Last updated: 5/8/2012
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Heat Transfer Today - |
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Purpose To assist
engineering students in understanding the Highlights
Computer System Requirements
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In the past most instructional-software packages for heat & mass transfer were based on the "computerization" of existing analytical solutions and experimental correlations. Often the result was a facility for doing more conventional calculations, only faster; and usually the computed result was just a single "answer" -- such as an overall convective heat-transfer coefficient or fin efficiency.
By contrast, our software uses modern numerical algorithms to solve the fundamental governing ordinary or partial-differential equations in real time. By combining this more fundamental approach with enhanced color-visualization techniques, our new software modules allow a student to "see" -- and thus perhaps to understand -- the physics underlying a particular process.
To date, we have developed software modules
for eight fundamental topics in heat transfer. About a twenty (20)
"mini-modules," which use a combination of an Excel
Spreadsheet for input and graphical display of output and Visual Basic for
Applications (VBA) macros for the serious calculations, have also been
developed and may be downloaded here.
Software Availability
All software and a manual (Heat Transfer
Tools) consisting of about 100 pages of documentation were published by
McGraw-Hill in July 2001. In addition to the software, the CD-Rom includes
about 60 additional pages in "pdf" files detailing the numerical
modeling used "behind the scenes," making these materials very
appropriate for use at the graduate level as well as by undergraduates. A few
copies of the book and CD may still be available through Amazon.
A complete heat transfer textbook (Heat Transfer Today) with totally
updated and integrated software is in preparation now and will be published by
Pearson in 2012. For now two sample
modules (HTTonedt for one-dimensional, transient conduction and HTT_2dss for
two-dimensional, steady-state conduction) and most of the Excel/VBA workbooks
may be downloaded below.
The algorithms and interfaces for each module
are uniquely tailored for the particular application - thus avoiding the
frequently-steep learning curves associated with much more powerful,
commercially available CFD packages. In most cases specific techniques
were derived from the authors' research, as well as from experience in graduate
and undergraduate teaching. All modules were used extensively for the
first time by some sixty university students taking undergraduate Heat and Mass Transfer
during the Spring 1996 semester and then fifteen more times in the Spring
1997-2012 semesters. All modules have been enhanced continuously and
extensively as a result of these experiences.
Many of the original Fortran programs were
developed and used as lecture demonstrations in distance education courses in Computational Fluid Dynamics
and Heat Transfer
taught through the Virginia Commonwealth
Graduate Engineering Program.
Then as facilities became
available, they were used in a similar mode for a number of years in a
projector-equipped, local classroom. The development of the
graphical-user-interfaces during the 1995-96 academic year made them
appropriate for student use as well, both on their own, or as we use them, in a
scheduled "studio" session.
Students attend two 50-minute-long, traditional classes a week, but also have a
two-hour working session in one of our computer
classrooms. A "virtual" tour of the classrooms used for this
course, MEC 339,
and MEC 214, is
also available. (You'll need to have Quicktime installed.) .
Originally Watcom Fortran 77 was used for the
intense numerical computations and for generation of the color plots, while a
tailored Visual Basic
executable was used for the user interface. Now all but two of the programs are
written in Visual Basic 6, allowing for much more interactivity than in the
past. These completely rewritten modules (screenshots of which are seen below)
will be will be included in the new Heat Transfer Today. The newest ones (HTTonedt and HTTflatp) are
written in VB.NET.
The development of the underlying
computational routines, the user-interface, on-line help file, the supporting
documentation, the student exercises, and in many cases a journal article is
extremely time-consuming. Consequently the topics for modules were chosen
with great care. Only fundamental subjects that cover at least ten pages
in a typical textbook were selected. In several cases virtually all the
concepts from a whole chapter in a graduate-level text can be illustrated using
one module. In addition, several of the modules are sufficiently general that
they may be used in a variety of related courses, both graduate and
undergraduate, in mathematics, science and engineering.
General
References
Ribando, R.J., Heat
Transfer Tools,
Ribando, R.J., Richards, L.G., and O'Leary,G.W.,
"A "Hands-On" Approach to Teaching Undergraduate Heat
Transfer," Symposium on Mechanical Engineering Education, Paper IMECE2004-61165, ASME IMECE '04, Anaheim, CA, Nov.
14-19, 2004.
Ribando, R.J., Scott, T.C., Richards, L.G.
and O'Leary, G.W., "Using Software with Visualization to Teach Heat
Transfer Concepts," Paper # 2002-1536, Proceedings of the ASEE Annual
Conference and Exposition, Montreal, Canada, June 16-19,2002.
