Last updated:
3/19/2019

Internal
Forced Flow (Pipe Flow)

**(FREE, NEW (1/3/2018) DOWNLOAD BELOW!)**

Internal (pipe)
flows involving heating or cooling are usually treated using convection
correlations. For laminar flows the correlations are based on analysis; for
transition and turbulent flows they are generally based on experiment. Another
"on-screen" laboratory, the internal flow module solves the thermal
entry length problem (velocity profile already fully developed when a change in
the wall thermal boundary condition is introduced) for laminar, transition and
turbulent flows. The thermally (and hydrodynamically)
fully-developed condition is, of course, the asymptotic limit of this case.
(Solution of the third internal flow scenario, the combined-entry length
problem, while certainly feasible, requires the solution of the axial momentum
and continuity equations, in addition to the energy balance equation solved
here.) Either a fixed wall temperature or prescribed wall heat flux may be
specified. A single pass, spacewise marching
technique, which is implicit in the radial direction and uses backward
differencing in the axial direction, is used to solve the discretized form of
the governing advection-diffusion equation.

**Module Description**

Inputs to
the model are the Prandtl number of the fluid, the Reynolds number based on
diameter, the Length/Diameter ratio for the pipe and whether a constant wall
temperature or constant heat flux is applied to the surface. In addition the
user can specify a radial magnification factor so that gradients can be
observed more easily in the plot. The temperature distribution as a function of
axial location and radius is displayed in the form of a color contour plot and
the velocity profile (which is unchanging, of course) is depicted at the inlet.
"Heatlines" may be superimposed on the
isotherms. Using a scrollbar mechanism the user can take data from the screen
for the wall temperature, mixed mean temperature and the surface temperature
gradient as a function of axial position along the pipe. Using the former and
an integral heat balance on a short length of the pipe or the latter directly,
the user can develop a local or overall correlation for Nusselt number. This
module allows the user to use the mouse as a probe and "measure"
local values of velocity and temperature. For values of Reynolds number greater
than critical, it gives the user the illusion of turbulence (the
"fuzz" seen below).

4. Laminar, Transition and Turbulent Thermal
Entry Length Flow in a Smooth Pipe

Like the
external flow module, this simulation allows an infinite number of flow and
fluid input parameters -- with virtually negligible setup time and no hazardous
materials! Using either of these forced flow modules the user becomes
immediately aware of the tremendous difference in the heat transfer
characteristics of ordinary (Pr = ~ 1.0) and extreme
Prandtl number fluids and understands physically the reason why. Conditions
under which the use of heat transfer enhancement techniques might be justified
also become readily evident. An Excel
spreadsheet that was developed to aid in verification of this internal flow
module and evaluates a broad range of the conventional internal flow
correlations may be downloaded here.

**New
Free Update – 1/3/2018**

**Reference**

The
algorithm and laminar flow results (corresponding to the well-known Graetz problem and not including the mixing length model
used in the transition and turbulent regime) are described in: Ribando, R.J.,
and O'Leary, G.W., "Numerical Methods in Engineering Education: An Example
Student Project in Convection Heat Transfer," *Computer Applications in
Engineering Education*, Vol. 2, No.3, 1994, pp. 165-174.

**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).

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