Scientia Iranica B (2011) 18 (1), 66–74

Sharif University of Technology

Scientia Iranica
Transactions B: Mechanical Engineering
www.sciencedirect.com

New thermo-mechanical analysis of cylinder heads using a

multi-field approach
M. Fadaei a,∗ , H. Vafadar b , A. Noorpoor c
a
Department of Automotive Engineering, Iran University of Science and Technology, Tehran, P.O. Box 1883743671, Iran
b
Iran Khodro Diesel Research and Design Department, Tousee Khodrocar Co, Karaj, P.O. Box 3148983798, Iran
c
Energy and Environment Laboratory, Department of Automotive Engineering, Iran University of Science and Technology, P.O. Box 1684613114, Iran

Received 9 January 2010; revised 22 September 2010; accepted 28 November 2010

KEYWORDS Abstract The results of a thermo-mechanical analysis of a natural gas, internal combustion engine
Heat transfer; cylinder head are presented in this paper. The results are pertinent to the evaluation of overheating
Thermo mechanical; damage in critical areas. The three-dimensional geometries of the cylinder head and the water jacket were
Cylinder head; modeled by means of a computer-aided engineering tool. Commercial finite element and computational
Engine cooling; fluid dynamics codes were used to compute details of mechanical stress in the head and flow details in
CFD; the cylinder and cooling jacket, respectively. A six-cylinder, four-stroke diesel engine and a spark-ignition
FEA. natural gas engine were modeled over a range of speeds at full load. Computed results, such as maximum
allowable cylinder pressure, output power, BMEP and BSFC, were validated by experimented data in the
diesel engine model. The results were in good agreement with experimental data. The results show high
stresses at the valve bridge. Cylinder head temperatures and comparison of output power with high stress
measurements, often exceeding the elastic limit, were found at the valve bridge.
© 2011 Sharif University of Technology. Production and hosting by Elsevier B.V.
Open access under CC BY license.

1. Introduction detailed information is not available, and the logic behind a

specific design cannot be verified. As a result, engineers attain
In the past, optimization of engine components, such as little general information from each test [3]. Therefore, the
cylinder heads, was based on building a series of physical Finite Element Analysis (FEA) methodology was introduced and
prototypes, and performing a series of different experiments became a systematic methodology in the early stages of engine
and tests [1]. Unfortunately, the traditional process of design design to save time and cost in manufacturing processes. The
and development was time-consuming, and it was difficult Finite Element Analysis methodology (FEA) assists engineers
to build physical prototypes during the early stages of the in predicting the best method for heat removal prior to
design. The construction and testing of many prototypes is often building the first prototype, by calculating the temperature
required to meet a stringent design requirement [2]. This can and stress distribution of each component. Therefore, Finite
turn into an expensive process and delay the entire design Element Analysis (FEA) is considered one of the most powerful
and development cycle. Although the building and testing of computer-aided design tools for engineers [4]. In the process
engine component prototypes can yield an accurate design, of an engineering analysis, a theoretical and numerical model
is the starting point for researchers to develop or design an
∗ engineering system. This technique has been accepted for
Corresponding author.
E-mail address: mehrdadfadaie@yahoo.com (M. Fadaei).
designing and developing complex geometry over a shorter
period of time and at much lower cost.
1026-3098 © 2011 Sharif University of Technology. Production and hosting by The cylinder head is one of the most complicated and
Elsevier B.V. Open access under CC BY license. challenging parts of an engine, in the optimization of which FEA
Peer review under responsibility of Sharif University of Technology.
plays an important role [5]. A limited amount of information
doi:10.1016/j.scient.2011.03.009 is available regarding thermal stresses in cylinder heads. Komo
and Bryzik investigated the development of thermal stresses
in engine components with isolative ceramic coatings [6]. A
twin-cam 16-valves cylinder head and cylinder block structure,
accompanied by several important subcomponents, under
firing load and assembly loads, were investigated using FEM.
 M. Fadaei et al. / Scientia Iranica, Transactions B: Mechanical Engineering 18 (2011) 66–74 67

Nomenclature
A area (m2 )
d average diameter of inlet and outlet ports (m)
g acceleration of gravity (m/s2 )
Gr Grashoff number
h convective heat transfer coefficient (W/m2 K)
k thermal conductivity coefficient (W/mK)
ṁ mass flow rate (kg/s)
Nu Nusselt number
P gas pressure (Pa)
P0 intake cylinder pressure (Pa)
Pe exhaust gas pressure (Pa)
P4 exhaust gas pressure at the starting point of the
exhaust valve opening
Pr Prandtl number
Ra Rayleigh number
Re Reynolds number
T temperature (K) Figure 1: Experimental set-up.

