The laminar boundary layer flow, heat and mass transfer of a third- grade non-Newtonian fluid past a vertical porous plate have been numerically studied. A similarity transformation is utilized to non-dimensionalize the governing nonlinear partial differential equations into a system of dimensionless coupled nonlinear partial differential equations. The dimensionless coupled nonlinear partial differential equations were successfully solved by the bivariate-spectral quasi-linearization method (BSQLM). The method has proved to be a very robust method due to its efficiency and accuracy.

non-Newtonian fluid, third-grade fluid, boundary layer, spectral collocation, Chebyshev differentiation, Chebyshev-Gauss-Lobatto collocation points, bivariate Lagrange interpolation.

Received: April 27, 2021; Accepted: June 12, 2021; Published: December 8, 2021

How to cite this article: S. Shateyi and V. M. Magagula, A numerical study of laminar boundary layer flow, heat and mass transfer of a third-grade non-Newtonian fluid past a vertical porous plate, JP Journal of Heat and Mass Transfer 24(2) (2021), 241-263. DOI: 10.17654/0973576321003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References

[1] A. Hussanan, M. Zuki Salleh, R. M. Tahar and I. Khan, Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating, PLoS One 9(10) (2014), e108763.
doi:10.1371/journal.pone.0108763.
[2] Nadir Yilmaz, Akshin S. Bakhtiyarov and Ranis N. Ibragimov, Experimental investigation of Newtonian and non-Newtonian fluid flows in porous media, Mech. Res. Commun. 36(5) (2009), 638-641.
[3] T. Hayat, F. Shahzad and M. Ayub, Analytical solution for the steady flow of the third-grade fluid in a porous half space, Appl. Math. Modelling 31 (2007), 2424-2432.
[4] Z. Shah, T. Gul, S. Islam, M. A. Khan, E. Bonyah, F. Hussain, S. Mukhtar and M. Ullah, Three dimensional third grade nanofluid flow in a rotating system between parallel plates with Brownian motion and thermophoresis effects, Results in Physics 10 (2018), 36-45.
[5] M. Ayub, A. Rasheed and T. Hayat, Exact flow of a third grade fluid past a porous plate using homotopy analysis method, Internat. J. Engrg. Sci. 41 (2003), 2091-2103.
[6] F. Abdul Gaffar, P. O. Anwar Beg and V. R. Prasad, Mathematical modeling of natural convection in a third-grade viscoelastic micropolar fluid from an isothermal inverted cone, Iran J. Sci. Technol. Trans. Mech. Eng. 44 (2020), 383-402.
[7] M. Hosseini, Z. Sheikholeslami and D. D. Ganji, Non-Newtonian fluid flow in an axisymmetric channel with porous wall, Propuls. Power Res. 2(4) (2013), 254-262.
[8] L. L. Debruge and L. S. Han, Heat transfer in a channel with a porous wall for turbine cooling application, ASME Journal of Heat Transfer 94(4) (1972), 385-390.
[9] A. Aziz and T. Aziz, MHD flow of a third-grade fluid in a porous half space with plate suction or injection: an analytical approach, Appl. Math. Comput. 218 (2012), 10443-10453.
[10] I. Pop and T. Watanabe, The effects of suction or injection in boundary layer flow and heat transfer on a continuous moving surface, Technische Mechanik 13 (1992), 49-54.
[11] S. S. Motsa, et al., A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations, The Scientific World Journal 2014 (2014), ID: 581987.
[12] M. Nazari, F. Salah and Z. A. Aziz, Analytic approximate solution for the KdV equation with the homotopy analysis method, Matematika 28(1) (2012), 53-61.
[13] J. W. Cahn and J. E. Hillard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958), 258.
[14] Vinay Chandraker, Ashish Awasthi and Simon Jayaraj, Numerical treatment of Burger-Fisher equation, Procedia Technology 25 (2016), 1217-1225.
[15] S. S. Motsa and M. S. Ansari, Unsteady boundary layer flow and heat transfer of Oldroyd-B nanofluid towards a stretching sheet with variable thermal conductivity, Thermal Science 19(1) (2015), S239-S248.
[16] V. R. Prasad, S. A. Gaffar, K. E. Reddy, O. A. Beg and S. Krishnaiah, A mathematical study for laminar boundary-layer flow, heat, and mass transfer of a Jeffrey non-Newtonian fluid past a vertical porous plate, Heat Transf. Asian Res. 44 (2015), 189-210.
[17] H. Muzara, S. Shateyi and G. Tendayi Marewo, On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem, Open Physics 16(1) (2018), 554-562.
[18] S. A. Gaffar, V. R. Prasad and E. K. Reddy, Computational study of Jeffrey’s non-Newtonian fluid past a semi-infinite vertical plate with thermal radiation and heat generation/absorption, Ain Shams Eng. J. 8(2) (2017), 277-294.
[19] R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems, Amer. Elsevier, New York, 1965.
[20] B. Ahmad, J. J. Nieto and N. Shahzad, The Bellman-Kalaba-Lakshmikantham quasilinearization method for Neumann problems, J. Math. Anal. Appl. 257 (2001), 356-363.
[21] Lloyd N. Trefethen, Spectral methods in MATLAB Software, Environments, and Tools, 10, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000.
[22] M. Shamsi and M. Dehghan, Recovering a time-dependent coefficient in a parabolic equation from overspecified boundary data using the pseudospectral Legendre method, Numerical Methods for Partial Differential Equations 23 (2007), 196-210.
[23] C. G. Canuto, M. Y. Hussaini, A. M. Quarteroni and T. A. Zang, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation), Springer-Verlag, New York, Inc., 2007.