Numerical Simulation of Heat Transfer through Uniform Multilayer
Walls using ANSYS
STAN-IVAN FELICIA-ELENA, DINU RADU-CRISTIAN, DUINEA ADELAIDA-MIHAELA
Department of Department of Electrical, Energy and Aerospace Engineering,
University of Craiova,
Address Bld. Decebal, no. 107,
ROMANIA
Abstract: - The paper presents a study on modelling the main heat transfer parameters through opaque building
elements. The need for models to assess the thermal behavior of a building has increased greatly in recent
years, primarily to allow a more accurate determination of the energy consumption of buildings to evaluate the
performance of heating systems. In recent times, mathematical models and software have been implemented to
obtain simulations that are very close to the real functioning of the main components of buildings. The present
article consists in modeling a multi-layer homogeneous wall, which separates the interior space of an enclosure
(rooms) from the outside environment. The article aims to carry out a series of simulations on the structure of a
non-homogeneous multilayer wall using the ANSYS program. The simulations have been performed highlight
how the values vary (both numerically and graphically) for a series of characteristic parameters such as heat
fluxes, temperatures, convection coefficients. The values of the parameters obtained with the ANSYS program
were also compared with those obtained by classical numerical calculations.
Key-Words: - thermal transfer, buildings, multilayer wall, modeling, mathematical model, thermal simulation.
Received: June 11, 2023. Revised: November 13, 2023. Accepted: December 23, 2023. Published: December 31, 2023.
1 Introduction
The buildings sector has the highest energy
consumption in the world, due to the increasing
demand to construct buildings.
Several attempts have been made to improve energy
consumption and increase energy efficiency in the
building sector. To reduce carbon emissions,
energy-efficient buildings are one way to save
energy and reduce energy demand. Energy
consumption in buildings is becoming increasingly
important as it accounts for a large amount of
overall energy consumption. Energy is a basic
element and requirement for human existence and
development.
To improve the energy efficiency of buildings
the thermal properties of building materials are of
great importance, [1].
A comfortable environment for people's
activities, especially in terms of temperature, is very
important. For this reason, thermal comfort becomes
a key factor in the design and construction of a
building as a place to carry out activities, especially
a house as a place for everyday life. In general, the
process of creating building comfort cannot be
separated from efforts to limit the influence of
outdoor temperature on the building. The warm
outdoor temperature is the most difficult to deal
with in tropical countries so as not to affect the
indoor temperature. For a four-season country, the
challenge becomes a little more complex, as the
performance of the building in winter must also be
able to withstand the heat (warm temperatures)
inside the building without losing it easily. Heat loss
from buildings occurs mainly through the exterior
walls, ceiling, windows and basement of the
building and through infiltration, [2]. In response, a
well-designed building insulation system is needed
to help achieve thermal comfort in buildings.
Buildings consume a third of the world's total
annual energy, a ratio that continues to rise as
population and urbanization increase, [3]. Most of
the energy is consumed in buildings located in urban
areas in developing countries and, due to the
modernization of buildings in the construction
sector, local climatic conditions and materials are
neglected, [4]. Buildings play a vital role in creating
a safe and comfortable living environment. To
create thermal comfort in buildings, heating,
ventilation and air conditioning (HVAC) systems
use about 50% of the building's energy, [5].
Providing thermal comfort in buildings has always
been one of the main concerns of architects around
the world, and among these, residential buildings
have always been of particular importance, [6].
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.28
Stan-Ivan Felicia-Elena,
Dinu Radu-Cristian, Duinea Adelaida-Mihaela
E-ISSN: 2224-3461
325
Volume 18, 2023
The temperature in steady-state heat transfer
remains constant throughout time, whereas the
temperature in transient heat transfer fluctuates.
Mathematical formulas can be used to describe
these processes. Even today, a variety of software is
available to assist the calculation process by
providing more displays that make reading and
providing information easier to generate.
The internal thermal climatic condition of a
house is directly affected by how the building