Te exhaust gas temperature (K)

T∞ ambient temperature (K) Table 1: Engine specifications.
T4 exhaust gas temperature at the starting point of No. of cylinders 6
the exhaust valve opening
Displacement 11.97 L
φ fuel/air equivalence ratio Bore 128 mm
Stroke 155 mm
Greek Symbols Diesel compression 17.75
Natural gas compression 11.2
β coefficient of volumetric thermal expansion Firing order 1–5–3–6–2–4
(k−1 ) Moment of inertia of the flywheel 1.09 kg m2
mu dynamic viscosity (kg/ms) Moment of inertia of the engine (with flywheel) 2.16 kg m2
ν kinematic viscosity (m2 /s)

Table 2: Measured values of coolant flow.

The physical behavior of the gasket bead and liner, the stiffness Diesel Natural gas engine
distribution of the cylinder head, the preload of the cylinder engine
head bolts, the residual insertion loads of valve guides and
Coolant flow (L/s) 4.2 6.4
valve seats, and the firing pressure have been thoroughly Coolant inlet temperature (°C) 77 86
discussed [7]. Coolant outlet (°C) 84 95
Other investigators carried out sealing and structural temperature
response analyses in assembly and firing load cases for several
areas of interest. Recommendations obtained from the project
were forwarded to designers for successful incorporation into, combustion simulation and boundary condition calculations
and adjustment of, other areas for design evaluation. They of the inlet, outlet ports and water jacket, the mass, pressure
provided information in regard to the nature and magnitude of and velocity of the fluid (water, air, fuel and exhaust gases)
thermal and mechanical stresses in the cylinder heads [8–10]. must be measured. Calculation of the boundary condition was
For the calculation of boundary conditions from the combustion conducted at 1750 rpm, at which speed the maximum torque
chamber side, the model of the engine combustion was created for a natural gas engine is achieved. Tables 1–4 indicate engine
by commercial computer software [8,9,11,12]. The goals of the specifications and experimental investigations, respectively.
analysis were to: Validation of the model has been achieved via calculation
of the structural component temperatures in a 4-valve gas
1. Provide validation of the natural gas engine thermo-
engine under firing conditions in dynamometer tests, and
mechanical simulation results, as compared with the results
comparison of the calculation results with the corresponding,
of a base diesel engine; experimentally obtained data. The experimental temperature
2. Achieve thermal and mechanical stresses; data were obtained via thermocouples applied to the cylinder
3. Compare stress magnitude with limits of elasticity [13–15]. head. The engine under investigation was equipped with 8
thermocouples, which were applied to all 6 cylinder heads of
2. Experimental set-up and model validation the engine, with additional elements located at cylinder head
3. As shown in Figure 2, the locations of the thermocouples
To provide the necessary information for calculations, an were selected to specifically enable investigation of areas of
engine was installed on the dynamometer test, which is high thermal loading, e.g. one of the thermocouples is located
shown in Figure 1. Four temperature probes were used on the at the valve bridge, near the spark plug, and one of the other
outside surface of the cylinder head. The mean temperature thermocouples is located beside the exhaust valve seal seat.
reached 363.5 K, which will be used in the outside boundary An example of the absolute average temperature measure-
condition of the cylinder head calculation. In addition to ments obtained at 1750 engine speed for a natural gas engine
68 M. Fadaei et al. / Scientia Iranica, Transactions B: Mechanical Engineering 18 (2011) 66–74

Table 3: Inlet air experimental data for natural gas engine.

Natural gas engine (1750 rpm)

Minimum heat to be Peak pressure drop charge air Boost pressure Charge air Rate of air Output with Viscose type
dissipated from system (mbar) before charge air temperature before flow (g/s) fan (kW)
charge air (kW) cooler (mbar) engine max. (°C)

31 68 1218 63.9 325.82 207

Table 4: Inlet air specification for diesel engine.

