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Due to the diversity and width applications of polymeric fluids in various industries the investigation of viscoelastic fluids is noted by many researchers. In this study, non-creep flow of viscoelastic fluid has investigated inside planar channel with gradual expansion for the expansion ratio of 1:3. The laminar and incompressible flow of viscoelastic fluid has been simulated numerically using finite volume method and PISO algorithm. The nonlinear PTT rheological model has been applied to study effect of elasticity property on the length of vortices in polymeric fluid flow. The investigation of symmetric and asymmetric vortices length in a wide range of Reynolds and Weissenberg numbers is the main purpose of present study. The three angles of 30, 45 and 60 degrees have been considered for influence of the expansion angles on the length of vortices. The study of polymeric fluids flow through the planar channel with gradual changes in cross section (with expansion angles less than 90 degrees) is the innovation of this research. Also the critical values of first and second for Reynolds and Weissenberg numbers have been expressed in various expansion angles and furthermore length of second and third vortices has been presented as a function of Reynolds and Weissenberg numbers. The length of symmetric vortices decreases with increment of elastic property at all expansion angles for values of Weissenberg numbers less than one. Whereas the growth of expansion angle leads to increase in the length of symmetric and asymmetric vortices for low Reynolds and Weissenberg numbers.

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In this paper, the heat transfer of viscoelastic fluid flow have numerically simulated inside a symmetric planar channel with 1:3 abrupt expansion. For modeling the rheological and nonlinear behavior of inertial flow related to the viscoelastic fluid, exponential form of the Phan Thien-Tanner (EPTT) model has been used. The thermal boundary condition of constant temperature has been considered at the inlet and on the walls of channel. Also, velocity is uniform and constant at the inlet of channel and its value is determined by the Reynolds number of flow. Due to the significant effect of temperature on the viscoelastic fluid properties, viscosity, relaxation time, specific heat capacity and thermal conductivity have been taken as a function of temperature and dissipation term has been employed in the energy equation. For coupling the governing equations, the PISO algorithm is utilized and finite volume method (FVM) is employed for discretizing these equations. In this study, the effect of inertial force is investigated on the velocity distribution, temperature distribution and variation of local and average Nusselt numbers in the expanded part of channel. Despite the symmetry in the planar channel, increasing the Reynolds number forms the symmetric and asymmetric flows inside the expanded part of channel. For asymmetric flows, increase of Reynolds number from 40 to 100 (growth of 2.5 times the Reynolds number) resulted in a 1.7-fold increase for the maximum values of local Nusselt numbers in the vicinity of the upper and lower walls of the channel expanded part.