Last updated:
9/24/2015

Forced Convection over a
Heated Flat Plate

In this module
we solve the boundary layer equations for forced convection over a flat plate
in their primitive form, i.e., without the similarity restrictions of the Blasius
solution, and thus provide what might be considered a "virtual"
laboratory. The governing continuity, horizontal momentum and energy equations
have been transformed so that, in effect, the grid grows along with the
boundary layer in the direction normal to the plate. This strategy allows
better resolution near the leading edge and reduces the number of extraneous
grid points in the undisturbed free stream.

**Module Description**

The user inputs
the plate Reynolds and fluid Prandtl numbers, along with the freestream turbulence level (as a percent) and on an
accompanying input form may specify up to five independent zones where either
the surface temperature or surface temperature gradient will be specified
(subject to the boundary layer model being invalid in the immediate vicinity of
sudden changes). An algebraic model is used to estimate the transition point as
a function of the freestream turbulence level, and a
simple mixing length model is used to extend the calculation into the
transition and turbulent region. (The frequently-used transition criterion of
Re = 500,000 corresponds to 1% freestream
turbulence.)

3
Forced Convection Boundary Layer on a Flat Plate Module

The on-screen
output includes a white line indicating the edge of the velocity boundary layer
as a function of position on the plate.
The temperature field is shown in color contour form. In the case displayed the change in slope a
third of the way down the plate (corresponding to local Reynolds number Re_{x}
of 500,000) indicates the beginning of the transition to turbulence. A fixed
temperature has been used for the first three quarters of the plate and an
adiabatic section comprises the final quarter. Since the Prandtl number is
slightly less than unity (0.7, corresponding to air), the thermal boundary
layer does, as expected, grow faster than the velocity layer. Since the
equations are parabolic, a single calculation takes only an instant on any
modern personal computer.

For any
reasonable value of Reynolds number, both the velocity and thermal boundary
layers are very thin. For that reason
the user has the option of expanding the vertical scale of these plots in order
to see more detail. The local plate surface temperature and the local surface
temperature gradient may be taken directly from the screen using the scrollbar
seen in the lower left, and these may be used to develop local and overall
convection correlations. These "experimental-numerical" results
compare very favorably with those from the standard correlations based on similarity
and integral methods for laminar boundary layer flows and favorably with
experimentally derived correlations for turbulent flows. The horizontal
velocity at any point in the flow may be "measured" locally using the
mouse, and the boundary layer velocity profile at any point along the plate may
be displayed using the same scrollbar mechanism.

The numerical
procedures used in this forced convection module are certainly well beyond the
undergraduate level. However with this very well equipped "virtual"
laboratory, students can run a large number of parameters quickly and
"see" what happens physically -- even to the point of deriving their
own correlation. We follow up with an exercise involving a geometry (an
infinite cylinder) which does not yield to a relatively simple numerical
solution, but at least by that point students have developed an appreciation
for the physical basis of convection correlations.

**Reference**

A very thorough
exposition of the modeling involved in this module may be found in Ribando,
R.J., Coyne, K.A., and O'Leary, G.W., "Teaching Module for Laminar and
Turbulent Forced Convection on a Flat Plate," *Computer Applications in
Engineering Education*, Vol. 6, No.2, pp. 115-125,1998. The transition and turbulence models are
from other sources.

**Software Availability**

If you are up to date with your Windows updates, this executable
should work directly without any installation needed. It will not work on Mac computers (unless
installed in cloud environment). You are
welcome to contact me with suspected errors and suggestions for
improvements. Because this program is
still under active development, this version has a “drop dead” date of January
1, 2018.

**Notice to International Users **(in those countries where decimal points
(periods) are used instead of commas to break up long numbers): If, after you
have installed this module, it does not work properly, then in the
International Setting of the Windows Control Panel, please change the language
to English (US).

**New Free Update –
9/22/2015**

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