envelope (walls, windows and roof) is designed to
suit the environment it is exposed. How the building
envelope is constructed has a great effect on the
energy required for heating and cooling to maintain
human thermal comfort. Understanding how the
internal climatic conditions react to the building
envelope construction is therefore of great value,
[7].
This study aims to provide an overview of how
much influence the configuration system has on the
installation of an insulating wall layer by using
ANSYS software and the steady-state analysis
approach, [8]. It is possible to assess how quickly
and how much energy is transferred down the
insulating wall by using the value of heat flow or
heat transfer rate, [9].
2 Problem Formulation
2.1 Numerical Modeling of Heat Transfer in
Multilayer Walls
Numerical modeling and energy simulation of
buildings is a mature but growing field, benefiting
from new computer and automation techniques that
are increasingly expanding into even the most
mundane sectors of activity.
The problem is that the contribution of
computerized technology means that the majority of
beneficiaries run the risk of forgetting the meaning
of the phenomena that are at the basis of ensuring a
pleasant climate in buildings; for the systems
designer, on the other hand, it is a field that brings
new challenges and new ways of optimizing
problem solving.
A second risk that the development of
technology can pose for people is the enclave of
science for certain private research centers and the
promotion of specific products, which, under patent
or copyright protection (which nowadays are more
likely to block the development of science than to
promote it), only esoterically keep certain research
results within themselves for commercial
exploitation. In this sense, the present paper aims to
deal with the fundamentals of numerical modeling
of energy transfer phenomena in buildings,
explicitly exposing both mathematical and
descriptive models.
Energy optimization in buildings is done for
people, so it starts from their needs for an acceptable
microclimate, and the research results must
converge to these needs, [10].
It is known that in the use of the finite difference
method most expositions tend to present this method
considering the uniform grid, being the most
mathematically simple situation. However, it should
be pointed out that complex geometrical models
already require a more complex mathematical
apparatus, and consequently a more elaborate grid,
more flexible on the geometry of the modeled body.
Conditions that must be fulfilled by a numerical
analysis to be considered valid:
- Consistency - the discretization of partial
differential equations must be done in the sense of
zero-tending of the mesh (so the truncation error
must be reduced as much as possible);
- Stability - the errors generated in solving the
discretized equations should not amplify;
- Convergence - the numerical solution must be
close to the exact solution of the differential
equation and must converge towards zero as the
mesh tends to zero;
- Conservation - The underlying conservation
laws must be respected at the discrete domain level
(artificial sources of values or pits must be avoided -
e.g. in rigid solid analysis artificial stress
concentrators must be avoided);
- Marginalization - quantities such as mass,
density, and temperature must appear strictly
positive in any results;
- Repeatability - the model built and analyzed in
one place should give the same results as a model
built with the same initial conditions in another
place.
There are several ways of numerically
calculating heat transfer, but the most important are:
- The finite difference method - starting from the
equations governing the phenomenon and arriving at
a system of trivial equations after discretization and
setting boundary conditions;
- Finite element method - starting from the
equations governing the phenomenon at the scale of
the whole, then after discretization the form of the
equation is still recognized at the level of the
resulting finite elements, each finite element is
represented by a matrix, and the global matrix of the
whole studied is the sum of all the matrices. of the
finite elements.
- Finite volume method;
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.28
Stan-Ivan Felicia-Elena,
Dinu Radu-Cristian, Duinea Adelaida-Mihaela
E-ISSN: 2224-3461
326
Volume 18, 2023
- Spectral method.
Figure 1 presents a composite wall, a wall made
of several layers of different materials. The
composite wall consists of three layers of
thicknesses δ1, δ2, and δ3, [11].
Fig. 1: Composite wall, [11]
The thermal resistance for each layer of the
composite wall is determined with the relation (1).
,
,
[m2K/W] (1)
In a plane wall, the rate of heat transfer is as
follows, relation (2), [11]

