The Influence of Geometry on Free Convection in Roman
Hypocaust Systems
Group 3
Mike Brown
Eric Konicki
Laura Wong
Abstract
The natural convective flow of the Roman hypocaust system has been subjected to many
qualitative studies but few quantitative examinations. There are claims from ancient Roman
authors implying the temperature distribution within the walls of public baths and other
hypocaust heated structures was remarkably even. By constructing a model of a semicircular
tubuli wall, we were able to examine the affects of geometry, tubuli connection holes, exhaust
method, and chimney placement on these claims. From the resulting temperature data and visual
observations, we can conclude that the claims of the ancient authors are unfounded and the
temperature does, in fact, rely heavily on position and tubuli configuration.
Introduction
Though dozens of Roman baths and other hypocaust heated structures have been
remarkably well preserved, little is known about the airflow and subsequent heat flow within
these buildings. Archaeological studies have provided an understanding of the geometry and
construction of the tubuli within the walls of these structures. However, these examinations have
not provided a quantitative understanding of the efficiency and operation of this system.1 The
remains of ancient Roman buildings and scale modeling of these structures show that the use of
tubuli, in addition to hypocaust flooring, greatly improved the effectiveness of the heating
system.2 Contemporary Roman authors commented on the uniformity of the heat throughout the
walls and room interior achieved by the use of tubuli.1
Our examination of the Roman hypocaust system focuses on the free convective fluid
flow within the tubuli of a semicircular wall. We are primarily concerned with the temperature
gradient within the wall and the validity of the ancient authors’ claims of uniformity.2 The
purpose of the connecting tubuli holes has never been fully established and is, therefore, also of
great interest to this examination. By placing the heat source at one end of the wall, we are able
to examine the flow between the individual channels resulting from the holes connecting the
ducts. This configuration allows for the formation of dramatic temperature differences between
the tubuli and the subsequent exploration of the heat flow within the structure.
In addition to the exploration of geometric effects we have chosen to study the secondary
influence of both exhaust methods and chimney placement. It is known that many tubuli were
capped with only a single chimney present, while others were connected at the top by an open
channel that ran the entire length of the wall.3 We will look at the effective change in heat transfer
when open tubuli are used and the chimney position is changed with respect to the heat source.
Formulation & Procedure
The primary experimental procedure for the analysis of heat flow through the
semicircular wall is similar for a variety of configurations. The construction of the scaled wall
allows for the use of interchangeable components that could be altered to create a new set of test
parameters. The experimental apparatus, seen in Figure 1, was designed and built based upon an
analysis of scaled Roman structures. It is easy to use and manipulate the apparatus for the
necessary tests because of the versatility of the design.
2
Figure 1: Scaled Semi-Circular Tubuli Wall
The model is approximately 4 feet tall with a 2 foot inner radius. The wall houses 13
tubuli constructed from 1/8” polycarbonate sheets and ½” plywood. The tubuli are wedge-shaped
to produce the curve of the wall.4 Instead of making separate blocks, each tubuli runs the entire
height of the wall. Circular holes are placed every 12” to simulate individual blocks of this
height.5 At the base of each duct, large holes are cut to simulate an open channel through which
heat is supplied to the system. A 1500 W radiant space heater is used to model the praefrunium,
or furnace, and supply the necessary heat and temperature gradient to the wall. The costs incurred
in producing this experimental apparatus are tabulated in Appendix A. The general layout of the
apparatus can be seen below in Figure 2.
Figure 2: Schematic of System
3
The exhaust system allows us to simulate both a closed cap tubuli and an open channel
with a single chimney (Figures 3 and 4). By changing the location of the chimney, we can alter
the relative position of the heat source.5 The exhaust system has been constructed with
interchangeable plywood components to allow for several different configurations to be tested.
Figure 3: “Closed Cap” Exhaust System
Figure 4: “Open Channel” Exhaust System
To acquire data for our experiment, we rely extensively on thermocouples and visual
observations. We utilize 18 thermocouples in conjunction with 2 data acquisition boxes (DAQ).
