A publication of
CHEMICAL ENGINEERING TRANSACTIONS
The Italian Association
VOL. 43, 2015 of Chemical Engineering
Online at www.aidic.it/cet
Chief Editors: Sauro Pierucci, Jiří J. Klemeš
Copyright © 2015, AIDIC Servizi S.r.l.,
ISBN 978-88-95608-34-1; ISSN 2283-9216
TRANSIENT HEAT TRANSFER ANALYSIS OF STORAGE
DEPOTS FOR HEAT SENSITIVE SUBSTANCES UNDER
SUMMER WEATHER CONDITIONS
Giovanni Cocchia,b
a
Arson Fire Safety and Environmental Investigations S.r.l., Via Zannoni 58, 40134, Bologna
b
DICAM, Via Terracini 28, 40131,Bologna
g.cocchi@arson.it; giovanni.cocchi2@unibo.it
Heat sensitive substances, like propellants and organic peroxides, may experience severe self accelerating
decomposition reactions, if stored or transported in conditions which expose them to exceedingly high ambient
temperature. This may be especially true for ship transportation across the tropical regions and the historical
data by Bowes (Bowes 1966) and the more recent work by Steensma et al. (Steensma et al. 2008) are the
most important literature reference on the topic. Summer weather conditions in many European countries like
Italy may, in principle, prompt similar concerns. In this work a rigorous methodology for transient thermal
analysis of storage depots is discussed in detail, including the use of appropriate natural and forced (due to
wind) convection coefficients and a procedure for predicting diurnal time dependent air temperatures and
solar radiation heat fluxes. Time dependent boundary conditions enable a better analysis of thermal conditions
inside the depot, effetively including the effect of diurnal cycle. This may prove useful for both accident
investigations and safety assessments.
1. Introduction
Substances liable to self accelerating decomposition processes are indeed heat sensitive, since the kinetic of
decomposition reactions, including those which may be regarded as auto –catalytic, is strongly influenced by
temperature of the reacting system. In fact, commonly an increase in temperature results in an exponential
rise of the reaction rate. Since thermal runaway happens when the heat generated by the decomposition
reactions is greater than heat losses to the surrounding environment, an increase of the reaction rate may
renderer unstable and thus trigger supercritical behaviour in a package of heat sensitive substance. This is a
relevant safety concern in storage and shipping of such substances. In the scientific literature it is widely
accepted that the best risk mitigation measure is the control of the temperature at which liable substances are
being transported or stored. The UN regulations on the transportation of hazardous substances are based on
temperature control rules and state that only products with self accelerating decomposition temperature
greater than 55°C may are suitable for uncooled transport. The relationship between reactivity of a substance
(represented by its heat of reaction, by the activation energy and by the frequency factor of the decomposition
reaction(s)), critical temperature, package size and heat transfer conditions (represented by internal and
external heat transfer coefficients and by the thermal properties of the substance itself) may be elicited by
means of the well known Semenov and Frank Kamenetskii theories, or with the Gray Wake approach. These
theoretical treatments enable to take into account the effect exerted by external heat transfer and by the
package geometry on the onset of supercritical conditions. Moreover, these theories enable to extrapolate
from lab scale experiments, to real world or industrial scale conditions (the accuracy of such extrapolation may
vary greatly, especially for complex decomposition process with multiple reaction pathways). Examples of heat
sensitive substances may be easily found among explosives, propellants and organic peroxides. Such
products are commonly stored and shipped all around the globe and thus may be exposed, sometimes for
small amount of time, sometimes for longer periods, to extreme weather conditions and thus to challenging
thermal conditions. This may be especially true for ship transportation across the tropical regions and the
historical data by Bowes (Bowes 1966) and the more recent work by Steensma et al. (Steensma et al. 2008)
are the most important literature reference on the topic. According to Bowes (Bowes 1966), ship’s deck
temperatures as high as 60°C were recorded in the Caribbean, Panama Canal and Guayaquil harbor and a
value of 70°C is quoted for the voyage of another ship vessel, while according to Steensma et al. during a sea
voyage of 2 month through the tropics temperatures as high as 63°C were recorded as the air temperature of
the grey top of a container, but only for 1 hour. In the same voyage, the highest recorded air temperature in
the air space of one of the container’s compartment was 50.7°C, but recorded liquid temperature of the top
packages was only 32.3°C and the most inward packages even did not followed the day-night temperature
cycle. Similar statement may be found in Bowes. According to Steensma et al., in the same voyage, the worst
day the 24 h average temperature of the roof of the sea container (a grey coloured ISO container sized
20’x8’x8’6’’) was 8.5°C higher than the average ambient temperature. The average temperature of the sun
exposed side was 7.5°C higher than the average ambient temperature, while on the other side, which
remained in the shade, the average temperature was almost equal to the ambient average. Similar values are
reported by Bowes, which for safety reasons rounds the average deck temperature excess to 10°C above the
ambient average. Steensma et al. concluded that even taking into account adverse temperatures conditions
(which are undoubtedly at the upper bound of the values recorded in ship holds), the question “Are transport
incidents always due to bad quality products or bad handling practices?” Must also be answered by “yes, if
there is a transport incident there has been something wrong with the product quality”. In fact, Steensma et al.
