Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

55, 3, pp. 911-922, Warsaw 2017
DOI: 10.15632/jtam-pl.55.3.911

THERMAL MODELLING, SIMULATION AND EXPERIMENTAL

VALIDATION OF HEAT ACCUMULATION IN A FRAMED GLASS CABIN

Tarun K. Bera, Sushank Dixit

Mechanical Engineering Department, Thapar University, Patiala, India

e-mail: tarunkumarbera@gmail.com

Anirban Bhattacharya

Mechanical Engineering Department, Indian Institute of Technology (IIT) Patna, India

Devender Kumar

Mechanical Engineering Department, Thapar University, Patiala, India

Arun K. Samantaray

Mechanical Engineering Department, Indian Institute of Technology (IIT) Kharagpur, India

Thepresentwork concerns prediction of the amount of heat accumulationwithin the interior
of a framed glass cabin and proposes some remedial measures to reduce temperature in the
cabin.Various configurations suchas double layer glass boxfilledwith static air, static argon
gas and flowing argon gas within the space between the two glass-layers are considered to
conduct the experiments. Multi-physics bond graph models for these configurations are
developed considering thermo-fluidic aspects. The experimental results are compared with
the simulations using bond graph models. Though, direct application to a vehicle is not
made,without loss of generality, themodelling and experimental procedure can be extended
to analyze the heat accumulation inside a vehicle cabin when the vehicle is parked under
direct sunlight.

Keywords: car cabin, experimental thermal analysis, bond graph modelling, double layer
glass window

1. Introduction

During summer season, the environmental temperature generally varies between 40◦C-50◦C in
southern Asia. The interior of a vehicle heats up significantly when parked in an open envi-
ronment under direct sunlight in such conditions. As the heat wave passes through the glass,
the wavelength of the electromagnetic wave increases, and higher wavelength electromagnetic
waves cannot escape outside the car compartment. Thus, the heat entrapment expedites interior
temperature of the car by nearly 20◦C to 30◦C above the surrounding atmosphere (Dadour et
al., 2011).
As a solution to the problems, vanadium dioxide coating for window glasses has been pro-

posed (Chen et al., 2012). This multilayer coating structure is transparent to visible light and
is opaque to infrared light at high temperature. A mathematical study was done in (Xamána
et al., 2014) on two layer windows with a solar control film. It was shown therein that the use
of the solar control film along with the double pane window reduces the heat flow from inside
to outside by up to 52%. Transmittance of solar radiation through the glazed window can be
reduced by using two glass panes without any air space between these panes (Mazzoni, 1977).
The effect of solar radiation over the air flow and temperature distribution in the compartment
of a car was studied (Lee et al., 2014). The thermal modelling of the car cabin and controlling
the temperature by means of a fuzzy logic controller were developed in (Sanaye et al., 2012).



912 T.K. Bera et al.

A comprehensive review of different models developed to predict thermal comfort of vehicular
cabins in addition to different experimental techniqueswas provided in (Alahmer et al., 2011). In
(Al-Kayiem et al., 2010), experiments were performed by parking a salon car in direct sunlight
and in an un-shaded area. Temperatures at 12 different locations weremeasured and then those
values were used in 3-D CFD simulation performed with FLUENT software.
The bond graph is amulti-energy domainmodelling tool (Merzouki et al., 2012). Itwas used

therein to model the heat transfer from the external environment to the inside of a building.
Many authors have worked on the bond graph modelling of thermo-fluidic systems: general
modelling framework development, thermo-fluid library for process engineering systems (Sa-
mantaray et al., 2004), multi-phase systems (Brown, 2002) and applications to steam generators
(Ould Bouamama et al., 2006).
The usual control of cabin temperature is based on the feed-back principle. However, when a

vehicle moves from a shaded zone to a sunny area or vice-versa, the feed-back control is usually
too slow to timely react due to the inherently slow dynamics of thermal systems. Therefore,
it is preferable to use feed-forward control strategies with estimation of the cabin temperature
change profile based on environmental temperature, air-conditioning load (number of passengers
and interior furniture), and exposure to sunlight and its intensity. It is further useful to combine
both feedback and feed-forward controls in a cascaded loop. However, such control laws require
a well-developed and validated thermal model of the system. In the present work, bond graph
models for such systems are developed and validated through experiments. The bond graph
model of a double layer toughened glass with air (stagnant) and argon (stagnant and flowing)
in between the two glasses is developed and experimentally validated.