The thermocouples are placed systematically throughout the wall and can easily be moved to
accommodate different areas of interest.
This allows us to acquire temperature readings
throughout the structure. By using a light mist of talcum powder sprayed into the tubuli system,
we are able to visually observe the fluid motion throughout the apparatus. This provides us with
the necessary data to better understand the free convection-driven fluid flow.
For this experiment, it is not crucial that the thermal resistance of our model be
equivalent to Roman materials. We are primarily concerned with the flow within the wall.
However, the scaled wall, seen in Figure 1, is constructed with further experimentation in mind.
For this reason, the thermal resistivity of the wall is matched, as closely as was practical, to that
of ancient Roman terracotta. Therefore, the inner wall of our model is acrylic plastic, which
allows us to visualize the airflow, while the rest of the structure is made of plywood. The
terracotta originally used to construct the tubuli has an approximate thermal conductivity
4
k = 0.90
W
and approximate thickness of 2.5 cm.
m⋅ K
conductivity k = 0.19
The acrylic plastic has a thermal
W
and the approximate thickness, L, is found by matching the thermal
m⋅ K
resistance, r:
r=
Lacry
Lterr Lacry
0.025m
=
⇒
=
⇒ Lacry = 0.0053m = 0.2087in
W
W
kterr k acry
0.90
0.19
m⋅ K
m⋅ K
(1)
The heat flow on the plywood-side of the model is negligible due to further insulation.
To obtain a better understanding of the performance of the thermocouple array, a simple
“mini experiment” is performed to determine the limit of the thermal boundary layer that is
present in our model. The limiting boundary layer is produced by the forced convection’s high
fluid velocity, which leads to a larger temperature gradient. Under these conditions, convection
occurs much more rapidly.6 We are able to observe the limiting boundary layer by monitoring the
fluid flow, created by a fan-forced heater impinging on a flat plank imbedded with type-E
thermocouples.
The general setup of this mini experiment can be seen in Figure 5.
The
boundary layer produced in our main experiment differs because our fluid flow is driven solely
by natural convection and is for internal, rather than external, flow. Despite these differences the
thermal boundary layer experiment provides invaluable insight into the performance of the
thermocouple array.
Figure 5: Boundary Layer Mini Experiment Configuration
5
At the completion of the “mini experiment,” we turn to the main experimental apparatus
and begin testing the heat and airflow throughout the semicircular wall. Once the thermocouples
are attached to the structure, and the 1500 W radiation heater is connected to the inlet channel,
LabView is set to compile temperature data from the 16 thermocouples every 5 seconds for
approximately one hour. By placing the heater in an enclosure, we can ensure that most of the
heat is focused into the tubuli and not dissipated to the room. Each unique test run relies on the
same experimental procedure. The position of the chimney and exhaust system can be altered to
accommodate the various configurations. The temperature data is saved as an Excel file for
future analysis and manipulation.
Results
From the “mini experiment,” we obtained a plethora of useful information. By using the
model of a fluid impinging on a flat plate propelled by a fan-driven space heater, we are able to
determine a limiting thermal boundary layer. The results from the test can be seen in Figure 6.
Figure 6: Boundary Layer Test Results
The results obtained match those described for the given configuration.7 In Figure 6,
channels 5 and 6 are given a zero-value because they are in the direct flow of the heater. This
makes it impossible to obtain accurate boundary layer thicknesses at these points.
6
Natural convection occurs at a much slower rate than forced convection. Therefore, the
forced convective case produces the upper limit for heat transfer within our experiment. The
maximum velocity, from the “mini experiment,” is 2 m/s. Much lower speeds are present under
the natural convection conditions.
The results of this experiment give us a fundamental
understanding of the convective heating process. The boundary layer obtained in the “mini
experiment” provides a benchmark with which to compare the free convective data.
