An exact analysis on heat convection of nonlinear viscoelastic flows in isothermal microtubes under slip boundary condition

Abstract

In this paper, forced convective heat transfer of Phan–Thien–Tanner fluid in isothermal microtubes is studied analytically. The nonlinear Navier slip law is used to model the slip boundary condition at microtubes wall. The second-order eigenvalue form of related ODE is solved using the Frobenius method and the temperature distribution obtained in the form of power series. The Nusselt number is also calculated using the modal analysis technique. The effects of Weissenberg number, slip coefficient, and Navier index on velocity profile, temperature distribution and Nusselt number are investigated in detail. The results show that the increases in both slip coefficient and Navier index cause to increases in slip velocity and maximum dimensionless temperature at the wall and the microtube center, respectively. Moreover, the Nusselt number is enhanced by increasing the slip coefficient and Navier index parameters.