Analytical solution for the convection of Phan-Thien-Tanner fluids in isothermal pipes

• A solution for heat convection of exponential PTT fluid is presented.
• The Frobenius method is used to find the solution of an isothermal system.
• Accurate correlations for Nusselt number of LPTT and EPTT fluid are obtained.

In this paper, EXACT analytical solutions for convective heat transfer of both linear and exponential Phan-Thien Tanner fluids (LPTT and EPTT) through an isothermal pipe are presented. The previous studies are limited to the successive approximations or guessing method for just LPTT fluid (simplified PTT). Here, due to the eigenvalue form of heat convection equation, the temperature distribution and Nusselt number are calculated based on the modal analysis technique. The non-singular Taylor series of temperature distributions of LPTT and EPTT viscoelastic flows are obtained using the Frobenius method. The accurate correlations for the Nusselt number and core temperature are derived. The solutions are validated in three ways and the effect of the Weissenberg number and extensional parameter of PTT model on heat convection in isothermal pipes are investigated in detail. The proposed method of solution could be generalized to solve the other non-Newtonian flows in isothermal pipes.