# Effects of fluid inertia and elasticity and expansion angles on recirculation and thermal regions of viscoelastic flow in the symmetric planar gradual expansions

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## Abstract

The formation and growth of symmetric and asymmetric recirculation regions play an important role in the viscous dissipations, temperature distribution, and heat transfer rate. In this study, the inertial and non-isothermal flow of viscoelastic fluid has been simulated in the planar channel with a 1:3 symmetric gradual expansion for different Reynolds and elasticity numbers at three expansion angles of 30°, 45°, and 60°. Also, the thermal boundary condition of constant temperature has been used on the walls, and the constitutive equation of exponential Phan Thien–Tanner has been employed for modeling the polymeric stresses of the viscoelastic fluid. Due to the significant effect of temperature on the properties of the viscoelastic fluid, and the role of viscous dissipation in heat generation, the fluid properties are considered temperature dependent, and the terms of viscous dissipation are considered in the energy equation. The main purpose of current study is to investigate the effects of fluid inertia and elasticity and the expansion angles on the flow pattern, heat transfer characteristics, and viscous dissipation of inertial viscoelastic flow in the planar channel with gradual expansions. Therefore, the streamlines, length of vortices, isothermal lines, total viscous dissipations, and local and mean Nusselt numbers (*Nu*) have been examined inside the channel expansion for different Reynolds and elasticity numbers in the range of \( 10 \le Re \le 100 \) and \( 0.01 \le El \le 2 \). The results show that the maximum values of local Nusselt numbers are enhanced by increasing the Reynolds and elasticity numbers and the expansion angle for the hydrodynamically and thermally developing conditions.

## Keywords

Expansion angle Reynolds number Elasticity number Nusselt number Total viscous dissipations Length of vortices## References

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