In this article, the steady-state flow of a Hagen-Poiseuille model in a circular pipe is considered and entropy generation due to fluid friction and heat transfer is examined. Because of variation in fluid viscosity, the entropy generation in the flow varies. In this model, Arrhenius law is applied for temperature equation-dependent viscosity, and the influence of viscosity parameters on the entropy generation number and distribution of temperature and velocity is investigated. The governing momentum and energy equations, which are coupled due to the dissipative term in the energy equation, were solved by analytical techniques. The solutions of equations via perturbation method and homotopy perturbation method are obtained and then compared with those of numerical solutions. It is found that the fluid viscosity influences considerably the temperature distribution in the fluid close to the pipe wall, and increasing pipe wall temperature enhances the rate of entropy generation.