• Version
• 152 Downloads
• 1.01 MB File Size
• 1 File Count
• December 14, 2016 Create Date
• December 14, 2016 Last Updated

National Advisory Committee for Aeronautics, Technical Notes - Analytical Investigation of Fully Developed Laminar Flow in Tubes with Heat Transfer with Fluid Properties Variable

Relations were analytically obtained for the prediction of radial
distributions of velocity and temperature for fully developed laminar
flow of gases and of liquid metals in tubes with fluid properties
variable along the radius. The relations are applicable to both heat-—
ing and cooling of the fluid. By use of the relations for velocity and
temperature distributions, relations were obtained among Nusselt number,
friction parameter, and ratio of wall to bulk temperature.

The Nusselt number and friction parameter were found to be inde-
pendent of Reynolds number and Prandtl number. The effects of ratio of
wall to bulk temperature on Nusselt number and friction parameter could
be eliminated by evaluating the fluid properties at specified tempera—
tures in the fluid.

Most of the analyses of laminar flow and heat transfer in tubes,
for instance the uniform-wall—temperature solution given in reference 1,
have been carried out under the assumption that the fluid properties do
not vary with temperature. Somewhat more work on variable fluid prop-
erties has been done for the laminar boundary layer of a flat plate.
(See, for instance, references 2 and 3). In reference 4, velocity
distributions for laminar flow in tubes with variable viscosity and some
approximate relations for temperature distributions and heat-transfer
coefficients are given.

In the analytical investigation reported herein, which was con-
ducted in the NACA Lewis laboratory, both velocity and temperature dis-
tributions are obtained for fully developed laminar flow in tubes of
gases and of liquid metals with variable fluid properties . These
relations are applicable to both heating and cooling of the fluid. By
use of these velocity and temperature distributions, Nusselt numbers
and friction parameters are obtained. file results should be applicable
to flow at points where the ratio of distance from entrance to diameter
of the tube is on the order of one—twentieth of the Reynolds number or
greater.