Ribando, R.J., Scott, T.C., and O'Leary,
G.W., "Application of the Studio Model to Teaching Heat Transfer," Proceedings
of the 2001 American Society for Engineering Education Annual Conference &
Exposition,
Ribando, R.J., Scott, T.C. and O'Leary, G.W.,
"Teaching Heat Transfer in a Studio Mode," Session on Energy Systems
Education, 1999 ASME IMECE, Nashville, TN, HTD - Vol. 364-4, Edited by
L.C.Witte, Nov. 1999, pp. 397-407.
Ribando, R.J., "Teaching Modules for
Heat Transfer," Workshop on Advanced Technology for Engineering
Education, Feb. 24-25, 1998,
Ribando, R.J. and O'Leary, G.W.,
"Teaching Modules for Heat Transfer," ASME Proceedings of the 32nd
National Heat Transfer Conference, HTD-Vol.344, Volume 6, Innovations in
Heat Transfer Education, pp. 75-82, August 1997.
One-Dimensional,
Transient Conduction (HEISLER CHARTS)
New
Free Update – 5/8/2012
Two-Dimensional,
Steady-State Conduction
New
Free Update – 5/8/2012
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 per cent) 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.)
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 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.
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).
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.
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.
Thorough implementation instructions suitable for use in a graduate-level
course are included as "pdf" files on the Heat Transfer Tools
CD-ROM.
Natural
Convection in a Saturated Porous Layer
This module covers natural convection in a
fluid-saturated, porous material, a topic covered in a number of recent
graduate-level heat transfer texts. The problem is analogous to classical
Rayleigh-Benard natural convection in homogeneous fluid layers. The fluid is
assumed to be "Boussinesq," i.e., the fluid density is considered
only a function of temperature and variable only in the body force term, and to
completely fill all interstices. Fluid motion is assumed governed by the Darcy
equations. Heating may be either from the bottom of the layer or from side to
side.
Module
Description
Before any run the user selects the aspect
ratio of the layer and the number of grid points to be used in the vertical
direction. The same grid spacing is used in both directions, so different
aspect ratios are obtained simply by adding or subtracting columns of grid
points in the horizontal direction. These two parameters may not be changed
once a calculation is begun. Before as well during a run the user may set the
Rayleigh number for the calculation and also change the heating mode from
either bottom-to-top or side-to-side. (The remaining sides are taken as
adiabatic.)
Unless the user elects to stop prematurely,
the program runs to a prescribed non-dimensional time. During that interval a
succession of 200 color contour plots of temperature are drawn in the left-hand
window creating an animation effect. Contours of streamfunction are
superimposed on top if the user selects that option. The Nusselt number
computed at both the bottom and top (or at the left and right sides if that
heating option has been selected) is plotted in the right hand window as a
function of time. Switching the heating direction or changing the Rayleigh
number in the midst of a run produces interesting transients which may be
monitored in both windows.
Unless one has selected a very large number
of grid points (which may happen especially with a low height/width ratio), performance
is satisfactory on most current platforms. Very thorough implementation
instructions of this algorithm are included on the HTT CD-ROM, making it
suitable as a several-week-long project in a graduate-level computational
methods or convection heat transfer course.
The normal textbook treatment of heat
transfer from fins involves the solution by analytical means of an ordinary
differential equation describing transport by conduction along the fin and
convection from its surface. Even with a straight, rectangular fin, there is
the quandary about what boundary condition to apply at the tip (which is
usually resolved using an extended length), and the solution is expressed in
terms of hyperbolic functions. In the case of straight fins of triangular
cross-section and annular fins of constant thickness, the solutions are given
in terms of Bessel functions, which the student may or may not have studied.
Also in the latter cases he or she never sees the temperature distribution
along the fin; only an overall parameter, the fin efficiency, is usually
graphed.
Module
Description
In this module a finite-volume solution of
the governing heat balance equation is used instead. Terms representing
conduction into and out of a short representative segment of the fin and
convection from its surface are included and the necessary derivatives of
temperature in the conduction terms are expressed in terms of changes over
small increments. The resulting triadiagonal system of equations is solved
using publicly available software and the student has the complete temperature
distribution at his or her disposal immediately. With that plot a good or poor
fin design is readily apparent and in the latter case, may be rectified
quickly. Since the algorithm does not require the evaluation of different
functions for each distinct geometry, but only input of the appropriate areas
for axial conduction and for convection to the fluid, this solution may be
easily carried out for virtually any one-dimensional geometry.