Diesel engine

Engine speed (rpm) 2000 1800 1600 1400 1200 1000

Output with viscose type fan (kW) 220 130 157 182 204 218
Rate of air flow (g/s) 430 420 365 300 235 165
Charge air After turbocharger (°C) 145 153 140 125 108 91
Temperature Before engine max. (°C) 42 43 41 40 39 38
Boost pressure before charge air cooler (mbar) 1200 1400 1250 1050 850 630
Peak pressure drop charge air system (mbar) 120 107 82 59 41 24
Minimum heat to be dissipated from charge air (kW) 45 47 36 26 16 9

Figure 2: Photographs of the engine equipped with thermocouples.

package [16]. A one-cylinder, single-zone, zero-dimensional

model was used in order to simulate the combustion phenom-
ena. The chemical kinetic mechanism incorporated the GRI-3.0
mechanism, which considers 66 species and 376 reactions to-
gether for combustion of a natural gas-air mixture. An over-
all zero-dimensional, 6-cylinder, four stroke diesel engine has
been modeled using engine specifications in an engine cy-
cle simulation code; GT-Power. Modeling has been conducted
at full load, with a wide open throttle, over a wide range of
engine speeds and with conventional diesel and natural gas
engine operations. The amount of output power for a diesel en-
gine with diesel fuel and technical data has been compared for
validation, and very good agreement between simulation and
technical data is shown in Figure 4. Figure 5 shows the gas pres-
sure and temperature profiles in the combustion chamber of a
diesel engine and a natural gas engine, which are calculated by
GT modeling.

Figure 3: Measured metal absolute temperatures at determined location in the

cylinder head. 3.1. Diesel engine model

and at 1100 engine speed for a diesel engine at full load, is A high speed turbocharger boosted the air introduced into
shown in Figure 3. the cylinders. Due to the boosting process, ambient air pressure
and temperature, according to Tables 3 and 4, were raised
3. Combustion simulation to 630 mbars (relative pressure) and 364 K, respectively, at
1000 rpm. By increasing engine speed to 1200 and 1800 rpm,
The combustion of natural gas in the considered engine was the inlet air pressure rose to 850 and 1400 bars and the inlet
simulated by the chemical reaction computation, CHEMKIN, air temperature reached 381 and 426 K, respectively. Direct
 M. Fadaei et al. / Scientia Iranica, Transactions B: Mechanical Engineering 18 (2011) 66–74 69

Figure 4: Comparison of output torque and output power diesel engine with
technical data.

Figure 6: Flowchart of the thermo-mechanical analysis procedure.

applying thermal stress and displacement boundary conditions.

The results of stress analysis, the stress field in the firedeck
and material evaluation are provided. The analysis procedure
is shown in Figure 6. The first step in the process is to
define the model geometry. This was accomplished by a three-
dimensional solid modeling through using a computer-aided
engineering tool, such as Solid Works [11]. The data is imported
from the solid model to the mesh generation software.
Mechanical boundary conditions and model constraints are
defined and/or calculated to maximize the validity of the
Figure 5: In-cylinder temperature and pressure comparison between stoichio-
metric SI gas engine (φ = 1.0) and diesel engine.
analysis given for the model [10]. Thermal and mechanical
boundary conditions are applied to the finite element mode.
The finite element analysis was carried out using a commercial
injected diesel engine combustion was based on the Wiebe
finite element analysis software package; ANSYS [12]. The
function [17] to calculate the burn rate and heat release rate. results are post processed into a form suitable for engineering
A diesel injector unit injected No. 2 diesel fuel via a semi- assessment, which accesses the analysis of a binary code
sinusoidal periodic pressure profile. Its calculation method database and extracts the appropriate results [13]. Local
includes a model for Nox formation, which allows the kinetics properties may be a function of surface finish, heat treatment,
of the extended Zeldovich mechanism in all models to operate notch sensitivity, temperature, etc. which are the inputs by
during the combustion of each incremental quantity of fuel [18]. the user. Where temperature dependency exists, user-input
tables of temperature dependency calculate the local material
3.2. Natural gas spark–ignition model property [14,15]. The numerical analysis for calculation of
the temperature and stress distribution in a cylinder head is
The considered diesel engine model has been fueled with achieved by a multi-field technique. The essence of multi-
natural gas indirectly injected into the engine cylinders, and the field analysis is coupled-field analysis, which allows users
engine worked via a spark ignition cycle. The flame temperature to determine the combined effects of the multiple physical
of fuels, especially methane, is highest near stoichiometric and phenomena (fields) of a design. If the input of one field analysis
depends on the results of another analysis, the analysis is
lower near flammability limits. It is evident from Figure 5
called multi-field. The applications of this technique include
that the SI gas engine with the stoichiometric air–fuel mixture
fluid-thermal and thermal-structure analysis. The computation
dramatically overheated.
process of the analysis is shown in Figure 7.

