Investigation of pitchfork bifurcation phenomena effects on heat transfer of viscoelastic flow inside a symmetric sudden expansion

• Published in: Physics of fluids (1994) 2017-11, Vol.29 (11), p.113101
• Main Authors: Shahbani-Zahiri, A., Hassanzadeh, H., Shahmardan, M. M., Norouzi, M.
• Format: Article
• Language: English
• Subjects: Bifurcations; Computational fluid dynamics; Computer simulation; Elasticity; Finite volume method; Fluid dynamics; Fluid flow; Fluids; Heat transfer; Mathematical models; Nusselt number; Physics; Rheological properties; Temperature dependence; Temperature distribution; Viscoelastic fluids; Viscoelasticity; Viscosity
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.5009434

In this paper, the inertial and non-isothermal flows of the viscoelastic fluid through a planar channel with symmetric sudden expansion are numerically simulated. Effects of pitchfork bifurcation phenomena on the heat transfer rate are examined for the thermally developing and fully developed flow of the viscoelastic fluid inside the expanded part of the planar channel with an expansion ratio of 1:3. The rheological model of exponential Phan Thien-Tanner is used to include both the effects of shear-thinning and elasticity in fluid viscosity. The properties of fluids are temperature-dependent, and the viscous dissipation and heat stored by fluid elasticity are considered in the heat transfer equation. For coupling the governing equations, the PISO algorithm (Pressure Implicit with Splitting of Operator) is applied and the system of equations is linearized using the finite volume method on the collocated grids. The main purpose of this study is to examine the pitchfork bifurcation phenomena and its influences on the temperature distribution, the local and mean Nusselt numbers, and the first and second normal stress differences at different Reynolds, elasticity, and Brinkman numbers. The results show that by increasing the Brinkman number for the heated flow of the viscoelastic fluid inside the expanded part of the channel, the value of the mean Nusselt number is almost linearly decreased. Also, the maximum values of the local Nusselt number for the thermally developing flow and the local Nusselt number of the thermally fully developed flow are decremented by enhancing the Brinkman number.