Read More.

Call for Paper - December – 2022 Edition   

(SJIF Impact Factor: 5.966) (IJIFACTOR 3.8, RANKING: A+) (PIF: 3.460)

IJATCA solicits original research papers for the December – 2022 Edition.
Last date of manuscript submission is December 30, 2022.


Analysis of stability and dual solution of MHD outer fluid velocity with partial slip on a stretching cylinder

Volume: 1 Issue: 1
Year of Publication: 2019
Authors: Vikas Poply, Phool Singh, A. K. Yadav


This manuscript discuss about the dual nature of solution, in MHD outer velocity flow, along with the stability analysis on stretching cylinder with partial slip. Differential equations are acquired by converting heat and momentum governing equations with similarity transformations. The numerical solutions of the transformed equations were computed by the Runge-Kutta Fehlberg scheme using shooting procedure. For stretching cylindrical surface, we obtained that the solution is not unique having partial slip. The dual nature of the solution exists in small range of outer velocity parameter on stretching surface. Stability analysis reveals that for lower branch (unstable solution) and upper branch (stable solution), the smallest eigenvalue is negative and positive respectively for the distinct entries of outer velocity parameter. The limit of the dual solution is -0.03211 = λ_c≤λ≤λ_r= 0.12651 for slip parameter, V = 0.1. Also, the influences of slip parameter, outer velocity parameter and magnetic parameter have been discussed on heat and flow transportation, which are presented through tables and figures.


  1. Ali, M. E. (1994). Heat transfer characteristics of a continuous stretching surface. Wrme - und Stoffbertragung, 29, 227-234.

  2. Andersson, H. I. (2002). Slip flow past a stretching surface. Acta Mechanica, 158, 121-125.

  3. Ariel, P. (2008). Two dimensional stagnation point flow of an elastico-viscous fluid with partial slip. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift fr Angewandte Mathematik und Mechanik, 88, 320-324.

  4. Awaludin, I. S., Weidman, P. D., & Ishak, A. (2016). Stability analysis of stagnation-point flow over a stretching/shrinking sheet. AIP Advances, 6, 045308.

  5. Crane, L. J. (1970). Flow past a stretching plate. Zeitschrift fr angewandte Mathematik und Physik, 21, 645-647.

  6. Dhanai, R., Rana, P., & Kumar, L. (2015). Multiple solutions of MHD boundary layer flow and heat transfer behavior of nanofluids induced by a power-law stretching/shrinking permeable sheet with viscous dissipation. Powder Technology, 273, 62-70.

  7. Dhanai, R., Rana, P., & Kumar, L. (2016). Critical values in slip flow and heat transfer analysis of non-Newtonian nanofluid utilizing heat source/sink and variable magnetic field: Multiple solutions. Journal of the Taiwan Institute of Chemical Engineers, 58, 155-164.

  8. Gupta, P. S., & Gupta, A. S. (1977). Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering, 55, 744-746.

  9. Harris, S. D., Ingham, D. B., & Pop, I. (2009). Mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport Porous Media, 77, 267-285.

  10. Ishak, A., Nazar, R., & Pop, I. (2008). Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder. Energy Conversion and Management, 49, 3265-3269.

  11. Lin, H., & Shih, Y. (1980). Laminar boundary layer heat transfer along static and moving cylinders. Journal of the Chinese Institute of Engineers, 3, 73-79.

  12. Lok, Y. Y., Merkin, J. H., & Pop, I. (2012). Mixed convection flow near the axisymmetric stagnation point on a stretching or shrinking cylinder. International Journal of Thermal Sciences, 59, 186-194.

  13. Mahapatra, T. R., Nandy, S. K., Vajravelu, K., & Van Gorder, R. A. (2012). Stability analysis of the dual solutions for stagnation-point flow over a non-linearly stretching surface. Meccanica, 47, 1623-1632.

  14. Malik, M. Y., Salahuddin, T., Hussain, A., & Bilal, S. (2015). MHD flow of tangent hyperbolic fluid over a stretching cylinder: using Keller box method. Journal of Magnetism and Magnetic Materials, 395, 271-276.

  15. Mat, N. A. A., Arifin, N. M., Nazar, R., & Bachok, N. (2015).Boundary layer stagnation point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface. Applied Mathematics, 6, 466-475.

  16. Merkin, J. H. (1985). On dual solutions occurring in mixed convection in a porous medium. Journal of Engineering Mathematics, 20, 171-179.

  17. Mukhopadhyay, S. (2013). MHD boundary layer slip flow along a stretching cylinder. Ain Shams Engineering Journal, 4, 317-324.

  18. Paullet, J., & Weidman, P. (2007). Analysis of stagnation point flow toward a stretching sheet. International Journal of Non-Linear Mechanics, 42, 1084-1091.

  19. Poply, V., Singh, P., & Yadav, A. K. (2018). Stability analysis of MHD outer velocity flow on a stretching cylinder. Alexandria Engineering Journal, 57, 2077-2083.

  20. Sharma, R., Ishak, A., & Pop, I. (2014). Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet. Computers and Fluids, 102, 94-98.

  21. Singh, P., Tomer, N. S., Kumar, S., & Sinha, D. (2010). MHD oblique stagnation-point flow towards a stretching sheet with heat transfer. International Journal of Applied Mathematics and Mechanics, 6(13), 94-111.

  22. Takhar, H. S., Chamkha, A. J., & Nath, G. (2000). Combined heat and mass transfer along a vertical moving cylinder with a free stream. Heat and Mass Transfer, 36, 237-246.

  23. Vajravelu, K., Prasad, K. V., & Santhi, S. R. (2012). Axisymmetric magneto-hydrodynamic (MHD) flow and heat transfer at a non-isothermal stretching cylinder. Applied Mathematics and Computation, 219, 3993-4005.

  24. Wang, C. Y. (1988). Fluid flow due to a stretching cylinder. The Physics of Fluids, 31, 466-468.

  25. Wang, C. Y., & Ng, C. O. (2011). Slip flow due to a stretching cylinder. International Journal of Non-Linear Mechanics, 46, 1191-1194.

  26. Yadav, R. S., & Sharma, P. R. (2014). "Effects of porous medium on MHD fluid flow along a stretching cylinder," Annals of Pure and Applied Mathematics, 6(1), 104-113.


Partial slip, Stretching cylinder, MHD, Stability analysis.

© 2022 International Journal of Advanced Trends in Computer Applications
Foundation of Computer Applications (FCA), All right reserved.
Vision & Mission | Privacy Policy | Terms and Conditions