The user selects the fin type (straight
rectangular, cylindrical pin, straight annular or triangular) and a schematic
of that geometry pops up so that he or she can see how the requisite dimensions
are defined. More general two-dimensional, spine and annular fins having a
cross-section that may be described by a simple polynomial are also handled
readily. For all geometries the user may input the thermal conductivity of the
material and the surface convection coefficient for as many as six cases
simultaneously. A scaled cross-sectional profile of each fin is plotted in the
left window, while the resulting 1-D temperature distribution along the fins is
plotted in the right window. Numerical values of the efficiency, effectiveness,
total heat transferred and thermal resistance are reported in tabular form.
This module also provides an input sheet so that data from a simple
accompanying desktop experiment may be plotted along with the numerical
predictions. Photos of a number of extended surface heat transfer applications may be accessed from the module.
The usual treatment of heat exchanger thermal
design and analysis is based on two analytically-based solution methods applied
to the governing, coupled heat balance equations for the two fluids. Because
the solution of these differential equations by analytical means is challenging
for all but the simplest configurations, the numerical results have been
graphed in non-dimensional form and the resulting charts have been used
routinely for the last half century. The LMTD method is commonly used for heat
exchanger design, that is, determining the required thermal size, while
the Effectiveness - NTU method is used for performance calculations.
Unfortunately the charts and equations associated with these two methods do not
give a complete picture of what is happening inside the exchanger, only a
single overall measure. In these two modules, the same governing equations are
solved in discretized form using modern numerical techniques, yielding not only
the same "bottom line" results as the traditional methods, but giving
a complete picture of what is happening within the device.
Module
Description
Our software for heat-exchanger education
consists of two separate modules:
- HTT_hx1d
-- for double-pipe, shell-and-tube and
2-pass,2-pass plate heat exchangers (i.e.,
configurations which may be approximated as "one-dimensional"),
- HTT_hx2d
- for single-pass, cross-flow heat-exchangers with
the two fluids mixed or unmixed.
Both modules solve discretized, coupled
heat-balance equations along the paths of the two fluids as they each traverse
the heat exchanger. Separate modules have been developed because in the former
case (HX1D), a coupled set of ordinary differential equations apply, while in
the latter a coupled set of partial differential equations govern. The detailed
temperature distribution is presented to the user in both modules, and the
performance and design numbers associated with the conventional (LMTD and
effectiveness-NTU) methods are reported for comparison. Samples of the main
user-interface for both modules are shown below.
Both modules allow for several geometric
options. The single pass, cross-flow heat exchanger module allows the four
generic textbook options: neither fluid mixed, both fluids mixed and either one
or the other, but not both mixed. A fifth selection, a two-pass geometry
related to an experiment we do in our undergraduate lab, is also included. The
user selects this option in the bottom right hand corner and a small schematic
of the selected geometry appears.
The HTT_hx1d module allows for several
generic geometries, including double pipe designs (parallel and counterflow),
shell-and-tube designs and 2-pass, 2-pass plate configurations. Upon selection
of the "Configuration" button, another box appears, and the user can
select one of the three geometries. On the sheet which appears when
shell-and-tube is selected, two slider bars are provided for specifying the
number of shells (two tube passes per shell pass are assumed) and the number of
baffles per shell.
The latter may or may not
correspond to actual baffles, but in any case provides a convenient means of discretizing
the shell. Separate setup forms are for simple double pipe designs and for
2-pass, 2-pass plate heat exchangers.
In both modules after the geometry has been
selected, the user specifies the heat-capacity rates for both fluids and indicates
which of the two calculation methods to use. For the Design option, the user
then specifies the desired outlet temperature of the hot fluid. For the
Performance option the user inputs the product of the overall heat transfer
coefficient and area (UA product). (Input boxes are shown in white on all user
interfaces while numbers appearing on the gray background are program outputs.)
Based on this user input, the temperature
distributions in both fluids are computed and displayed in a fraction of a second.
For the cross-flow module the temperature distribution in both fluids is
depicted in the form of color contour plots as seen above. The hot fluid is
shown flowing vertically in the leftmost plot. The cold fluid flows from left
to right and is shown in the center. The local difference between the two
fluids, which can be helpful in assessing the quality of a design, is shown in
the right hand plot.
