Shear thinning fluids are widely used in the food and polymer industries due to their unique flow characteristics. The flow behavior of these fluids has been commonly studied using the Powell Eyring model under a small shear rate assumption. However, this assumption is not always valid. In this study, we explore the transport characteristics of a Powell Eyring fluid over a variable thicker sheet, not only at small shear rates but also at medium and high shear rates. Furthermore, we calculate the rate of entropy generation based on the assumptions. Generalized Powell–Eyring model of viscosity is used for the fluid, representing the re-arrangements of molecules in the forward and backward directions through the theory of potential energy. The model concludes the sensitivity of the viscosity from zero to infinite shear rate along time sale and exponent parameters. The model is used in the transport phenomena equations. The solution of the equation is obtained by using the numerical method and used to calculate the rate of entropy generation. The results are presented in the form of velocity and temperature profiles, the average rate of entropy generation, skin friction coefficient and Nusselt number under the influence of various viscosity parameters. It is found that velocity and temperature profiles are decreased and increased respectively against the time scale parameter.