
  16. [16]  Vijaya, N., Hari Krishna, Y., Kalyani, K., and Reddy, G.V.R. (2018), Soret and radiation effects on an unsteady flow of a casson fluid through porous vertical channel with expansion and contraction, Frontiers in heat and mass transfer, (FHMT) 11, 1-11.
  17. [17]  Reddy, G.V.R. and Krishna, Y.H. (2018), Soret and dufour effects on MHD micropolar fluid flow over a linearly stretching sheet, through a non-darcy porous medium, International Journal of Applied Mechanics and Engineering, 23(2), 485-502
  18. [18]  Arundhati, V., Chandra Sekhar, K.V., Prasada Rao, D.R.V., and Sreedevi, G.(2018), Non-Darcy convective heat and mass transfer flow through a porous medium in vertical channel with soret, dufour and chemical reaction effects, JP Journal of Heat and Mass Transfer, 15(2), 213-240
  19. [19]  Suneetha, K., Ibrahim, S.M., Reddy, G.V.R.(2018), Radiation and heat source effects on MHD flow over a permeable stretching sheet through porous stratum with chemical reaction, Multidiscipline Modeling in Materials and Structure, 14(5), 1101-1114
  20. [20] Vijaya, N., Madhavi, M.R., and Krishna, Y.H. (2018), Boundary layer flow of a mixed convective nanofluid over a vertical circular cylinder under the influence of magnetic field, heat radiation and external surface temperature, International Journal of Mechanical and Production Engineering Research and Development, 8(2), 411-420,
  21. [21]  Krishna, Y.H., Reddy, G.V.R., and Makinde O.D. (2018), Chemical reaction effect on MHD flow of casson fluid with porous stretching sheet, Defect and Diffusion Forum, 389, 100-109.
  22. [22]  Kumar, D.S., Murthy, C.H.V., Anusha, S., and Makinde, O.D. (2019), Mixed convective flow of a visco elastic fluid between two porous parellel plates, International Journal of Recent Technology and Engineering, 8(3), 4830-4834.
  23. [23]  Manjula, V. and Chandra Sekhar, K.V. (2019), Effect of Soret number and heat source on unsteady MHD Casson fluid flow past an inclined plate embedded in porous medium, ARPN Journal of Engineering and Applied Sciences, 14(11), PP.2069-2079.
  24. [24]  Vijaya, K. and Reddy, G.V.R. (2019), Magnetohydrodynamic casson fluid flow over a vertical porous plate in the presence of radiation, soret and chemical reaction effects, Journal of Nanofluids, 8(6), 1240-1248.
  25. [25]  Sujatha, T., Reddy, K.J., and Kumar, J.G. (2019), Chemical reaction effect on nonlinear radiative MHD nanofluid flow over cone and wedge, Defect and Diffusion Forum, 393, 83-102.
  26. [26]  Kallepalli, N.S., Rajasekhar, K., and Murthy, C.V.R., (2019), Influence of critical parameters on an unsteady state mhd flow in a porous channel with exponentially decreasing suction, Journal of Mathematical and Computational Science, 9(6), 764-783.
  27. [27]  Sivaiah, G., Reddy, K.J., Reddy, P.C., and Raju, M.C. (2019), Numerical study of mhd boundary layer flow of a viscoelastic and dissipative fluid past a porous plate in the presence of thermal radiation, International Journal of Fluid Mechanics Research, 46(1), 27-38.
  28. [28]  Motsa, S.S. (2012), New iterative methods for solving nonlinear boundary value problems. Fifth annual workshop on computational applied mathematics and mathematical modeling in fluid flow, School of mathematics, statistics and computer science, Pietermaritzburg Campus, 9-13.
  29. [29]  Ali, M.E. (1994), Heat Transfer Characteristics of a Continuous Stretching Surface, warme-und Stoffubertragung, 29(4), 227-234.