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National Advisory Committee for Aeronautics, Technical Notes - Temperature Distribution in Internally Heated Walls of Heat Exchanges with Noncircular Flow Passages Using Coolants with Very Low Prandtl Number

The conventional recuperative type of heat exchanger consists of
passages for two fluids separated by a heating surface. Heat from an
external source is transferred continuously from one fluid to the other
through the heating surfaces. In the regenerative type of heat
exchanger the two fluids pass alternately through the same passages.
During the heating period heat is transferred from a hot fluid to the
passage walls and is stored.within the solid wall material. During the
cooling period this stored heat is hen transferred to a cold fluid
passing through the heat exchanger.

The heat exchanger considered in this report is very similar to the
regenerative type. It differs from it only by the fact that the heat is
generated internally by heat sources located within the passage walls
and is transferred to a coolant flowing continuously through the pas-
sages. The heat—exchanger passages are formed by a number of plates
assembled to form a honeycomb. High temperatures may be anticipated
near the corners of the flow passages thus formed. A knowledge of the
magnitude of these temperatures is necessary in order to determine the
admissible operating temperature of the heat exchanger.

In a previous report (reference 1) the temperature distribution in
the walls of similar heat exchangers was studied with the assumption
that the coolant consists of a fluid with a Prandtl number in the neigh—
borhood of 1. In the present report, the investigation carried out at
the NACA Lewis laboratory, is extended to include coolants with a
Prandtl number very much less than 1. The Prandtl number is assumed
to be so low that the turbulent contribution to the heat transport
within the fluid can be neglected as compared with the conductive
contribution.

A knowledge of the velocity distribution within the passages is
necessary in order to determine the temperature distribution. A thor—
ough investigation of the flow of water through tubes with noncircular
cross sections was made by Nikuradse (references 2 and 3). The velocity
profiles obtained in this investigation will be used in the present
report.

The analysis presented applies to all passage shapes for which the
velocity distribution is known and to all possible configurations of
these passage shapes. 'Solutions are presented, however, only for heat
exchangers composed of triangular and rectangular passages. Cross-
sectional views of these configurations are shown in figures 1 and 2.