argument that even liquid organic peroxides having an of SADT 55°C can be safely transported in uncooled
sea containers, validating the previously cited UN criterion. Summer weather conditions in many European
countries like Italy may, in principle, prompt similar concerns, even if it is clear that less extreme conditions are
expected respect those found in tropical areas. In this work a rigorous methodology for transient thermal
analysis of storage depots is discussed in detail, including the use of appropriate natural and forced (due to
wind) convection coefficients and a procedure for predicting diurnal time dependent air temperatures and
solar radiation heat fluxes. Time dependent boundary conditions enable a better analysis of thermal conditions
inside the depot or inside a metallic container used for shipping or for temporary storage, including the effect
of diurnal cycle. This may prove useful for both accident investigations and safety assessment.
2. The diurnal cycle of air temperature and solar irradiance according to UNI10349
On average, excluding episodic meteorological phenomena like storms, the temperature of air will vary along
the day and the night according to a cyclic or periodic law. The maximum and minimum values, along with the
characteristic time constant of the air temperature cycle depends from the geographical location and from the
period of the year. The standard UNI10349 provide a simplified relationship, in tabular form, which give a
reasonable estimation of the summer air temperature cycle, if maximum and minimum air temperatures of the
site are available. In the hours between sunrise and sunset, the sun travels an apparent circle in the sky,
whose height and amplitude depends on latitude and longitude, during which a variable heat flux to the hearth
surface is produced. This heat flux is known as solar irradiance and is a function of the position on the globe
and of the day of the year. The standard UNI 10349 provide a table which enables to estimate, for every hour
after sunrise and before sunset, in a given latitude of the Italian territory, the maximum solar irradiance which
during summer impinge an horizontal surface and vertical surfaces oriented toward N, NE, E, SE, S, SW, W
and NW. Figure 1 and 2 report an example of summer air temperature cycle and solar irradiance for a location
in central Italy, estimated according to UNI10349. This data are the inputs for the following calculations.
Maximum and minimum air temperatures were obtained by a local weather station.
3. Heat transfer from the external surfaces of a building or of a container
The sun irradiance provide an incoming heat flux which impinge the external surfaces of the storage building
or of the container used for shipping or for temporary storage, raising their temperature above those of the
surrounding environment. The extent of that temperature rise depends from the energy budget of the wall,
since convective loss with the surrounding air and radiative loss toward to all the other solid bodies in view
field will subtract a relevant fraction of that incoming heat. Functions (originally in tabular form) like the ones
plotted in Figure 2 provide the value of the incoming solar irradiance as a function of day's hours and of the
surface's orientation. The function (originally in tabular form) plotted in Figure 1 provides the temperature of
the air which surrounds the storage building or of the container used for shipping or for temporary storage.
Convective heat transfer between the external surfaces of the building and the surrounding air is indeed a
relevant contribution to the energy budget of the building envelope or of the container used for shipping or for
temporary storage. Heat transfer coefficients may be estimated by means of empirical correlations like those
proposed by Jurges,(Defraye et al. 2010) which include the effect of wind and are extensively used for
building applications. The external surface will also lose heat through radiation toward all the other solid
surfaces which are within its field of view (the terrain, other buildings, vegetation etc etc). This contribution
may be calculated assuming that the air temperature is a reasonable estimate of the temperature of the
external environment as a whole. View factor is omitted, since if this radiative loss is toward solid targets found
in all the solid angles of the field of view of each point of the surface, it may be assumed to be unitary or close
to it. Emissivity factor of 0.9 may be assumed as a rough estimate of the emissivity of real world gray bodies.