4. Computational methodologies 5. Model definition and mesh generation

Details of efforts include: model definition, meshing, model The cylinder head geometry (Figure 7) and its associ-
analysis, validation of the Finite Element Analysis (FEA) model, ated thermal and structural constraint conditions are three-
70 M. Fadaei et al. / Scientia Iranica, Transactions B: Mechanical Engineering 18 (2011) 66–74

Figure 8: Solid works model of the engine cylinder head.

Figure 9: Model of the cylinder water jacket for CFD analysis.

near the firedeck, which has given the valve bridge a smaller
cross-section than any other location in the cylinder head. The
valve bridge area is a region of concern and is finely meshed
to determine stress gradients accurately as recommended [4].
Figure 7: Multi-field computations procedure for (a) thermal-structural, (b) So to achieve more accurate results in the combustion and
CFD-thermal, and (c) loops sequence. valve bridge area, normal mesh, which is shown in Figure 10a,
has been converted to precise mesh, which is shown in
dimensionally modeled using SOLIDWORKS 2008. The mesh Figure 10b. The completed three-dimensional model contains
and analysis for the cylinder head are constructed by ANSYS. For 47234 elements and 48234 nodes (for solid), and 62234
thermo hydraulic analysis, a model of the water jacket for the elements and 51245 nodes (for CFD). Element aspect ratios are
cylinder is constructed, as well as the cylinder head (Figures 8 approximately 1.9 in the combustion and valve bridge area,
and 9). Flow characteristics of the water jacket, critical or main- which is shown in Figure 10b. Away from the combustion and
taining uniform firedeck cooling, were analyzed using CFD and valve area, element aspect ratios are less than 4.5. However,
the model of the water jacket. A brick-element mesh was con- this is not considered to be a significant problem, because the
structed and analyzed for the CFD work by using ANSYS 10. stress gradients at these locations are very low. In the non-
For an accurate result, mesh generation plays an important sensitive regions, such as the top of the cylinder head, a coarse
role. The small and sensitive areas are meshed with high mesh is applied in order to reduce the number of elements
resolution. The shape at the valve opening tapers outward and CPU time. Then the water jacket model of the cylinder
 M. Fadaei et al. / Scientia Iranica, Transactions B: Mechanical Engineering 18 (2011) 66–74 71

convection coefficient, we use the following relation [21]:

NUf = C (Grf ∗ Prf )m , (1)

where m = 1/4 and C = 0.52.
The Rayleigh number is given by:
Ra = Grf ∗ Prf , (2)

Grf = [g β(Tw − T∞ ) ]/ν . 3 2

(3)

6.2. Inlet and outlet port boundary condition

To calculate thermal heat transfer coefficients of intake and

exhaust ports, the Christopher equation is used [22]:
h = kNu/d, (4)
where:

Nu = 0.0718 Re0.75 , (5)

Re = m°d/µA. (6)
The value of m° is acquired from CFD or experiment. Air
temperature in this turbocharged engine at the inlet port is
336.5 K, and the gas temperature at the outlet port is assumed
to be the same as the combustion chamber gas temperature,
which is calculated when the exhaust valve is open, as written
hereafter [23]:

Te = T4 (Pe /P4 )k /k .
−1
(7)