The main experimental data requires more time to obtain than the “mini experiment”
because it relied solely on free convective forces to move the heat through the wall. We are
unable to determine the maximum velocity for this configuration, as it would not register on any
available experimental equipment. However, we did obtain an abundance of data related to the
temperature distribution in the wall under several different configurations. Much of the resulting
data is repetitive and shows the same general relationship between temperature, position, and
time. While the magnitudes of these quantities vary, the correlation between them remains
consistent across the tests. We therefore believe that the included graphs (Appendix B) provide a
representative sample of our work.
The bulk of our data comes from extensive tests of the closed cap exhaust system with
the chimney in several different locations. Our first set of data, Appendix B-1, shows the
variation of temperature within an individual tubuli. An examination of the data set shows that
the system quickly approaches steady state. In fact, it takes approximately 10 minutes of the 60
minute test length to reach the condition. By recording the temperature at four points within each
tubuli it is apparent that the heat collects at the top of the wall due to buoyancy differences. The
upper portion of the wall reaches the highest temperatures because the closed cap exhaust system
retards flow between the tubuli in this region.
The most drastic example of the non-uniform temperature distribution can be seen in
Appendix B-2: Temperature at Top of Wall vs. Temperature at Bottom. Under the closed cap
exhaust configuration, the heat is forced into adjacent channels rather than immediately escaping
through the top. This causes a build up of heat that propagates through the upper portion of the
wall. Conversely, the bottom of the wall sees very little change in temperature. While the
temperature at the top of the tubuli increases by an average 20 °C, the bottoms are raised a paltry
3 °C. This suggests that most heat and airflow occurs through the uppermost portions of the
tubuli.
7
While the previous temperature assessments can be accomplished with data from a single
experiment, some information requires comparisons across several different tests. By adjusting
the chimney position with respect to the heat source, we can vary the temperature distribution
within the tubuli. The resulting data can be seen in Appendix B-3. When the chimney is placed at
tubuli 1, there is a relatively even temperature within the channel. When the chimney is moved to
tubuli 4, the temperature within tubuli 1 becomes much more position-dependent. It is interesting
to note that the chimney position has very little effect on the temperature at the bottom of the
tubuli. This sample data is representative of the behavior of the other tubuli and summarizes the
influence of chimney placement on temperature distribution in individual tubuli.
As in the comparison of temperature variation with chimney placement, the analysis of
“capped” vs. “uncapped” exhaust method requires colleting data from different testing
configurations. Appendix B-4: Effects of Capped vs. Uncapped Tubuli Termination on
Temperature Variation shows the effect of exhaust method on the uniformity of temperature
within the wall. It suggests that the closed cap method produces a build up of heat at the top of
the tubuli, while the open channel method produced a more even heat flow throughout the
structure. This is the expected result, due to the increased flow area available to the open channel
design. The closed cap configuration produces the maximum temperature increase of the tests
preformed, while the open channel creates a much shallower temperature gradient in the entire
wall.
The effects of the open channel exhaust system can be seen further in Appendix B-5:
Effects of Capped vs. Uncapped Tubuli Termination on Temperature Variation Across Top of
Tubuli. The open channel exhaust prevents the build up of heat at the top of tubuli by facilitating
flow across the wall. This reduces the maximum temperature achieved by this configuration.
Conversely, the closed cap configuration creates a heat reservoir at the top of the wall, forcing hot
air to flow through the structure after reaching a higher temperature.
Discussion and Conclusions
Due to the complexity of the flow within the structure, it is impractical, at this point, to
attempt to ascertain quantitative results regarding heat transfer within the tubuli. We are able,
however, to obtain qualitative data concerning the temperature variation within the wall. This
8
information will allow us to address the fundamental questions set forth at the beginning of the
experiment.
We remain primarily concerned with heat flow within the wall and the claim of ancient
Roman authors that the temperature would remain roughly uniform throughout. Our data and
resulting analysis refute this claim. Under all configurations that we tested, we observed a
definitive variation of temperature throughout the wall. Regardless of chimney placement or
exhaust method, the upper portion of the wall is consistently at a higher temperature than the
bottom section. This can be attributed to buoyancy differences and the rapid rise of the warmer
air within the tubuli. The discrepancy between the ancient Roman claims and our findings may be
attributed to the experiment’s run time. The Roman hypocaust system was heated continuously,
our test were very short by comparison.