Therefore, the net heat flux from the exterior, as a function of time and surface's orientation may be estimated
as:
q˙' ' net , ext =q˙' ' sun irradiance +h ( T amb−T wall ) +σε ( T 4amb−T 4 wall ) (1)
Figure 1: The daily cycle of air temperature, estimated according UNI 10349.
Figure 2: The daily cycle of sun irradiance at 44° latitude, estimated according UNI 10349.
4. The thermal environment inside a building or inside a container used for shipping or for
temporary storage
The wall and the roof of any enclosure exchange heat also with the air and with the objects inside. According
to Steensma et al. (2008), values between 4 to 8 W/m2K give a reasonable representation of free convection
heat transfer. Radiative heat transfer contribution may be accounted as well, assuming appropriate values for
the view factor between the enclosure walls and the object surfaces.
q˙' ' net , ∫ ¿=h( T −T air ) + ∑ Fwall , j σε (T
4
−T
4
)¿ (2)
wall wall object j
For thermally thick walls, which is indeed the case of insulated walls or roofs, a relevant temperature gradient
will develop across the thickness of the wall and the temperature cycle will exhibit a cyclic behavior that is
shifted from the diurnal cycle of solar irradiance by a time factor that may be estimated from the thermal
penetration theory. Heat transfer through thermally thick walls must be modelled through Fourier equation. For
thermally thin walls, temperature gradient across it will be negligible and the diurnal temperature variation will
closely follow the diurnal variation of the sun irradiance and, during the night, the hourly variation of air
temperature. The energy balance equation for a thermally thin wall is:
d T wall
δρCp =q˙' ' net , ext −q˙' ' net , ∫ ¿¿ (3)
dt
Since the net heat flux from the external environment is explicitly time dependent, this equation must be
solved by means of numerical method. Since the internal heat exchange of the wall with the internal air and
the internal objects depends on the temperature difference with air and objects itself, the energy balance of
the walls must be solved along with their energy balance equations. In the present case, a simple Euler
method was implemented, adopting a 60 s time step, which is adequate to simulate a week of daily long
cycles. Further refinement of the time discretization led to the same numerical result. The above equation
must be written for each wall and for the roof, while heat transfer through the bottom of the container, when
lying on the ground, may be neglected. Since during summer terrain temperature is lower than that of air or of
any sun exposed surface, and thus the ground may act as an heat sink, this choice may be considered to be
conservative.
Figure 3: The daily cycle of the wall temperature of a 3 m3 metallic enclosure.
Figure 4: The daily cycle of the air temperature inside a 3m3 metallic enclosure.
Figure 3 shows the results of the transient heat transfer analysis applied to a 3m x3m x 3m enclosure used for
storage (as it may be a container used for temporary storage). The walls and the roof are 3 mm thick steel
plates and are exposed to sun irradiance, whose intensity and diurnal variation is given by the functions
plotted in Figure 2. The enclosure is aligned along the N-S axis. Air temperatures are those plotted in Figure
1. Wind velocity is assumed to be 14 km/h (i.e. 7 knots). Thanks to the limited thickness or the walls and to the
high thermal conductivity of the steel, the surfaces of the metallic enclosure will behave as thermally thin
objects, with no temperature gradient between their internal and external surfaces. The surface of the roof
reaches 58.2°C at midday, while its average value is around 35°C, which is 9 °C higher than average
temperature of ambient air. This result is indeed in excellent agreement with the experimental result of
Steensma et al. (Steensma et al. 2008) and with the simple rule proposed by Bowes (Bowes, 1966).The
reader is encouraged to compare the plot of Figure 3 of this work with the plot of Figure 4 of Steensma et al.,
which recollects the temperature–time records for the first 2 weeks of the sea voyage in the Tropics, for the
sun-exposed surfaces of a container. The time temperature records for the top of the container are indeed
quite close to the roof surface temperatures calculated with the approach of this work and the direct
comparison with the daily maxima recorded in the sea voyage indicate that our approach is indeed
conservative. Moreover, temperatures recorded at night during the sea voyage are lower than those estimated
in our case. Figure 4 shows the results of the calculation of the air temperature inside the 3m x3m x 3m
enclosure. Even if the surface of the roof reaches 58.2 °C, the maximum predicted air temperature inside of
the enclosure is 44.7°C. The average air temperature is estimated to be 31°C. Therefore, air temperature
remains lower than that of the metallic surfaces which are under direct sunlight.
