First and second laws analysis of viscoelastic fluid with temperature dependent properties for Couette-Poiseuille flow

The entropy analysis of viscoelastic fluid obeying the simplified Phan-Thien-Tanner (SPTT) model with variable thermophysical properties are obtained for laminar, steady state and fully developed Couette-Poiseuille flow. The homotopy perturbation method (HPM) allows us to solve nonlinear momentum and energy differential equations. The Reynold's model is used to describe the temperature dependency of thermophysical properties. Results indicate that the increase of the group parameter ($Br/\Omega$) and the Brinkman number (Br) which show the power of viscous dissipation effect; increases the entropy generation while increasing fluid elasticity ($\epsilon {De}^2$) decreases the generated entropy. Increasing the Reynolds variational parameter ($\alpha$) which control the level of temperature dependence of physical properties attenuate entropy generation when moving plate and applied pressure gradient have the opposite direction and decreases entropy generation when moving plate and applied pressure gradient have the same direction or both plates are at rest. Also, increasing elasticity reduces the difference between variable and constant thermophysical properties cases. These results may give guidelines for cost optimization in industrial processes.