The relatively low output of our heat source thwarted our efforts to examine the influence
on the semicircular wall geometry. Since we are only able to obtain data in the first four tubuli,
we can not fully develop the effect of the curved surfaces on the airflow within the structure.
Also, there is little available data for a flat wall with which to compare our results.
Our project configuration lends itself to a concerted examination of the heat flow through
the connecting holes between the tubuli. The uneven temperature distribution, produced by
buoyancy differences, creates an elevated temperature state in the upper portion of the wall. This
causes most of the heat to flow through the connecting holes in the top half of the wall. There
was very little flow through the bottom connections. This suggests that airflow occurs closest to
the chimney with the warmest air moving most rapidly throughout the structure. Without the
holes, there would have been very little, if any air movement in the wall. This shows the crucial
role the connecting holes played in the efficiency of the tubuli system.
By moving the chimney to several different positions on the wall, it is possible to see
how crucial chimney placement is. If the chimney is placed close to the heat source, the majority
of the heat escapes from the wall immediately. The further the chimney is placed from the heat
source, the more heat is available to be transferred throughout the structure. This indicates that
for maximum efficiency, the chimney should be placed at the opposite end of the room from the
furnace inlet.
Furthermore we found that the exhaust method also plays a substantial role in regulating
the heat flow throughout the tubuli. The closed cap configuration produces the most significant
9
temperature gradient and, therefore, the highest overall temperatures. The open channel setup, on
the other hand, allows heat to flow more evenly throughout the wall. This method is therefore the
more efficient means of heat transfer and convection. The graphs in Appendix B-5 indicate that
the temperatures for the open channel configuration are lower than those for the closed cap
method. This occurs because the open channel configuration transfers more heat along the wall
and more evenly raises the temperature in the entire structure. This would seem to suggest that
the most effective means for obtaining elevated temperatures across a large structure would be to
have an open, interconnected channel at the termination of the tubuli, in order to facilitate airflow.
At the end of our testing, we visualized the flow through the wall by using a fan driven
space heater and a fine spray of talcum powder. Since we are not concerned with the heat
transfer in this experiment, the effects of the forced convection allow us to speed up the
notoriously slow process of natural convection.
The talcum powder left streaks on the
polycarbonate front panels in the heaviest flow areas. Several of these “streaks” can be seen in
Figure 7. The flow was most easily seen as it exited the chimney. A substantial plume is visible
for the duration of the experiment, suggesting that the chimney quickly sucked air through the
entire structure.
Figure 7: Flow Visualization
Since so little was previously known about the tubuli walls of Roman hypocaust systems
we experienced many obstacles in attempting to formulate an accurate representation. Our
current design, with the space heater placed at one end of the wall, allows us to observe the
10
maximum influence of the connecting tubuli holes because the heat was forced to flow only
through these openings. While this was a desirable result, it also minimized the temperature
increase at the far end of the wall, forcing a limited examination of the heat flow. Additionally,
there are several outside circumstances, over which we have no control that influence the
accuracy of our data.
For instance, the room temperature constantly varies, which caused
fluctuation of the base temperature for each individual test.
The largest obstacle we encountered was the automatic shutoff feature of the space
heater.
This safety feature turned the heater off while it was being used to perform an
experiment. We purchased a second identical heater in an attempt to override or disable the
temperature sensors in the heater. This is done by removing the exterior casing and pulling the
sensors outside of the heater box to keep them cooler than the rest of the heater. Despite our best
efforts, we could not get the heater to remain on indefinitely. In fact, while testing the heaters,
both died in the same day. We have not been able to ascertain what is wrong with them. We
went as far as to completely dismantle one of the heaters but still can not find and open
connection within the circuit.
Due to the breadth of this experiment and the scarcity of quantitative information on the
subject, we are unable to examine all aspects of heating through the use of tubuli wall systems.