6.3. Water jacket side boundary condition

Prediction of the temperature distribution is achieved

by solving the energy, momentum and mass conservation
Figure 10: (a) Top views of nodes distribution with selected path. (b) Precise
mesh in combustion chamber of cylinder head in natural gas engine and diesel
equations simultaneously. Therefore, inlet pressure and the
engine for comparison. water jacket and/or velocity are required for application as
boundary conditions in the CFD model. For this purpose, the
head is meshed until the nodes of the interface of the cylinder inlet water flow rate and temperature are measured [23,24].
head and water jacket models merge together. The analysis was
carried out using two methods, multi-field and single field, for 7. Stress boundary conditions
verification of the analysis. In order to achieve accurate results
in computation, about four types of meshing were established, In order to decrease the complexity of the boundary
and the mesh independency solution occurred. conditions, interaction between the cylinder head, cylinder
head gasket and cylinder block was not modeled. In fact, the
6. Thermal boundary conditions cylinder head and the cylinder block were assumed to expand
at the same rate for all points of contact between the cylinder
In any thermal analysis, proper selection of boundary condi- block and cylinder head. This simplification does not allow
tions is challenging, particularly when boundary conditions in the cylinder head bolts to constrain the thermal expansion
the engine combustion chamber components may vary signifi- of the cylinder head. Therefore, thermal stresses are expected
cantly, both in space and time [19]. The boundary conditions for to be predictable. Another boundary condition is the pressure
stress analysis are achieved from the results of thermal analysis load which is applied to the combustion chamber. Maximum
and the suitable displacement boundary conditions of the cylin- pressures of 13.07 MPa and 13.411 MPa for a gas engine and
der head. In this analysis, only thermal and pressure loads from a diesel engine are used in this analysis, respectively. The
the combustion chamber were considered. The pressure load in boundary condition of the bolt is very significant. In an actual
producing stress in the cylinder head is not as important as ther- model, a pre-load is necessary in order to define how to tighten
mal stress which is dominant [20]. The high-stressed regions the bolt. Therefore, a pre-load is applied to the cylinder head.
were sought and evaluated accurately and closely. To consider In this analysis, it is assumed that the surface interface of
all boundary conditions, one of which was achieved in previous the cylinder head and bolt move inward. There is no outward
sections (combustion simulation), the convective heat transfer movement for this surface. Therefore, for bolt modeling, the
coefficient should be calculated for the following regions. beam element is used [14].

6.1. Outside boundary condition 8. Discussion and result

To apply outside boundary conditions, the Raleigh equation A comparison of diesel engine thermal analysis results
is used in the form of a free convection surface. For the and natural gas engine results is shown in Figure 11. The
72 M. Fadaei et al. / Scientia Iranica, Transactions B: Mechanical Engineering 18 (2011) 66–74

Figure 12: Comparison of average thermal results of natural gas and diesel
engines corresponding to selected path in Figure 10a.

Figure 11: Temperature contours on the firedeck of the combustion surface of

(a) diesel engine, and (b) natural gas engine (K).

temperature at the centre of any cylinder is high and decreases

far away from the centre. This causes a high temperature Figure 13: Comparison of calculated and measured metal absolute tempera-
gradient at the surface of the combustion chamber. This is due ture adopting coupled CFD/FEM approach for natural gas engine.
to the fact that far away from the centre, the cooling water
flow rate is greater than at the centre of the firedeck, but it According to computation results for thermal analysis of
is assumed that the temperature in the water jacket is almost a natural gas engine, the 6 nodes at the combustion area
constant. As the figure shows, the temperature at the cylinder (Figures 10–12) are 1.18 times more than the same points
bridge is high (in the natural gas and diesel engines), and in a diesel engine. Figure 13 shows the results of the metal
consequently the temperature gradient at this region remains surface temperatures of a natural gas engine, determined by the
high. The maximum temperature at the firedeck is 727.837 K coupled CFD/FEM method from a close view. For verification
in a natural gas engine and 616.227 K in a diesel engine purposes, the analysis was carried out using two methods;
(it is one of the reasons for the high stress of the natural multi-field and single field (mechanical stress analyses and
gas engine). The computations show that the temperature thermal analyses in a normal computational method are done
gradient at the gas side of the cylinder head in a natural gas separately, and their results are combined for conclusion).
engine is approximately 68 °C/mm, as opposed to 7.1 °C/mm There is a good correlation between the calculated absolute
for the coolant side of the cylinder head. Inside the liner, temperature values at the measurement locations in the
the temperature on the firedeck changes from about 566 to cylinder head and the experimentally obtained values, as
727 K under high load conditions, while outside the liner, the shown in Figure 13 for two selected measurement points in
temperatures are relatively low at 323 to 646 K for a natural gas the cylinder head. However, absolute temperature values differ
engine. Due to the cooling water flow, temperature distribution specifically in critical areas, such as the valve bridge. Figure 14
is not approximately similar in all cylinders. Although cooling shows distribution stress analysis between the diesel engine
water enters the left side of the bottom of the cylinder head and the natural gas engine on the cylinder head. There is high
and exits from the right side of the bottom of the cylinder stress in the valve bridge and near the valve seat, as predicted.
head, and is almost similar in this engine type, there is, a As mentioned in these areas, the temperature gradient is
little difference between the temperature of cooling water higher; therefore, the stress is higher in this region, and thermal
that enters at cylinder head 1 and cylinder head 3. Therefore, expansion of the hot region is constrained by the stiffer cool
temperature distribution is non-uniform in all cylinders. Also region which undergoes less thermal expansion. As a result, a
The FEM predicts a large compressive strain and stress field at compressive thermal stress field is created inside the liner. The
the valve bridge and at the valve seats on the firedeck of the thickness of material in the valve bridge is high and, in this
cylinder head. These stresses are assumed primarily to be the region, the cooling flow is not enough; consequently, the stress
result of the relatively large temperature differential existing at is increased. The large compressive strain and stress field is at
the liner interface. the valve bridge and valve seats on the firedeck of the cylinder
 M. Fadaei et al. / Scientia Iranica, Transactions B: Mechanical Engineering 18 (2011) 66–74 73