 


 
[W/m2] (2)
Where: R1, R2, Rn are the thermal resistance
for each material of the composite wall, [m2K/W];
is the unit thermal flux through the wall, [W/m2]; k
is the overall heat transfer coefficient, [W/m2K];
is the temperature difference between the indoor and
outdoor environment, [K]; is the thickness for
each component layer, [m], A the surface, [m2].
The thermal conductivities of these layers are k1,
k2, and k3, respectively. The temperature of the outer
layers of the wall is T1 and T4 as shown in the
Figure 2, with interface temperatures as T2 and T3. It
is being assumed that different layers are having
perfect contact between them and hence the adjacent
surfaces are at the same temperature. In the steady-
state condition, the heat flow q is the same for all
the layers and is constant, [10], [11].
The equations of unit thermal flux through these
layers are:

, [W/m2] – for the first layer

, [W/m2] – for the second layer
(3)

, [W/m2] – for the third layer
The temperature differences across the layers,
resulting from the above equations are presented in
the formula (4):
󰇡
󰇢[C]
󰇡
󰇢[C]
(4)
󰇡
󰇢[C]
In a composite wall the rate of heat transfer is
presented in formula (5):

 
 , [W/m2] (5)
3 Case Study for Modeling Thermal
Transfer Parameters for a
Multilayer Composite Wall
Figure 2 presents a multilayer composite wall that
will be analized. It is a multilayer wall composed of
4 layers with different materials structures and
thicknesses. The materials and their thermal
characteristics are presented in Table 1. The interior
temperature is considered 20 C and the outside
temperature is -15 C.
Fig. 2: The analized multilayer composite wall
Table 1. The type of material used and the
dimensions of the wall
Layer
Thickness,
[mm]
Thermal conductivity,
[W/mK]
Exterior plaster
25
0.93
Thermal
insulation -
polystyrene
150
0.04
BCA
400
0.27
Interior plaster
15
0.87
Int
Ext
te =-15C
ti =20C
=25
=150
=400
=15
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.28
Stan-Ivan Felicia-Elena,
Dinu Radu-Cristian, Duinea Adelaida-Mihaela
E-ISSN: 2224-3461
327
Volume 18, 2023
The validation of the numerical solution will be
made by comparison with the overall analytical
solution.
The computational relationship characterizing
the heat transfer through a multi-layer plane wall is
presented in equation (6):
 [W/m2] (6)
The calculation relation for the overall heat
transfer coefficient, k, it is described in equation (7):


[W/m2K] (7)
Were:  is the convection coefficient between
the wall and the outside air, [W/m2K];  is the
convection coefficient between the wall and the
indoor air, [W/m2K]; is the thickness of each wall
layer, [m], is the thermal conductivity of each wall
layer, [W/mK];
The value of the convection coefficient between
the wall and the outside air was taken as 24 W/m2K.
The value of the convection coefficient between the
wall and the indoor air was assumed to be 8 W/m2K.
The outside air temperature is -15C. The
temperature considered for indoor air is 20C.
Applying the above calculation equation (7) for
the overall heat transfer coefficient, k, result:



 
 
 

 
W/m2K
k = 0.1843 W/m2K
Substituting k into the relation for unit thermal
flux through the wall will result:
󰇛󰇜 
  W/m2
q = 6.45 W/m2
Recall that the value of the unit thermal flux
through the wall obtained by numerical simulation
is: 6.58 W/m2.
In the next presented figures will be described
the composite wall structure and the numerical
simulations regarding the temperature variations, the
influence of the convective coefficient and the
thermal flux variation.
In the Figure 3 is represented the wall structure
from outside to inside- the model was implemented
in ANSYS workbanch.
The temperature T2 it can be determine, using
equation (4):