2. Thermal model of the system through the bond graph method

A wooden frame structure with toughened glass windows each having a dimension of
548mm×310mm×5mm is constructed (shown in Fig. 1a) and exposed to direct sunlight for
experimentations. This assembly of wooden frame and the glass is assumed to be equivalent to
the internal compartment of a car. The glass is properly sealed with sealant (clay based) so that
no air can escape from the assembly. The frame is insulated with expanded polystyrene sheets
at the top and the bottom panels so that no heat or little heat could escape from those sides.

Fig. 1. (a) Cabin with single glass windows and (b) its bond graphmodel

2.1. Thermal modelling of the cabin system with single layer glass panel windows

The system made of single glass windows is modelled with the help of the bond graph so
that the results can be validated experimentally. Thebond graphmodel of the system is given in



Thermal modelling, simulation and experimental validation... 913

Fig. 1b.Note that thepseudo-bondgraph formalism is adoptedhere for simplicity of formulation
without unnecessarily bringing entropy into the picture.
The heat flux on the glass surface is absorbed, reflected or transmitted. An effort sensor or

detector (De) measures the temperature Tg of the glass. The stiffness K10 of the C10 element
is given by

K10=
1

mgCg
(2.1)

wheremg andCg are mass and specific heat of the glass panel, respectively.
As shown in Fig. 1b, SF14 represents the amount of heat absorbed by the glass surfaceQga,

and this is given by

Qga = IrAgag (2.2)

where Ir,Ag and ag are the irradiance, area and absorptivity of glass, respectively. The amount
of heat radiated by the glass surface into the surroundings Qro is modelled by SF12 element,
and is given by

Qro = egσAg(T
4
g −T

4
s ) (2.3)

where eg,σ,Tg andTs are the emissivity of glass, Stefan-Boltzmann constant, glass temperature
and space temperature, respectively.
Some of the heat from the glass surface is taken away by the surrounding air through convec-

tion. Qco is the heat flow by convection into the surroundings (modelled by SF13 in Fig. 1b),
and is given by

Qco =haoAg(Tg−Tao) (2.4)

wherehao andTao are the convective heat transfer coefficient of the outside air and atmospheric
temperature, respectively. Rci (modelled as R9 in the bond graph model) is the convective
thermal resistance to the heat transfer between the inside air and the inner surface of the glass.
The general heat transfer equation can be written as

Qci =Ahai∆T Qci =
∆T

Rci
(2.5)

Thus, the convective thermal resistanceRci is given by

Rci =
1

Ahai
(2.6)

where hai is the convective heat transfer coefficient of the fixed (inner) air.
Similarly,Rri is the radiative thermal resistance (denoted by the resistive element R7 in the

bond graphmodel) to the radiative heat flow from the inside air to the surface of the glass. This
heat flow can be obtained as

Tac−Tg =
Qri

Ageaσ(T
2
ac+T

2
g )(Tac+Tg)

(2.7)

Defining the above in terms of resistance asQri =∆T/Rri, the radiative thermal resistance
Rri can be obtained as

Rri =
1

Ageaσ(T2ac+T
2
g )(Tac+Tg)

(2.8)



914 T.K. Bera et al.

whereTac is the air temperature of the cabin. SF1 element represents theheat transmittedby the
glass, and this heat is absorbedby the air of the cabin.Thus, the amount of heat transmittedQgt
by the glass is given by

Qgt = IrAgtg (2.9)

where tg is the transmissivity of glass. The element C3models the heat stored by the inside air
and in the given integral causality, it outputs the effort information (temperature of the air of
the cabin). Its stiffness is defined as

