• Version
• 119 Downloads
• 1.80 MB File Size
• 1 File Count
• January 17, 2017 Create Date
• January 17, 2017 Last Updated

National Advisory Committee for Aeronautics, Technical Notes - An Analysis of Laminar Free Convection Flow and Heat Transfer about a Flat Plate Parallel to the Direction of the Generating Body Force

The free-convection flow and heat transfer (generated by a body
force) about a flat plate parallel to the direction of the body force
are formally analyzed and the type of flow is found to be dependent on
the Grashof number alone. For large Grashof numbers (which are of
interest in aeronautics), the flow is of the boundary-layer type and the
problem is reduced in a formal manner, which is analogous to Prandtl's
forced-flow boundary-layer theory, to the simultaneous solution of two
ordinary differential equations subject to the proper boundary conditions.‘

Velocity and temperature distributions for Prandtl numbers of 0.01,
0.72, 0.733, 1, 2, 10, 100, and 1000 are computed and it is shown that
velocities and Russelt numbers of the order of magnitude of those
encountered in forced—convection flows may be obtained in free-convection
flows. The theoretical and experimental velocity and temperature distri-
butions are in good agreement.

A flow and a heat-transfer parameter, from.which the important phys—
ical quantities such as shear stress and heat-transfer rate can be com-
puted, are derived as functions of Prandtl number alone. Comparison of
theoretically computed values of the heat-transfer parameter with values
obtained from an approximate calculation and experiments yielded good
agreement over a large range of Prandtl number. Agreement between the
theoretical values and those obtained from.a frequently used semiempiri-
cal heat-transfer law was good only in restricted Prandtl number ranges
(depending on an arbitrary constant).

Two important types of fluid flow problems involving heat transfer
are those of forced and those of free convection. By forcedfconvection
flow is meant flows maintained mechanically as, for example, by a pres—
sure drop or an agitator. Free—convection flow, on the other hand,
results from the action of body forces on the fluid, that is, forces
which are proportional to the mass or the density of the fluid. The
flow is generally produced in the following manner: Consider, for
example, a fixed object (such as a plate) in a quiescent fluid subject
to a body force. When the plate is at the same temperature as the sur—
rounding fluid, the body forces acting on the fluid are in equilibrium
with the hydrostatic pressure and no flow ensues in the steady state.