This article presents a research for boundary layer flow and heat transfer of a Maxwell fluid over an exponential stretching surface with thermal stratifications. The effect of homogeneous and heterogeneous reaction are incorporated. Cattaneo–Christov heat flux model is used instead of Fourier law of heat conduction, which is recently proposed by Christov. This model predicts the impacts of thermal relaxation time on boundary layer. The transformed boundary layer equations are solved analytically by using Optimal homotopy analysis method. The effect of non-dimensional fluid relaxation time, thermal relaxation time, Prandtl number, Schmidt number and strength of homogeneous and heterogeneous reaction are demonstrated and exhibited graphically. The comparison of Cattaneo–Christov heat flux model and the Fourier’s law of heat conduction is also displayed. Keywords: Cattaneo–Christov heat model, Maxwell fluid, Thermal stratification, Homogeneous and heterogeneous reaction