K3=
1

maCa
(2.10)

where ma and Ca are mass and specific heat of the inside air. The effort detector (De) is used
to measure the temperature of the air inside the glass compartment. In the bond graph model
given in Fig. 1b, all other parameters exceptRri and the flow sources are constant values which
depend upon material properties and geometric dimensions. The parameter values used in the
simulation of thebondgraphmodel shown inFig. 1b are given inTable 1.Theheat fluxobtained
from the experiment has been used as the input to the bond graph model of a single layer of
the glass. The results obtained from the simulation of the bond graph model of the single
glass layer configuration are shown in Fig. 2a. It is seen from Fig. 2a that the central cabin
temperature increases very fast during the first half an hour and, after that, the rate of increase
of temperature slows down.Themaximum temperature reached after 2.5h is about 59.4◦Cand,
after that, the temperature becomes steady. The temperature of the glass also increases in the
similar fashion as the cabin air; however, its value remains between temperatures of the cabin
air and the atmospheric air. After almost 2h, the difference between temperatures of the central
cabin and the atmosphere becomes almost steady at 20.3◦C. This simulation indicates that the
temperature inside a closed car parked in direct sunlight increases rapidly.

Table 1.Parameter values of the single layer glass cabin

Parameter Value Description

ag 0.25 Absorptivity of glass

Ag 0.68m
2 Total area of all four glasses

Ca 919kJ/(kgK) Specific heat of air

Cg 720kJ/(kgK) Specific heat of glass

ea 0.01 Emissivity of air

eg 0.9 Emissivity of glass

hai 8W/m
2K Convective heat transfer coefficient of fixed air

hao 10W/m
2K Heat transfer coefficient of outside

air with speed of 14km/h

Ir 110W/m
2 Heat flux

ma 0.063kg Mass of air inside cabin

mg 23.4kg Mass of glass

tg 0.5 Transmissivity of glass

Ts 12K Temperature of space

σ 5.67 ·10−8 Boltzmann constant

2.2. Thermalmodellingof the cabin systemwithair-trapped two-layer glasspanelwindows

In the second phase of the experiment and simulation, two layers of toughened glass having
dimensions of 548mm×310mm×5mm are used in each window panel. These two layers are



Thermal modelling, simulation and experimental validation... 915

Fig. 2. Simulation results of (a) single layer glass and (b) double layer glass with entrapped air

assembled together in such a way that there is a fixed gap of 10mm in between them. For this
purpose, some separators are used. This entire setup is placed in an open environment under
direct sunlight. The bond graph model of this modified system is shown in Fig. 3a. A part of
the heat flux falling on the outer glass is absorbed by the glass; a part is reflected back and
the remaining part is transmitted. The heat absorbed by the outer glass is represented byQga2
and is modelled by the SF14 element. As there are two layers of glasses separated by the air
gap of 10mm, the trapped air absorbs some part of the heat transmitted by the outer glass.
The remaining transmitted heat after getting absorbed by the air is reflected by the inner glass.
From this reflected heat, again a part of the heat is absorbed by the air present in between the
two glasses. The rest of the reflected heat after getting absorbed by the air in between the two
glasses is further absorbed by the outer glass. So, the total heat absorbed (Qga2) by the outer
glass is

Qga2 = IrAgag+ IrAgtg(1−aa)rg(1−aa)ag (2.11)

where aa and rg are absorptivity of air and reflectivity of glass, respectively. The heat radiated
and convected from the outer glass are expressed by (2.3) and (2.4), respectively. The radiative
thermal resistance is obtained by replacing Tac and Tg by Ta2 (temperature of the atmospheric
air present in between two glasses) and Tga2 (temperature at the outer glass) in (2.8). The total
amount of heatQaa2 absorbed by the air in between the two glasses is given by

Qaa2 = IrAgtgaa+ IrAgtg(1−aa)rgaa (2.12)

The temperature of the inner glass is detected by the effort detector (De) connected to
0g1-junction. The heat absorbedQga1 by the inner glass is given by

Qga1 = IrAgtg(1−aa)ag (2.13)

The transmitted heatQgt1 that directly enters into the cabin is given by

Qgt1 = IrAgtg(1−aa)tg (2.14)

The parameter values in the earlier simulations are given in Table 1, and the additional
parameters related to the double layer configuration are given in Table 2.



