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National Advisory Committee for Aeronautics, Report - Theoretical and Experimental Investigation of Heat Transfer by Laminar Natural Convection between Parallel Plates

sults are presented of a theoretical and etperimental
investigation of heat transfer involving laminar natural con-
vection of fluids enclosed between parallel walls oriented in the
direction of the body force, where one wall is heated uniformly,
and the other is cooled uniformly. For the experimental work,
parallel walls were simulated by using an annulus with an
inner-to-outer diameter ratio near 1.

The results of the theoretical investigation are presented in the
form of equations for the velocity and temperature profiles and
the ratio of actual temperature drop across the fluid to the
temperature drop for pure conduction. No ecperimental
measurements were made of the velocity and temperature profiles,
but the experimental results are compared with theory on the
basis of the ratio of the actual temperature drop to the temperature
drop for pure conduction. Good agreement was obtained
between theory and experiment for aerial temperature gradients of
40° F per foot or larger.

Increased application of heat transfer to and from fluids in
channels has recently required further knowledge as to the
heat-transfer coefficients and temperature profiles occurring
with natural convection. Turbine-blade and nuclear-reactor
cooling are two of the fields concerned with this problem.
Work on free-convection heat transfer over a vertical plate
gave good agreement between theory and experiment. Few
results have been obtained for the similar case of flow in
channels. Reference 1 obtains a theoretical solution for
free-convection heat transfer for fluids enclosed in channels.
The reference uses a postulated velocity distribution to obtain
a solution. References 2 and 3 extend this analytical work to
give an exact solution of the equations in more general form
for constant wall temperature and constant heat flux,
respectively. Reference 3 includes the effect of forced as
well as natural convection. These three references treat the
case of infinite channels with the channel arm‘s oriented in the
direction of the body force and are subject to the same
assumptions; namely, two—dimensional laminar flow, uniform
axial temperature gradient, and constant fluid properties,
except that the density is allowed to vary in the bouyancy
term.