5. The temperature of a package of reactive substance
Let us consider a package of a liquid reactive substance, like the organic peroxide considered by Steensma et
al., stored inside the above described metallic enclosure, for which the thermal environment has been already
characterized as described in chapter 4 of the present work. The thermochemical and kinetic parameters of
the liquid organic peroxide adopted in the present work are the same of Steensma et al. by Steensma et al.
(Steensma et al. 2008). With this set of thermochemical parameters a 25 kg package of liquid organic
peroxide will exhibit a SADT equal to 55”C,which is the highest SADT for which uncooled transport and
storage may be allowed per UN regulations. The same calculations of chapter 4 have been redone including
1 m3, 4 m3 and 12 m3 packages of the above mentioned self reactive substance. It is assumed that the
liquid is perfectly stirred and thus the temperature of the package is assumed to be homogeneous. The
reaction consumption is neglected, as it is commonly assumed in thermal stability calculations. The energy
balance equation for the package, which is assumed to be exchanging heat with the surrounding air through
convection and with the surrounding walls through radiant heat transfer, is:
d T package 4 4
mCp =∑ A i h i ( T air −T package ) + ∑ Ai F package ,i σε ( T wall ,i −T package ) +mQ 0 exp (−E
(4)/RT )
dt
Figure 5 shows the results for the three package considered. It is found out that even the biggest package
considered in the present work remains subcritical (i.e. do not experience thermal run away) and that the
bigger the package, the lower is the effect of diurnal cycle (i.e. increasing the thermal inertia of the system the
liquid temperature takes longer to reach a steady state period, but get closer to the average value). The
maximum liquid temperature do not exceed 35°C and the liquid average temperature are close to 33°C. This
value is quite close to the values predicted by Steensma et. al.., which used experimentally determined values
for the wall temperature, but used directly the 24 hour averaged values. In order to assess the effect of the
organic peroxide reactivity, the calculations have been repeated assuming that the liquid be inert (setting
equal to zero the pre exponential factor). It is found that the average temperatures predicted for the reactive
liquid are 1.4 K or less higher than the values predicted for the inert liquid: this is the same results obtained by
Steensma et al..
Figure 5: The daily cycle of the temperature inside a liquid organic peroxide stored in a 3m 3 metallic
enclosure.
6. Conclusions
This work presents a method to predict the thermal environment that develops inside sun exposed storage
depots or containers during summer period in Italy. This method has been applied to a metallic enclosure with
thin walls and has been shown to produce results which are in good qualitative agreement with experimental
data recorded for containers during ship voyage through tropical seas. From the quantitative point of view, the
results produced by this method are found to be conservative, since provide values slightly higher than those
recorded in the tropical region. The method then has been applied to estimate the temperature of packages of
various size of reactive substance stored inside the sun exposed metallic enclosure. It is found that even if the
maximum temperature of the metallic walls may reach 58.2°C, its average temperature do not exceed 35°C,
while the maximum temperature in the package of liquid organic peroxides is around 35°C and the average
temperature of the liquid organic peroxides are close to 33°C. Therefore, even a reactive substance with
SADT equal to 55°C may be stored uncooled inside such enclosure. The results of this work confirms the
conclusion reached by Steensma et..
References
Bowes, P.C. (1966) High mean temperatures in ship’s holds, Fire Research Note n°633
Defraeye, T., Blocken, B., Carmeliet, J., (2010) Convective heat transfer coefficients for exterior building
surfaces:Existing correlations and CFD modelling, Energy Conversion and Management.
Steensma, M., Schuurman, P., Mak, W.A., (2008) Validation of the UN criteria for the uncooled sea transport
of liquid organic peroxides: Full-scale test and modeling. Journal of Loss Prevention in the Process
Industries, 21, 2008, 615-641.
UNI 10349:1994, Riscaldamento e raffrescamento degli edifici - Dati climatici, Ente Italiano di Normazione.
