Last updated: 1/3/2018
Heat Transfer Today  
Transient
Conduction in Cylinder 
Purpose To assist
engineering students in understanding the Highlights
Computer System Requirements

Introduction
In the past most instructionalsoftware 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 heattransfer coefficient or fin efficiency.
By contrast, our software uses modern numerical algorithms to solve the fundamental governing ordinary or partialdifferential equations in real time. By combining this more fundamental approach with enhanced colorvisualization 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 eleven (11) fundamental topics in heat transfer. About a twenty (20)
"minimodules," 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 originally
published by McGrawHill in July 2001. In addition to the software, the CDRom 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 may be published by
Pearson in 2016. For now several sample
modules and many of the Excel/VBA workbooks may be downloaded below.
While originally developed strictly for use
in a Windows environment, all modules have been installed in the
University’s “cloud” system and work equally well in
Macintosh and Unix environments as well as on mobile (Ipad
and Androidbased) devices.
The algorithms and interfaces for each module
are uniquely tailored for the particular application  thus avoiding the
frequentlysteep learning curves associated with much more powerful,
commercially available and often costly 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 19972012 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.
1 Early Years in the Broadcast Studio
Then as facilities became
available, they were used in a similar mode for a number of years in a
projectorequipped, local classroom. The development of the graphicaluserinterfaces
during the 199596 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
50minutelong, traditional classes a week, but also have a twohour working
session in one of our computer classrooms.
2
Twoperson Teams Working in the Studio Session
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. Later all
modules were ported to Visual Basic 6, allowing for much more interactivity
than in the past. Now in 2018 all
modules are written in VB 2013 and have been installed and tested in the
“cloud.”
The development of the underlying
computational routines, the userinterface, online help file, the supporting
documentation, the student exercises, and in many cases a journal article is
extremely timeconsuming. 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 graduatelevel 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 "HandsOn" Approach to
Teaching Undergraduate Heat Transfer," Symposium on Mechanical Engineering
Education, Paper IMECE200461165, ASME IMECE
'04, Anaheim, CA, Nov. 1419, 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 # 20021536, Proceedings of the ASEE Annual
Conference and Exposition, Montreal, Canada, June 1619,2002.
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. 3644, Edited by L.C.Witte, Nov. 1999, pp. 397407.
Ribando, R.J., "Teaching Modules for
Heat Transfer," Workshop on Advanced Technology for Engineering
Education, Feb. 2425, 1998,
Ribando, R.J. and O'Leary, G.W.,
"Teaching Modules for Heat Transfer," ASME Proceedings of the 32nd
National Heat Transfer Conference, HTDVol.344, Volume 6, Innovations in
Heat Transfer Education, pp. 7582, August 1997.
OneDimensional,
Transient Conduction (HEISLER CHARTS)
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TwoDimensional,
SteadyState Conduction
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Transient
Conduction in a Finite Cylinder (Cooking)
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Natural
Convection in a Saturated Porous Layer
This module covers natural convection in a
fluidsaturated, porous material, a topic covered in a number of recent
graduatelevel heat transfer texts. The problem is analogous to classical
RayleighBenard 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 bottomtotop or sidetoside. (The remaining sides are taken as
adiabatic.)
5.
Natural Convection in a Saturated Permeable Layer
Unless the user elects to stop prematurely,
the program runs to a prescribed nondimensional time. During that interval a
succession of 200 color contour plots of temperature are drawn in the lefthand
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 CDROM,
making it suitable as a severalweeklong project in a graduatelevel
computational methods or convection heat transfer course.
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The usual treatment of heat exchanger thermal
design and analysis is based on two analyticallybased 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 nondimensional 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 heat balance
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 heatexchanger education
consists of one module that covers both “1D” and “2D”
exchangers:
Both algorithms solve discretized, coupled
heatbalance equations along the paths of the two fluids as they each traverse
the heat exchanger. Separate algorithms (on the two tabs) have been developed
because in one case, a coupled set of ordinary differential equations apply, while
in the other a coupled set of partial differential equations govern. The
detailed temperature distribution is presented to the user in both tabs, and
the performance and design numbers associated with the conventional (LMTD and
effectivenessNTU) methods are reported in both cases for comparison. Samples
of the main userinterface for both algorithms are shown below.
Both algorithms allow for several geometric
options. The single pass, crossflow 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 twopass geometry
related to an experiment we have done in our undergraduate lab, is also
included. The user selects this option in the top left corner and a small
schematic of the selected geometry appears.
6
Interface for CrossFlow Heat Exchanger Option
The 1D option (tab seen below) allows for
several generic geometries, including double pipe designs (parallel and counterflow), shellandtube designs and 2pass, 2pass
plate configurations. After selection of the "Configuration" option,
the user specifies a few other inputs relevant to that particular case. In the case of a shellandtube
configuration, the baffle arrangement is used as a convenient means of discretizing
the shell for the numerical solution.
7
The Interface for a ShellandTube Arrangement
In both modules after the geometry has been
selected, the user specifies the heatcapacity 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 crossflow 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 onedimensional geometries HTT_HX 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 analyticallybased methods, including nonuniform thermal properties,
nonuniform overall heat transfer coefficient and condensation or evaporation
of either fluid occurring in only a portion of the device. Such capability is available in
commercial HX design software.
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 CarlsonSkalak,S.E.,
"A General, Numerical Scheme for Heat Exchanger Thermal Analysis and
Design," Computer Applications in Engineering Education, Vol. 5,
No. 4, 1997, pp 231242.
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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 threedimensional 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 view factor between
two parallelograms arbitrarily positioned in threedimensional 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 onscreen 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
muchneeded reinforcement of training in 3D 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 3D space. In the event that
either surface cannot "see" the other surface completely, a warning
is returned.
In addition to the experience with 3D
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.
281283.
About 20 "minimodules" 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 original development of the interfaces
during the 199596 academic year was supported by a fellowship from
the
Professor Robert J. Ribando
122 Engineer's Way
email: rjr at
virginia.edu