 
Fig. 3: Wall structure from outside to inside-model in ANSYS
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.28
Stan-Ivan Felicia-Elena,
Dinu Radu-Cristian, Duinea Adelaida-Mihaela
E-ISSN: 2224-3461
328
Volume 18, 2023
Fig. 4: Wall structure - with values for temperatures
and convection coefficient on the outer/inner faces
Fig. 5: Simulation of temperatures variations in the
multilayer wall, from outside to inside
Fig. 6: Heat flow simulation for the multilayer wall,
q = 6.585 W/m2
Fig. 7: The temperature after the external plaster
layer, between the plaster and the thermal
insulation, t1=-14.79C
Fig. 8: Simulation of temperatures between the
thermal insulation layer and the BCA layer,
t2=9.3727C
Fig. 9: Simulation of temperatures between the BCA
layer and the interior plaster, t3=19.878C
4 Conclusion
The study presents a comparison of the
determination and simulation of heat transfer,
temperatures, convection coefficient for a multi-
layer wall made of several component elements,
different in structure and thickness.
The modeling of these types of structures with
the Ansys simulation software allows a very good
accuracy of the delineation of the component layers
and the consideration of different heat transfer rates,
coefficients, etc.
Of course, to simplify the calculations and the
simulation model, both the influence of convective
coefficients and indoor and outdoor temperatures
have been taken into account.
As can be seen, the numerical calculations
performed using the calculation relations (1) .. (7)
and the values obtained from the simulations
performed using Ansys are very close.
Figure 3 shows the analyzed model of the wall
structure, modeled in ANSYS.
In the drawing you can see each component layer
of the wall, external plaster, thermal insulation -
polystyrene, BCA, and internal plaster.
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.28
Stan-Ivan Felicia-Elena,
Dinu Radu-Cristian, Duinea Adelaida-Mihaela
E-ISSN: 2224-3461
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Volume 18, 2023
Figure 4 shows the structure of the wall detailing
the values of indoor/outdoor temperatures and
convection coefficient for the interior and exterior
surfaces.
After determining the temperatures between each
component layer of the wall structure, Figure 5
shows the simulation of temperature variations in
the multi-layer wall from outside to inside using the
Ansys software.
The calculated value for the heat flow was q =
6.45 W/m2, and according to Ansys simulation
program the obtained value was q = 6.585 W/m2
also very close comparing to the calculated one.
Figure 6 presents the heat flow simulation at the
multilayer wall.
Figure 7, Figure 8 and Figure 9 show the
simulation of the temperatures at the level of each
component layer of the multilayer wall, on the inner
surface, t3, between the inside component layers, t2,
and at the level of the layer in contact with the outer
surface, t1.
The temperature inside the wall varies from
+20C, to -15C, as considered and the temperatures
determined using the Ansys program simulation
from outside to inner surface are: t3=-14.79C,
t2=9.3727C and at the t1= 19.878C.
It can be seen that the largest temperature
variation is, as expected after the thermal insulation
layer, i.e. a difference of 10 degrees Celsius, from,
t2=9.3727C to t1= 19.878 C (Figure 8 and Figure
9).
The heat flow transmitted from the inside of the
room to the outside environment depends on both
the overall heat transfer coefficient and the
temperature difference between the two
environments separated by the wall.
The simulation was made, of course, taking into
account some simplifying assumptions such as,
considering the values of indoor/outdoor
temperatures constant throughout the simulation
period, the simulations were performed in steady
state regime.
References:
[1] Gowtham, Rajakumar, Design and Analysis
of Concrete Building without Insulation and
with Insulation using ANSYS 15 Software,
International Research Journal of