916 T.K. Bera et al.

Fig. 3. Bond graphmodel of (a) double glass cabin with trapped air and (b) double layer glass cabin
with entrapped argon

Table 2.Parameter values of the double layer glass cabin with entrapped air

Parameter Value Description Parameter Value Description

aa 0.01 Absorptivity of air mg1 23.4kg Mass of outer glass

Ir 118W/m
2 Heat flux mg2 23.4kg Mass of inner glass

ma2 0.00806kg Mass of air present rg 0.25 Reflectivity of glass
between two glasses

The results obtained from simulations performed are shown in Fig. 2b. The initial tempera-
ture of atmosphere is 36.5◦C. The temperature of the central cabin after 2.5h becomes 57.3◦C,
whereas for the single glass this temperature is 59.4◦Calthough the heat flux in the double glass
layer configuration (118W/m2) is greater than that in the single glass configuration (110W/m2).
Note that the environmental conditions for both simulations are different as they have been con-
ducted in different times. The maximum rise of the cabin temperature with the double glass
layer configuration is found to be 18.6◦C.The inner glass temperature is less than the outer glass
temperature for up to 1h duration after exposure to direct sunlight. However, after the initial
1h duration, the inner glass temperature exceeds the out glass temperature. Another important
observation is that the cabin air temperatures increases faster than the entrapped air.

2.3. Thermal modelling of the cabin system with argon-trapped two-layer glass panel

windows

The experiments for this configuration are performed in a similar manner to that performed
for the double glass layers with argon entrapped in between the glasses. The bond graphmodel
is given in Fig. 3b, which is similar to Fig. 3a in its structure. The total heatQga2 absorbed by
the outer glass is given by

Qga2 = IrAgag+ IrAgtg(1−aar)rg(1−aar)ag (2.15)

where aar is the absorptivity of argon. The total heatQar absorbed by the argon gas is given by

Qar = IrAgtgaar + IrAgtg(1−aar)rgaar (2.16)



Thermal modelling, simulation and experimental validation... 917

where Rca30 (1/(Ahar) and the Rra29 are convective and the radiative thermal resistances, re-
spectively, for argon present between the outer and inner glass. The heat absorbed by the inner
glass is given as

Qga1 = IrAgtg(1−aar)ag (2.17)

Out of the total heat transmitted by the outer glass, some of the heat is absorbed by the
argon gas and the inner glass. The remaining heat is transmitted through the inner glass into
the internal chamber of the closed cabin. This transmitted heatQgt1 is given by

Qgt1 = IrAgtg(1−aar)tg (2.18)

Most of the parameter values used in the simulation of the bond graph model developed in
Fig. 3b are givenTable 1 andTable 2. The values of themodified and additional parameters are
listed in Table 3.

Table 3.Parameter values for the double layer glass cabin with entrapped argon

Parameter Value Description Parameter Value Description

aar 0.1 Absorptivity of argon har 5.3W/(m
2K) Heat transfer
coeff. of argon

Car 520kJ/(kgK) Specific heat of argon Ir 100W/m
2 Heat flux

ear 0.05 Emissivity of argon mar 0.01209kg Mass of argon

The simulation results for the double layer glass cabin with entrapped argon are shown
in Fig. 4a. The initial temperature of the surrounding is 36◦C. The temperature of the central
cabin after 2.5h is 57.08◦C,whereas for the double glass with air, this temperature is 7.3◦C.The
temperature differences between the central cabin and the atmosphere are 16.7◦C and 18.6◦C,
respectively, for the double layer glass with argon and air insulation between the glass layers. So,
as expected, the use of the argon gas between the glass layers yields better thermal insulation.

