Engineering Transactions, 29, 2, pp. 213-227, 1981

Monisothermal Poiseuille Flow of a Newtonian Fluid with Temperature Dependent Viscosity

Z. Nowak
Technical University of Kraków

K. Rup
Technical University of Kraków

In the present paper an attempt is made to apply the method of Vujanovic to the nonisothermal flow of a Newtonian fluid in a circular pipe. It is assumed that the dynamic viscosity of the fluid varies with temperature in a prescribed manner. By using the concept of "penetration depth" the problem under consideration is solved in two stages. Both the temperature and velocity distributions are determined approximately. The results obtained are compared with the numerical solution given recently in [4].

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


J. R. SELLERS, M. TRIBUS AND J. S. KLEIN, Heat transfer to laminar flow in round tube or fiat conduit-the Graetz problem extended, Trans. ASME, 78, 441, 1956.

W. M. KAYS, Numerical solutions for laminar flow heat transfer in circular tubes, Trans, ASME, 77, 1265, 1955.

U. GRIGULL and H. TRATZ, Thermischer Einlauf in ausgebildeter, laminarer Rohrstromung, Int. J. Heat Mass Transfer, 8, 889, 1965.

K. N. KRISHNAN and V. M. K. SASTRI, Numerical solution of thermal entry length problem with variable viscosities and viscous dissipation, Warme- und Stoffubertragung (Thermo- and Fluid Dynamics), 11, 73, Springer-Verlag, 1978.

B. VUJANOVIC, The practical use of Gauss principle of least constraint, Trans, ASME, Series E. J. Appl. Mechanics, 8, 491, 1976.

B. VUJANOVIC and B. BACLIC, Applications of Gauss principle of least constraint to the non-linear heat transfer, Int. J. Heat Mass Transfer, 19, 721, 1976.

C. LANCZOS, The variational principles of mechanics, University of Toronto Press, Toronto 1962.

R. GUTOWSKI, Mechanika analityczna, PWN, Warszawa 1971.

A. CHAPMAN, Heat transfer, Mac Millan, 1967.

S. WHITAKER, Elementary heat transfer analysis, Pergamon Press Inc., 1976.