This paper deals with an unsteady magnetohydrodynamic (MHD) two-dimensional (2D) second-grade fluid flow towards a permeable exponentially stretching surface with homogeneous–heterogeneous reactions. The non-uniform heat source/sink, variable thermal conductivity and thermal radiation are considered to analyse the thermal attributes. The velocity slip effect is also taken into consideration at the boundary of the surface. The modelled equations of motions and energy are transformed into non-linear ODEs by suitable transformations. The Matlab Bvp4c approach is employed for the numerical solution of the equations. The impacts of various parameters are scrutinised using graphs. The physical quantities of interests such as Sherwood number,Nusselt number and skin friction are presented in the form of graphs and tables and discussed. The velocity profile diminishes by enhancing the values of the parameter of the porous medium. The temperature field rises with larger values of thermal radiation parameters. Decay in concentration profile is noted when the influence of homogeneous–heterogeneous reactions becomes larger. By increasing the values of the second-grade fluid parameter, the magnetic field parameter and the porous medium, the coefficient of skin friction increases, while it reduces by enhancing the values of the unsteady parameter.