Fig. 4. Simulation results of the double layer glass with (a) entrapped and (b) flowing argon

2.4. Thermal modelling of the cabin system with flowing argon between two-layer glass

panel windows

This configuration is intended for the double layer glass with the argon gas continuously
flowing through the system with a flow rate of 0.403182g/s. The bond graph model of the



918 T.K. Bera et al.

system is similar to that for the earlier case. However, the heat transfer coefficient for flowing
argon is different. The parameter values for the simulation are given Tables 1, 2 and 3. The
convective heat transfer coefficient har of argon is considered as 7W/(m

2K) for the flow rate of
0.403182g/s. The simulation results for the double layer glass with flowing argon are shown in
Fig. 4b. The initial temperature of the surrounding is 36.5◦C. The temperature of the central
cabin after 2.5h is 55.07◦C whereas for the double glass with static argon, this temperature is
57.08◦C.The steady-state temperature difference between the central cabin and the atmosphere
is 16.7◦C and 16.1◦C for the double glass layer configuration with static argon andwith flowing
argon, respectively. So, flowing argon between the two glass layers is preferable.

3. Experimental validation

3.1. Selection of the material and sensors

The materials and sensors used for the development of the experimental setup are wo-
oden frame, toughened glass, separator, air-oxygen separator, thermocouple, digital thermome-
ter, argon cylinder, pipe and T-connectors as shown in Fig. 5. The dimension of the frame
has been selected according to size of the toughened glass. The dimensions of the wooden
frame are 411.6mm×411.6mm×649.6mm. Laminated glass and toughened glass are widely
used in vehicles due to its non-breaking tendency. The size of the toughened glass used is
310mm×548mm×5mm. A solar power meter is used to measure the solar heat intensity x,
and this value is used to calculate the solar heat flux Y as obtained after calibrating with a
pyranometer (R2 =0.99)

Y =0.745x+1.839 (3.1)

Fig. 5. Experimental accessories (a) glass supporting structure, (b) digital thermometer, (c) argon
cylinder, (d) separator, (e) solar power meter and (f) argon-oxygen separator



Thermal modelling, simulation and experimental validation... 919

3.2. Experimentation on the cabin system with single layer glass panel windows

It is the first phase of the experiment; toughened glass having dimensions 548mm×
310mm×5mm is fitted into the wooden frame. The glass is properly sealed with the sealant
(clay) so that no air can escape from the assembly. The frame is insulated with expanded po-
lystyrene from the top and the bottom so that very little heat could escape. The entire setup
is exposed to direct solar heat waves. The heat starts to accumulate in the interior of the cabin
by means of conduction, convection and radiation. Most of the accumulated heat is due to the
radiation. Two digital thermometers are used to measure cabin temperature and atmospheric
temperature. A solar power meter is used to measure the solar light intensity which eventually
gives the value of the solar heat flux. The experiment starts at 11 am on a hot sunny day of
summer and readings are taken at an interval of 15 minutes for the first half hour and then
onwards at 30 minute intervals. Initially, the temperature difference between the atmosphere
and the cabin compartment is less, but as the time passes, this temperature difference goes on
increasing. The results obtained by the experiment are comparedwith the results from the bond
graphmodelling, and these are shown in Fig. 6a. As shown in Fig. 6a, the simulated results for
the central cabin temperature are very close to those obtained from the experiment.

Fig. 6. Experimental vs simulation results for (a) single layer glass and (b) double layer glass
with entrapped air

3.3. Experiments on the cabin system with air-trapped double layer glass panel windows

The top and the bottom portion of the cabin prepared with the double layer glass panel are
covered by expanded polystyrene sheets so that little heat could get escape through them. Two
digital thermometers are used to measure the temperature inside and outside the cabin. The
basic principle of such a type of arrangement is to formabarrier for theheat flow.The toughened
glass and trapped air inside the two layers of glasses have low thermal conductivity and thus
inhibit heat transfer.The experimental and simulation results for this configuration are shown in
Fig. 6bwhere the atmospheric temperature (an input to the simulationmodel) has a variation of
about 2◦-3◦C.Although there is notmuch variation in the atmospheric temperature, the central
cabin temperature goes on increasing. Initially, the temperature difference between the central
cabin temperature and the atmospheric temperature is less, but with time, this temperature
difference increases. When compared to Fig. 6a, i.e. the experiment performed on the single



920 T.K. Bera et al.

layer glass, the temperature difference obtained in the double layer glass panel configuration is
quite less.