Engineering and Technology (IRJET), Vol.
06, Issue 05, pp. 6392-3695.
[2] Bolattürk, A., Optimum insulation thicknesses
for building walls with respect to cooling and
heating degree-hours in the warmest zone of
Turkey, Build. Environ., Vol. 43, no. 6, pp.
1055–1064, Jun. 2008.
[3] Zheng G, Jing Y, Huang H, Shia G, Zhang X.
Developing a fuzzy analytic hierarchical
process model for building energy
conservation assessment, Renew Energy,
2010. https://doi.org/10.1016/j.renene.2009.07
.008.
[4] Bodach S, Lang W, Hamhaber J. Climate
responsive building design strategies of
vernacular architecture in Nepal, Energy
Build. 2014, 81, 227,
https://doi.org/10.1016/j.enbuild.2014.06.022.
[5] Wu Z, Li N, Wargocki P, Peng J, Li J, Cui H.
Field study on thermal comfort and energy
saving potential in 11 split air-conditioned
office buildings in Changsha, China. Energy.
2019, 182, 471–
482, https://doi.org/10.1016/j.energy.2019.05.
204.
[6] Akbari H, Rashid KH., Optimization of form,
aspect ratio and orientation of building based
on solar radiation and wind direction (Case
studies: Tabriz, Yazd and Bandar Abbas
cities), Vol. 9, Issue 34, Arid Reg Geogr Stud
December 2018; 9(34): pp.1–13.
[7] Hana Charvátová, Aleš Procházka, Martin
Zálešák, Jan Drápela, Computational
Analysis of Indoor Thermal Comfort in a
Terraced Family House With Thermal
Insulation, January 2023, IEEE Access
PP(99):1-1,
DOI:10.1109/ACCESS.2023.3290097.
[8] Ing. Baracu, T., Numerical modeling of
premises Report 1 of the thesis: Contributions
to the numerical modeling of buildings,
"POLITEHNICA" University Bucharest,
Faculty of Energy (Modelarea numerica a
incintelor Raport 1 al tezei: Contributii la
modelarea numerica a cladirilor, Universitatea
“POLITEHNICA” București, Facultatea de
Energetică, Aprilie), 2013, [Online].
https://www.researchgate.net/publication/280
082288_Numerical_models_of_the_enclosure
s (Accessed Date: May 23, 2023).
[9] Prasetiyo Wibowo, A., Saidani, M., Khorami,
M., Bai, M., The Heat Transfer Rate of
Composite Wall with Series and Parallel
Configuration, Advances in Social Science,
Education and Humanities Research, volume
671 International Webinar on Digital
Architecture 2021, IWEDA 2021, [Online].
https://www.researchgate.net/publication/362
074289_The_Heat_Transfer_Rate_of_Compo
site_Wall_with_Series_and_Parallel_Configur
WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.28
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Dinu Radu-Cristian, Duinea Adelaida-Mihaela
E-ISSN: 2224-3461
330
Volume 18, 2023
ation, DOI: 10.2991/assehr.k.220703.026,
(Accessed Date: October 7, 2023).
[10] Ghalambor S., Analitycal solutions of steady-
state heat conduction in multy-layer stack
packaging, Degree of doctor of philosophy
The University of Texas at Arlington, August
2014, pp.149, [Online].
https://www.academia.edu/70279068/Analytic
al_Solutions_Of_Steady_state_Heat_Conducti
on_In_Multi_layer_Stack_Packaging
(Accessed Date: January 1, 2024).
[11] Jaivignesh, J., Menon, S., Gadhwala, S.,
Prakash V., Punnus. B., Kandunoori, A.,
Babu, P., Sreekumar, R., Ankit Gokul Govind
B.Tech Students, Study of one dimensional
conduction heat transfer for constant thermal
conductivity through composite plane slab
and in cilinder at steady state condition,
School of Mechanical Engineering, VIT
University, Vellore, India, International
Journal of Mechanical Engineering and
Technology (IJMET), Vol. 8, Issue 11,
November 2017, pp. 457–466, Article ID:
IJMET_08_11_049.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- Stan Ivan Felicia Elena carried out the simulation.
- Dinu Radu Cristian has implemented the section
2.1. Numerical modelling of heat transfer in
multilayer walls
- Duinea Adelaida Mihaela has organized and
executed the calculations for Section 3.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on HEAT and MASS TRANSFER
DOI: 10.37394/232012.2023.18.28
Stan-Ivan Felicia-Elena,
Dinu Radu-Cristian, Duinea Adelaida-Mihaela
E-ISSN: 2224-3461
331
Volume 18, 2023