×

Analysis of viscoelastic fluid flow with temperature dependent properties in plane Couette flow and thin annuli. (English) Zbl 1185.76433

Summary: 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 \(\epsilon De^{2}\) (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 \(\epsilon De^{2}\) 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.

MSC:

76A10 Viscoelastic fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Maron, D. M.; Cohen, S., Hydrodynamics and heat/mass transfer near rotating surfaces, Adv. Heat Transfer, 21, 141-183 (1991)
[2] Beris, A. N.; Armstrong, R. C.; Brown, R. A., Perturbation theory for viscoelastic fluids between eccentric rotating cylinders, J. Non-Newtonian Fluid Mech., 13, 109-143 (1983) · Zbl 0548.76010
[3] Khellaf, K.; Lauriat, G., Numerical study of heat transfer in a non-Newtonian Carreau-fluid between rotating concentric vertical cylinders, J. Non-Newtonian Fluid Mech., 89, 45-61 (2000) · Zbl 0963.76008
[4] Mirzazadeh, M.; Escudier, M. P.; Rashidi, F.; Hashemabadi, S. H., Purely tangential flow of a PTT-viscoelastic fluid within a concentric annulus, J. Non-Newtonian Fluid Mech., 129, 88-97 (2005) · Zbl 1195.76099
[5] Pinho, F. T.; Coelho, P. M., Fully-developed heat transfer in annuli for viscoelastic fluids with viscous dissipation, J. Non-Newtonian Fluid Mech., 138, 7-21 (2006) · Zbl 1195.76104
[6] Phan-Thien, N.; Tanner, R. T., A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech., 2, 353-365 (1977) · Zbl 0361.76011
[7] Phan-Thien, N., A non-linear network viscoelastic model, J. Rheol., 22, 259-283 (1978) · Zbl 0391.76010
[8] Coelho, P. M.; Pinho, F. T.; Olivieira, P. J., Fully developed forced convection of the Phan-Thien-Tanner fluid in ducts with a constant temperature, Int. J. Heat Mass Transfer, 45, 1413-1423 (2002) · Zbl 1034.76053
[9] Hashemabadi, S. H.; Etemad, S. Gh.; Thibault, J.; Golkar Naranji, M. R., Analytical solution for dynamic pressurization of viscoelastic fluid, Int. J. Heat Fluid Flow, 24, 137-144 (2003)
[10] Hashemabadi, S. H.; Etemad, S. Gh.; Thibault, J., Forced convection heat transfer of Couette-Poiseuille flow of nonlinear viscoelastic fluids between parallel plates, Int. J. Heat Mass Transfer, 47, 3985-3991 (2004) · Zbl 1079.76633
[11] Hashemabadi, S. H.; Mirnajafizadeh, S. M., Secondary flows of simplified Phan-Thien Tanner (SPTT) non-linear viscoelastic fluid between parallel rotating disks, Macromol. Symp., 274, 55-64 (2008)
[12] Hashemabadi, S. H.; Mirnajafizadeh, S. M., Analytical solution of simplified Phan-Thien Tanner fluid between nearly parallel plates of a small inclination, J. Appl. Sci., 7, 9, 1271-1278 (2007)
[13] Tanner, R. I., Engineering Rheology (2000), Clarendon Press: Clarendon Press Oxford · Zbl 0533.76004
[14] Pinho, F. T.; Oliveira, P. J., Analysis of forced convection in pipes and channels with the simplified Phan-Thien-Tanner fluid, Int. J. Heat Mass Transfer, 43, 2273-2287 (2000) · Zbl 0965.76079
[15] Becker, L. E.; McKinley, G. H., The stability of viscoelastic creeping plane shear flows with viscous heating, J. Non-Newtonian Fluid Mech., 92, 109-133 (2000) · Zbl 0988.76032
[16] Bird, R. B.; Armstrong, R. C.; Hassager, O., Dynamics of Polymeric Liquids, vol. I (1987), John Wiley & Sons: John Wiley & Sons New York
[17] Turian, R. M.; Bird, R. B., Viscous heating in the cone-and-plate viscometer-II, Newtonian fluids with temperature-dependent viscosity and thermal conductivity, Chem. Eng. Sci., 18, 689-696 (1963)
[18] Hashemabadi, S. H.; Etemad, SGh; Golkar Narenji, M. R.; Thibault, J., Mathematical modeling of Laminar forced convection of simplified Phan-Thien-Tanner (SPTT) fluid between moving parallel plates, Int. Commun. Heat Mass Transfer, 30, 2, 197-205 (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.