Figure 15: Comparison of Von Mises stress results of natural gas and diesel
engines corresponding to selected path in Figure 10a.

Figure 16: Von Mises stress on the firedeck combustion surface is more than
yield stress in some areas.
Figure 14: Von Mises stress contours on the firedeck combustion surface of
(a) diesel engine, and (b) natural gas engine (MPa).
at the valve bridge, resulting from a constrained thermal
head. Based on computations results, the Von Mises stress for a expansion of the cylinder head, are generally compressive
natural gas engine in 6 nodes at the combustion area, shown in in those areas. For this natural gas engine, it is concluded
Figure 15, is 1.149 times more than the diesel engine stress at that about 91%–94% of total stress is due to thermal loading,
each point. The graph shapes for two engines are the same and and the remainder is due to pressure loading and mechanical
because of the temperature difference, the value of Von Mises at constraints. The temperature gradient at the surface of
each point is different. The temperature difference is the reason the combustion chamber is not uniform. According to the
for the Von Mises difference in the two engines. computation results, the Von Mises stress value exceeds
Another important result from the analysis is that the the elastic limit for cylinder head material in a natural gas
predicted Von Mises stresses exceed the elastic limit for a engine.
typical cylinder head material. The black regions in Figure 16 2. The use of cast iron GG-30 in the production process instead
depict regions of stress in a natural gas engine, which are high of the existing material of a natural gas engine, cast iron
and out of range (yield strength range). This high stress would GG25, leads to prevention of quick destructive fractures in
lead quickly to a destructive fracture in the cylinder head [25]. the cylinder head and makes the assurance factor increase.
3. Decrease of maximum compressive stress and high temper-
9. Conclusion ature in some critical areas, such as the valve bridge or valve
seat, the water-cooling system or water jackets in the cylin-
An investigation of stress and heat transfer by extensive der head, should be improved. The effect of coolant velocity
solid work, FEM/CFD and thermal analysis selected cylinder on the heat transfer coefficient is significant, so changing the
heads (converted engine) is conducted in the present work to water pump in order to increase the rate of coolant in the en-
determine their critical areas and weak points for development gine is recommended.
and design. Based on the reported results, the following
conclusions may be drawn: References
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2004).
[17] Günter, P.M., Christian, S., Gunnar, S. and Frank, O., Simulation of
Combustion and Pollutant Formation for Engine Development, Springer- A. Noorpoor is Assistant Professor at Iran University of Science and Technology.
Verlag, Heidelberg, Berlin, (2006). His research interests are: Fluid Mechanics, Aerospace, Automotive, Powertrain
[18] Heywood, J.B., Internal Combustion Engine Fundamentals, McGraw-Hill, especially Engine Control, Cement, Electricity, etc. He was also a member of
New York, (1988), Section 11.2. the Scientific Board at the Automotive and Railway Faculty of Iran University
[19] Wendl, M.C., Fundamentals of Heat Transfer Theory and Applications, of Science and Technology. At present, he is General Director of the Electrical
Washington University Press, (2005), ebook Version 2.1. and Metal Industry at the Iranian Ministry of Mines and Industries.