3.4. Experimentson thecabin systemwithargon-trappeddouble layer glasspanelwindows

The experiments are performed on the double glass with argon entrapped in between the
glasses. A hole of 3mm is drilled through the separator. A pipe of 3mm diameter is inserted
through the hole of the separator and this pipe is further connected to the argon gas cylinder.
This assembly is prepared so as to fill the gapwith argon (stored in the cylinder) andprevent any
leakage. A constant flow of the argon gas is maintained in all four double layer glass assemblies
so that atmospheric air is displaced by the pressurized argon gas. The constant flow is checked
by counting the bubbles coming out from the outlet pipe which is dipped in water. When the
bubble count per time unit is stabilized, the argon gas flow is stopped. The displacement of the
atmospheric air by the pressurized argon gas is also verified by a parallel arrangement installed
during the experiment. In this arrangement, the outlet line is made to pass through a closed
chamber (Fig. 5f) having a burning candle inside it. The candle stops burning as soon as there
is no oxygen available in the outlet pipe coming out from the double layered glass assemblies.
When the pressure at the supply and at the outlet of the assembly of the glasses becomes equal,
it indicates that the argon gas has been completely filled in the gap of the two glasses. Then the
entire setup is exposed to the sunlight at the scheduled time.
The experimental and simulation results for this case are shown in Fig. 7a. During this

experiment, the atmospheric temperature ranges between36◦-40.4◦Candthe rise in temperature
of the central cabin is 16.7◦C.Compared to the results obtained for the single glass panel cabin
(20.3◦C) and the double layer glass panel cabinwith air insulation (18.6◦C), the rise in the cabin
temperature is less for the double layer glass panel cabin with argon gas insulation between the
glass layers. The cabin temperature has fallen by nearly 3.6◦C from the single layer glass panel
configuration.

Fig. 7. Experimental vs simulation results for the double layer glass with (a) entrapped argon and
(b) flowing argon

3.5. Experiments on the cabin system with two-layer glass panel windows and argon

flowing between the glass layers

Experiments were further conducted using the same setup with argon flowing at a rate of
0.403g/s through the gap between the two glass layers. The simulation and experimental results



Thermal modelling, simulation and experimental validation... 921

for this configuration are shown in Fig. 7b. The temperature difference (16.1◦C) between the
central cabin temperature and atmospheric temperature is lower than that for the single glass
layer (20.3◦C) and the double glass with the entrapped air (18.6◦C), but nearly the same as
that of the double glass with entrapped argon (16.7◦C). The continuous flow of argon helps
carrying away the heat outside the cabin and, therefore, reduces a rise in the cabin temperature.
This reduction could bemore effective if the argon flow rate is increased. In addition, while the
sealed glass panels with permanently entrapped air or argon can be easily fabricated as a unit,
the flowing argon configuration requires additional components like air/argon pump, pipes, etc.
due to which themanufacturing andmaintenance problems encountered far outweigh theminor
performance gain.

4. Conclusions

Experiments have been conducted in a closed cabin of toughened glass to understand the heat
accumulation in the interior of a vehicle when it is exposed to direct sunlight. A bond graph
model of the setup has been developed to perform simulation studies. The simulations and
the experiments give an idea about the rate at which heat gets accumulated in the cabin.
Replacing the single layer toughened glass panels with double layer toughened glass panels with
static air trapped between the two glass layers, a reduction in the rate of increase of the cabin
temperature has been observed.When the argon gas was trapped between the two glass layers,
further reduction in temperature of the cabin air was observed. Moreover, when the argon gas
was allowed to flow continuously at a slow flow rate, the rate of heat accumulation inside the
cabin reduced further. The bond graph models developed for all these different configurations
give very goodpredictions of the rate of heat accumulation or temperature of the cabin air. Such
models can be used to develop predictive feed-forward or cascaded feedback and feed-forward
control systems for cabin temperature regulation in the place of purely feedback controllers
used in contemporary vehicles. This research work will be pursued further to deal with the heat
transfer and storage through/in the roof and interior materials of a vehicle with aim to develop
an optimized model-based control system of the cabin temperature.

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Manuscript received April 5, 2016; accepted for print March 31, 2017