In this article, the nonlinear, steady-state boundary layer flow and heat transfer of an incompressible Eyring–Powell non-Newtonian fluid from a vertical porous plate is investigated. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order versatile, implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Eyring–Powell rheological fluid parameters (ε), the local non-Newtonian parameter based on length scale x (δ), Prandtl number (Pr), Biot number (γ) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. It is found that the velocity is reduced with increasing ε but temperature is increased. Increasing δ enhances velocity but reduces temperature. The increasing γ is observed to enhance both velocity and temperature. And an increasing Prandtl number Pr is found to decrease both velocity and temperature. © 2017, The Brazilian Society of Mechanical Sciences and Engineering.