Analysis of viscoelastic fluid flow with temperature dependent properties in plane Couette flow and thin annuli

• Published in: Applied mathematical modelling Vol. 34; no. 4; pp. 919 - 930
• Main Authors: Hashemabadi, S.H., Mirnajafizadeh, S.M.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.04.2010; Elsevier
• Subjects: Analytical and numerical techniques; Annulus; Couette flow; Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Heat transfer; Perturbation; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Temperature dependent properties; Viscoelastic; Viscous dissipation; Annulus; Couette flow; Temperature dependent properties; Perturbation; Viscous dissipation; Viscoelastic; Constitutive equation; Viscoelastic fluid; Viscosity; Viscoelasticity; Nusselt number; Annular space; Steady flow; Rotation speed; Thermomechanical properties; Physical properties; Steady state; Relaxation time; Temperature effects; Modelling; Rotating cylinder
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2009.07.001

The steady state flow in very thin annuli has been studied analytically for the case where the annular gap is much smaller than the radius of the inner cylinder and for the outer cylinder rotating at constant angular speed and the inner cylinder at rest. The cylinders were subjected to two different thermal boundary conditions. The exponential effect of temperature on the relaxation time and the viscosity coefficient was accounted into the governing differential equations using Nahme’s law. Effects of viscous dissipation as well as εDe 2 (viscoelastic index for SPTT constitutive equation) on the dimensionless velocity and temperature profiles have been investigated. Results show that while the properties of the fluid depend on temperature, the velocity and temperature profiles are different compared to those obtained with constant physical properties. The Nahme–Griffith number increases whereas εDe 2 as a viscoelastic index decreases when temperature dependent physical properties are considered. In addition, the results indicate that the viscous dissipation has a sensible effect on heat transfer and the Nusselt number decreases with an increase in the Nahme–Griffith number.