For one-dimensional geometries HTT_hx1d
returns a plot of the temperatures of both fluids as a function of position. In
fact three curves are plotted. In the interface seen above, the temperature of
the shell fluid is shown in light blue. That of the tube fluid is plotted
twice; the yellow line shows the tube fluid temperature plotted in the
conventional way; i.e., as counterflow. The third (green line) shows the tube
temperature as "seen" by the shell fluid as it passes through the
exchanger. So for instance, shell fluid entering the top of the three shells
used in this example first encounters fluid that is exiting the shell, then
fluid that has just entered that shell, then fluid that is nearly ready to
exit, etc. This accounts for what appears to be a "ringing" behavior
in the curves. (The analytical solutions are based on the exchange of heat
between the shell fluid and the mean of the two local pipe fluid temperatures
at that horizontal position.)
In addition to the detailed temperature
distributions, both interfaces return all the design and performance measures
used with the traditional methods so that all results may be verified by
comparison with the conventional charts. While not currently configured, either
module could be adapted to handle situations which inherently cannot be handled
by the analytically-based methods, including non-uniform thermal properties,
non-uniform overall heat transfer coefficient and condensation or evaporation
of either fluid occurring in only a portion of the device.
Reference
A complete description of the numerical
algorithm used in these two modules may be found in: Ribando, R.J.,
O'Leary,G.W., and Carlson-Skalak,S.E., "A General, Numerical Scheme for
Heat Exchanger Thermal Analysis and Design," Computer Applications in
Engineering Education, Vol. 5, No. 4, 1997, pp 231-242
The View Factor from one surface to another
(also known as the Shape Factor and the Configuration Factor) is the fraction
of radiation leaving the first surface that is intercepted by the second. For
some very simple geometries this quantity can be determined by geometric
arguments. The reciprocity theorem and shape factor algebra may be useful for
other arrangements. For a very few geometries, e.g., perpendicular
rectangles with a common edge, coaxial parallel
disks, coaxial cylinders and aligned parallel rectangles, the very
complicated quadruple integral defining the view factor between two surfaces
may be integrated analytically. The resulting values are given in the form of
charts in virtually every heat transfer book. An Excel spreadsheet that evaluates
these analytical solutions for any of the four geometries listed above may be
downloaded by clicking on any of the links above. View factors for still other geometries
are tabulated in many sources. Several modern applications of radiation heat
transfer, including the thermal analysis of large space structures and the
rendering of complex three-dimensional scenes on computers using the radiosity
method, require the computation of the view factors between thousands of pairs
of surfaces. The numerical scheme used in this module is typical of modern
means developed for such applications.
Module
Description
This module computes the viewfactor between
two parallelograms arbitrarily positioned in three-dimensional space using a
numerical implementation of the Nusselt unit sphere method based on the NASA
TRASYS code. Users enter the x, y and z coordinates of three corners of each
plate into an on-screen table (contained on a separate sheet not seen in the
interface below); the coordinates for the fourth corner of each plate are
computed automatically. To aid in verifying the geometric input data, the
plates are drawn on the screen in a perspective view with hidden surface
removal. The slider bars seen in the upper right of the interface seen below
may be used to select any desired viewing angle - - also giving student
engineers some much-needed reinforcement of training in 3-D visualization. On a
modern PC the recomputation and refresh of the figure and the calculation of
the viewfactor itself is nearly instantaneous. In addition to the conventional
arrangements covered by viewfactor charts and equations which may be used for
program verification, this program computes completely arbitrary arrangements
in 3-D space. In the event that either surface cannot "see" the other
surface completely, a warning is returned.
In addition to the experience with 3-D
visualization, the radiation view factor module exposes students to a modern
analysis technique, which is used in industry, but simple enough for students
to implement in an elective, undergraduate computer graphics course.
Reference
A discussion of the verification process for
this module may be found in: Ribando, R.J. and Weller, E.A., "The
Verification of an Analytical Solution - An Important Engineering Lesson,"
Journal of Engineering Education, Vol. 88, No. 3, July 1999, pp.
281-283.
About 20 "mini-modules" implemented
using a combination of the Excel spreadsheet and Visual Basic for Applications
(VBA) may be downloaded here. Some of
these are for heat transfer; others cover thermodynamics, computational methods
and fluid mechanics.
Descriptions of eight projects intended for
student implementation are described here. Six were included in the first
edition of Heat Transfer Tools; two more, one of which may be downloaded, have
been prepared for the second edition.
It has been said that "the purpose of
computing is insight, not numbers." An online quiz that tests understanding
of the physical principles that may be learned partly through computer
"experimentation" using the HTT modules may be taken here.
Acknowledgment
The development of the interfaces was
supported by a fellowship during the 1995-96
academic year from the
Professor Robert J. Ribando
310 Mechanical Engineering
University of Virginia
122 Engineer's Way
P.O. Box 400746
Charlottesville, VA 22904-4746
e-mail: rjr at virginia.edu