Unsteady Stagnation Point Flow of Mass and Heat Transfer over a Stretching/Shrinking Sheet with Suction or Injection

References

[1] D. Ingham, I. Pop (Eds.), Transport Phenomena in Porous Media, Oxford, 2005.

[2] D.A. Nield, A. Bejan, Convection in Porous Media, third ed., Springer, New York, 2006.

[3] Okedoye, A.M., Unsteady MHD Mixed Convection Flow past an Oscillating Plate with Heat Source/Sink, J. Naval Architect. Marine Eng., vol. 11, pp. 167–176, 2014.

[4] G. Ahmed, Muhammad Sajid, Thin-film flow of MHD third grade fluid in a porous space, Porous Media 12 (2009) 65–75.

[5] Masood Khan, R. Ellahi, Exact solution of oscillatory rotating flows of a generalized Oldroyd-B fluid through porous medium.: J. Porous Media. 12 (2009) 777–788.

[6] S. Abelman, E. Momoniat, T. Hayat, Steady MHD flow of a third-grade fluid in a rotating frame and porous space, Nonlinear Anal.: Real World Appl. 10 (6) (2009) 3322–3328.

[7] R. Ellahi, T. Hayat, F.M. Mahomed, The analytical solutions for magnetohydrodynamic flow of a third order fluid in a porous medium, Zeitschrift Fur Naturforschung A 64 (9) (2009) 531–539.

[8] T. Hayat, H.M. Mamboundou, F.M. Mahomed, A note on some solutions for the flow of a fourth grade fluid in a porous space, Nonlinear Anal.: Real World Appl. 10 (1) (2009) 368–374.

[9] M. Husain, T. Hayat, C. Fetecau, A note on decay of potential vortex in an Oldroyd-B fluid through a porous space, Nonlinear Anal.: Real World Appl. 10 (4) (2009) 2133–2138.

[10] T. Hayat, R. Naz, M. Sajid, On the homotopy solution for Poiseuille flow of a fourth-grade fluid, Commun. Nonlinear Sci. Numer. Simul. 15 (3) (2010) 581–589.

[11] T. Hayat, S. Nadeem, S. Asghar, A.M. Siddiqui, effects of hall current on unsteady flow of a second-grade fluid in a rotating system, Chem. Eng. Commun. 192 (2005) 1272–1284.

[12] T. Hayat, S. Mumtaz, Resonant oscillations of a plate in an electrically conducting rotating Johnson–Segalman fluid, Comput. Math. Appl. 50 (2005) 669–1676.

[13] T. Hayat, Exact solutions to rotating flows of a Burgers’ fluid, Comput. Math. Appl. 52 (2006) 1413–1424.

[14] Z. Abbas, T. Javed, M. Sajid, N. Ali, Unsteady MHD flow and heat transfer on a stretching sheet in a rotating fluid, J. Taiwan Inst. Chem. Eng. 41 (2010) 644–650.

[15] N.T.M. Eldabe, Sallam N. Sallam, Mohamed Y. Abou-zeid, Numerical study of viscous dissipation effect on free convection heat and mass transfer of MHD non-Newtonian fluid flow through a porous medium, J. Egyptian Math. Soc. 20 (2012)139–151

[16] Mohamed Abd El-Aziz 1 and Ahmed A. Afify (2018): Influences of Slip Velocity and Induced Magnetic Field on MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet. Mathematical Problems in Engineering Volume 2018, Article ID 9402836, 11 pages https://doi.org/10.1155/2018/9402836.

[17] H. I. Andersson, J. B. Aarseth, and B. S. Dandapat, “Heat transfer in a liquid film on an unsteady stretching surface,” International Journal of Heat and Mass Transfer, vol. 43, no. 1, pp. 69–74, 2000.

[18] E. M. A. Elbashbeshy and M. A. A. Bazid, “Heat transfer over an unsteady stretching surface,” Heat and Mass Transfer/Waerme-und Stoffuebertragung, vol. 41, no. 1, pp. 1–4, 2004.

[19] T. G. Fang, “Boundary layer flow over a shrinking sheet with power-law velocity,” International Journal of Heat and Mass Transfer, vol. 51, no. 25-26, pp. 5838–5843, 2008.

[20] R. Tsai, K. H. Huang, and J. S. Huang, “Flow and heat transfer over an unsteady stretching surface with non-uniform heat source,” International Communications in Heat and Mass Transfer, vol. 35, no. 10, pp. 1340–1343, 2008.

[21] M. Sajid and T. Hayat, “The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet,” Chaos, Solitons and Fractals, vol. 39, no. 3, pp. 1317–1323, 2009.

[22] T. G. Fang, J. Zhang, and S. S. Yao, “Viscous flow over an unsteady shrinking sheet with mass transfer,” Chinese Physics Letters, vol. 26, no. 1, Article ID 014703, 2009.

[23] S. D. Adhikary and J. C. Misra, “Unsteady two dimensional hydromagnetic flow and heat transfer of a fluid,” International Journal of Applied Mathematics and Mechanics, vol. 7, no. 4, pp. 1–20, 2011.

[24] F. M. Ali, R. Nazar, N. M. Arifin, and I. Pop, “Unsteady shrinking sheet with mass transfer in a rotating fluid,” International Journal for Numerical Methods in Fluids, vol. 66, no. 11, pp. 1465–1474, 2011.

[25] T. G. Fang, C. F. F. Lee, and J. Zhang, “The boundary layers of an unsteady incompressible stagnation point flow with mass transfer,” International Journal of Non-Linear Mechanics, vol. 46, no. 7, pp. 942–948, 2011.

[26] K. Bhattacharyya, “Dual solutions in unsteady stagnation-point flow over a shrinking sheet,” Chinese Physics Letters, vol. 8, Article ID 084702, 2011.

[27] N. M. A. Nik Long, M. Suali, A. Ishak, N. Bachok, and N. M. Arifin, “Unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet,” Journal of Applied Sciences, vol. 11, no. 20, pp. 3520–3524, 2011.

[28] https://en.m.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient

@article{1704162,
      author = {Sindi M. Chigozie, Raphael E. Asibor, Akindele M. Okedoye},
      title = {Unsteady Stagnation Point Flow of Mass and Heat Transfer over a Stretching/Shrinking Sheet with Suction or Injection},
      journal = {Iconic Research And Engineering Journals},
      year = {2023},
      volume = {6},
      number = {9},
      pages = {113-126},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1704162.pdf},
      abstract = {The interest in this work is due to the many practical applications which can be modeled or approximated. as transport phenomena in porous media. We consider the impacts of unsteady stagnation point flow of mass and heat transfer over a stretching/shrinking sheet with suction or injection in a stretchable porous device. The higher order nonlinear partial differential equations are converted into first order simultaneous linear differential equations using suitable similarity variables and then transformed to initial value problem. and are solved numerically using Runge?Kuta fourth order method along with shooting technique. The solution for the non-magnetic and buoyancy case is chosen as an initial guess and the iterations using Euler scheme are continued till convergence within prescribed accuracy is achieved, with the corrections incorporated in subsequent iterative steps until convergence, which is used to obtain the values of our initial guesses.  As a result of the numerical calculations, the velocity, temperature and chemical species distributions for the flow are obtained and are displayed in figures and tables for different values flow governing parameters. From the result obtained it was observed that thermal Grashof number and buoyancy ratio aided the velocity for cooling problem while unsteadiness parameter increases the velocity distribution. Other emerging parameters were presented and discussed.},
      keywords = {Runge?Kutta, stagnation point, heat transfer, transport phenomena, porous media, shooting, stagnation point flow.},
      month = {March},
  }