Therefore, we hope that another group will continue our experiment next year and expand upon
our design. The primary design alteration that needs to be made is the procurement of a more
powerful and reliable heat source. One suggestion is to use an oven with an exhaust vent to pipe
the heat into the apparatus. By adding a raised hypocaust floor, the model would more accurately
represent the inlet flow into the tubuli of a Roman structure and presumably distribute the heat
more evenly.
Additionally, obtaining more DAQ boxes would allow for the use of more
thermocouples and better data resolution throughout the experiment.
11
References
1. Bansal, N.K. & Shail “Characteristic Parameters of a Hypocaust Construction” Building and
Environment 34 305-318 (1999)
2. Perucchio, R. personal communication
3. Yegül. “Baths and Bathing in Classic Antiquity” The Architectural History Foundation 356389 (1992)
4. Brodribb, G. “A Survey of Tile from the Roman Bath House at Beauport Park, Battle, E.
Sussex” Britannia 10 139-156 (1979)
5. Basaran, T. & Ilken, Z. “Thermal Analysis of the Heating System of the Small Bath in Ancient
Phaselis” Energy and Buildings 27 1-11 (1998)
6. Çengel, Yunus A. Heat and Mass Transfer: A Practical Approach, Third Edition chapter 6
McGraw-Hill: New York, NY (2007)
7. Young, Donald F., Munson, Bruce R., Okiishi, Theodore H. A Brief Introduction to Fluid
Mechanics, Third Edition chapter 9 Wiley: Hoboken, NJ (2004)
12
Appendices
Appendix A:
Costs and Expenditures
Appendix B:
Main Experimental Results
B-1
Individual Tubuli Temperature Variation
B-2
Temperature at Top of Wall vs. Temperature at Bottom
B-3
Effects of Chimney Placement on Temperature Variation
B-4
Effects of Capped vs. Uncapped Tubuli Termination on
Temperature Variation
B-5
Effects of Capped vs. Uncapped Tubuli Termination on
Temperature Variation Across Top of Tubuli
13
Appendix A
Project Expenditures
Vendor
Materials
Cost
Home Depot
Lumber, Screws, Caulk,
Weatherstripping
$87.77
Compact Appliance
1500 W Space Heater (2)
$120.20
U of R Machine Shop
Polycarbonate Panels
Estimated $200.00
14
Appendix B-1
Individual Tubuli Temperature Variation
Temperature Variation in Tubuli 3 for Closed Cap Exhaust Method
By observing the temperature at four points in an individual tubuli, it is apparent that the heat
collects at the top of the wall. The upper portion reaches the highest temperature because the
closed cap inhibits flow there.
15
Appendix B-2
Temperature at Top of Wall vs. Temperature at Bottom
Temperature Variation Across Bottom of First Four Tubuli
Temperature Variation Across Bottom of First Four Tubuli
Density differences cause rapid rise of heat. Therefore, more heat is available to flow between
the tubuli at the top of the wall.
16
Appendix B-3
Effects of Chimney Placement on Temperature Variation
Closed Cap Chimney Placed at Tubuli 1
Closed Cap Chimney Placed at Tubuli 4
The further from the heater, the greater the temperature variation within each tubuli.
17
Appendix B-4
Effects of Capped vs. Uncapped Tubuli Termination on
Temperature Variation
Open Channel Exhaust Method Temperature Variation within Tubuli 2
Closed Cap Exhaust Method Temperature Variation within Tubuli 2
The open-channel top produces a more even heat flow throughout the wall, while the closed top
provides a higher maximum temperature.
18
Appendix B-5
Effects of Capped vs. Uncapped Tubuli Termination on
Temperature Variation Across Top of Tubuli
Open Channel Exhaust Method Temperature Variation Across Top of Tubuli
Closed Cap Exhaust Method Temperature Variation Across Top of Tubuli
The Open Channel exhaust prevents the buildup of heat at the top of tubuli and facilitates flow
across the wall. Conversely, the closed cap configuration creates a heat reservoir at the top of the
wall.
19