Heat Transfer. 2020;1–30. wileyonlinelibrary.com/journal/htj © 2020 Wiley Periodicals, Inc. | 1 Received: 3 December 2019 | Revised: 22 February 2020 | Accepted: 22 March 2020 DOI: 10.1002/htj.21733 RESEARCH ARTICLE Nonlinear convective boundary layer flow of micropolar‐couple stress nanofluids past permeable stretching sheet using Cattaneo‐Christov heat and mass flux model Wubshet Ibrahim 1 | Gosa Gadisa 2 1 Department of Mathematics, Ambo University, Ambo, Ethiopia 2 Department of Mathematics, Wollega University, Nekemte, Ethiopia Correspondence Wubshet Ibrahim, Department of Mathematics, Ambo University, Ambo, Ethiopia. Email: wubshetib@yahoo.com Abstract The present work aims to examine the effects of viscous dissipation and unsteadiness parameters on nonlinear convective laminar boundary layer flow of micropolar‐couple stress nanofluid past a permeable stretching sheet with non‐Fourier heat flux model in the presence of suction/injection variable. The un- steadiness in the flow, temperature, and concentra- tion profile is caused by the time‐dependence of the stretching velocity, surface temperature, and surface concentration of the boundary layer flow. Similarity transformation is applied to transform the time‐ dependent boundary layer flow equations into the corresponding highly nonlinear coupled ordinary differential equations with appropriate boundary conditions. The robust numerical technique called Galerkin finite element method is used to solve the obtained dimensionless governing equations of the flow. The effects of Eckert number, unsteadiness parameter, suction/injection parameter, mixed con- vection parameter, material parameter, Schmidt number, and couple stress parameter on linear velo- city, angular velocity, temperature, concentration, local skin friction coefficient, local wall couple stress, local Nusselt number, and local Sherwood number is