Abstract
This paper considers the problem of viscous dissipation in power-law fluid flow through a tube of circular cross section. The solution to the problem is obtained by a series expansion about the complete eigenfunctions system of a Sturm-Liouville problem. The eigenfunctions and eigenvalues of this Sturm-Liouville problem are obtained by Galerkin’s method. The Graetz problem is also considered. Numerical examples are given for a viscous fluid with unit Brinkman number.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standard, Applied Mathematics Series (1972)
Agur, E.E., Vlachopoulos, J.: Heat transfer to molten polymer flow in tubes. J. Appl. Polm. Sci. 26, 765–773 (1981)
Barletta, A.: Fully developed laminar forced convection in circular ducts for power-law wall with viscous dissipation. Int. J. Heat Mass Transfer 40(1), 15–26 (1997)
Barron, R.F., Wang, X., Warrington, R.O., Ameel, T.: Evaluation of the eigenvalues for the Graetz problem in slip-flow. Int. Comm. Heat Mass Transfer 23(4), 563–574 (1996)
Ciarlet, P.C., Lions, J.L.: Handbook of numerical analysis, vol. II. Elsevier, Amsterdam (1991)
Gottifredi, J.C., Quiroga, O.D., Floree, A.F.: Heat Transfer to Newtonian and non-Newtonian Fluids Flowing in a Laminar Regime. Int. J. Heat Mass Transfer 26, 1215–1220 (1983)
Gradstein, S., Rijik, I.M.: Tables of Integrals, Sums, Serials, and Products, Nauka, Moscow (in Russian) (1971)
Graetz, L.: Uber die Wärmeleitungsfähigheit von Flűssigkeiten. Ann. Phys. Chem. 25, 337–357 (1885)
Housiadas, C., Larrodé, F.E., Drossinos, Y.: Numerical evaluation of the Graetz series. Int. J. Heat Mass Transfer 42, 3013–3017 (1999)
Johnston, P.R.: A Solution Method for the Graetz Problem for non-Newtonian Fluids with Dirichlet and Neumann Boundary Conditions. Math. Comput. Model 19, 1–19 (1994)
Őzisik, M.N., Sadeghipour, M.S.: Analytic solution for the eigenvalues and coefficients of the Graetz problem with third kind boundary condition. Int. J. Heat Mass Transfer 25(5), 736–739 (1982)
Papoutsakis, E., Ramkrishna, D., Lim, H.C.: The Extended Graetz Problem with Prescribed Wall Flux. AIChE J. 26(779), 779–787 (1980)
Papoutsakis, E., Ramkrishna, D., Lim, H.C.: The Extended Graetz Problem with Dirichlet wall Boundary Conditions. Appl. Sci. Res. 36(13) (1980)
Papoutsakis, E.: Nusselt numbers Hear Entrance of Heat-Exchange Section in Flow Systems. AIChE J. 27(4), 687–689 (1981)
Rice, R.G., Duong, D.D.: Applied Mathematics and Modeling for Chemical Engineers. John Wiley &Sons, New York (1995)
Sankarasubramanian, R., Gill, W.N.: Unsteady Convective Diffusion with Interphase mass Transfer. Proc. Roy. Soc. Lond. A 333(115) (1973)
Shah, R.K., London, A.L.: Laminar Flow Forced Convection in Ducts. Academic Press, New York (1978)
Shih, Y.P., Tsou, J.D.: Extended Leveque Solutions for Heat Transfer to Power-law Fluids in Laminar Flow in a Pipe. Chem. Eng. J. 15, 55–62 (1978)
Sneddon, I.N.: Fourier transform, McGraw-Hill Book Company, Inc., New York, Toronto, London (1951)
Valkó, P.P.: Solution of the Graetz–Brinkman Problem with the Laplace Transform Galerkin Method. Int. J. Heat Mass Transfer 48, 1874–1882 (2005)
Wei, D., Zhang, Z.: Decay estimates of heat transfer to molten polymer flow in pipes with viscous dissipation. Electronic Journal of Differential Equations 39, 1–14 (2001)
Wei, D., Luo, H.: Finite element solutions of heat transfer in molten polymer flow in tubes with viscous dissipation. Int. J. Heat Mass Transfer 46, 3097–3108 (2003)
William, H.P.: Numerical Recipes in Pascal. Cambridge University Press, Cambridge (1989)
Ybarra, R.M., Eckert, R.E.: Viscous Heat Generation in Slit Flow. AiChE Journal 26(5), 751–762 (1980)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Boaca, T., Boaca, I. (2008). Laminar Forced Convection in Circular Duct for Power-Law Fluid. In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science I. Lecture Notes in Computer Science, vol 4750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79299-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-79299-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79298-7
Online ISBN: 978-3-540-79299-4
eBook Packages: Computer ScienceComputer Science (R0)