Applied Mathematics and Computation 339 (2018) 820–836 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc Numerical simulation of couple stress nanofluid flow in magneto-porous medium with thermal radiation and a chemical reaction Hloniphile Sithole, Hiranmoy Mondal ∗ , Sicelo Goqo, Precious Sibanda, Sandile Motsa School of Mathematics, Statistics and Computer Science, University of KwaZulu Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa a r t i c l e i n f o Keywords: Couple stress nanofluid Boundary layer flow Spectral quasi-linearization method Thermal radiation a b s t r a c t We present a study of heat and mass transfer for a couple stress nanofluid flow in a magneto-porous medium with thermal radiation and heat generation. The flow is gener- ated by a stretching surface and the temperature and concentration distributions are stud- ied subject to nanoparticle Brownian motion and thermophoresis effects. The nonlinear model equations have been solved using a spectral quasi-linearization method. The solu- tion method has been used in a limited number of studies in the resent past. Its general reliability for a wider range of problems remains to be determined. Thus in order to deter- mine the accuracy of the solutions, and the convergence of the method, a qualitative pre- sentation of residual errors for different parameters is given. Additionally, for some special flow cases, the current results have been compared with previously published work and found to be in good agreement. A limited parametric study showing the influence of the flow parameters on the fluid properties is given. The numerical analysis of the residual error of PDEs and convergence properties of the method are also discussed. The method is computationally fast and gives very accurate results after only a few iterations using very few grid points in the numerical discretization process. The aim of this manuscript is to pay more attention of residual error analysis with heat and fluid flow on couple stress nanofluids to improve the system performance. Also the fluid temperature in the bound- ary layer region rise significantly for increasing the values of thermophoresis and Brownian motion parameter. The results show that wall shear stress increases by increasing couple stress parameter. © 2018 Elsevier Inc. All rights reserved. 1. Introduction Heat and mass transfer processes have been focused of extensive investigation for many decades due to the importance of these processes of physiological flows such as urine transport from kidneys to the bladder and the circulation of blood in small blood vessels. The theory of couple stress fluids, first introduced by Stokes [1] has been widely studied by researchers [2,3]. Couple stresses appear in fluids with very large molecules such as in synovial fluids, for example, Walicki and Walicka ∗ Corresponding author. E-mail address: hiranmoymondal@yahoo.co.in (H. Mondal). https://doi.org/10.1016/j.amc.2018.07.042 0096-3003/© 2018 Elsevier Inc. All rights reserved.