A METHOD OF SIMULATING RADIATION HEAT TRANSFER FROM ONE RADIATING SURFACE TO ANOTHER
FIELD OF THE INVENTION
[001] The present invention relates in general to stress analysis of
engineering components, and more particularly to systems and methods of simulating radiation heat transfer in thermal stress analysis using Finite Element Method.
BACKGROUND OF THE INVENTION
[002] Stress analysis involves determination of the internal
distribution of stresses in solid objects. It is an essential tool in engineering for the study and design of structures such as tunnels, dams, mechanical parts, and structural frames, under prescribed or expected loads.
[003] Stress analysis is a primary task for civil, mechanical and
aerospace engineers involved in the design of structures of all sizes, such as tunnels, bridges and dams, aircraft and rocket bodies, mechanical parts, and even plastic cutlery and staples. Stress analysis is also used in the maintenance of such structures, and to investigate the causes of structural failures. Differential equations are employed in solving problems of stress analysis. Many numerical procedures have been used and one of the most popular methods is finite element analysis (FEA),
[004] Finite element analysis (FEA) is a computer implemented
method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear

structural design and analysis.FEA has been implemented as FEA software. Basically, the FEA software is provided with a grid-based model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the component under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. Next the conditions at the boundary of the object like loads, physical constraints, temperature etc. are specified. In this fashion a FE model of the object and its environment is created.Once the model is defined, FEA software can perform a simulation of the physical behaviour under the specified loading or initial conditions.
[005] The input data for stress analysis are geometrical description
of the structure, the properties of the materials used for its parts, how the parts are joined, and the maximum or typical forces that are expected to be applied to each point of the structure. The output data is typically a quantitative description of the stress over all those parts and joints, and the deformation caused by those stresses.
[006] FEA is now becoming more common in a wide range of
fields. Therefore, instead of being limited to determining stress, strain, and displacement factors in mechanical components, FEA is now also used in connection with various fields, including heat transfer, fluid dynamics and electromagnetism. For example the thermal analysis of targeted regions of a component, such as a piston of an internal combustion engine, heat

transfer in pipes, components subjected to high temperature environment such as parts of blast furnace, machining etc.
[007] Thermal analysis involves thermal stresses caused due to
temperature, thermal load and heat transfer across components. Thermal analysis calculates the temperature and heat transfer within and between components in product design. It is an important consideration of design, as many products and material have temperature dependent properties. Product safety is also a consideration because if a product or component gets too hot, one may need to design a guard over it.lt is performed to determine thermal effects on a given design, or the impact of design changes on component temperatures.
[008] The heat flow through the components can be in a steady
state (where the heat flow does not change over time) or transient in nature. The thermal analogy of a linear static analysis is a steady-state thermal analysis, while a dynamic structural analysis is analogous to a transient thermal analysis.
[009] Thermal structural analysis is the application of the finite
element method to calculate the temperature distribution within a solid structure, which is due to the thermal inputs (heat loads), outputs (heat loss), and thermal barriers (thermal contact resistance) in the design. Thermal structural analysis solves the conjugate heat transfer problem with the simulation calculation of thermal conduction, convection, and radiation.Thermal simulations play an important role in the design of many engineering applications, including internal combustion engines, turbines, heat exchangers, piping systems, and electronic components. In many cases, engineers follow a thermal analysis with a stress analysis to

calculate thermal stresses (that is, stresses caused by thermal expansions or contractions).
[0010] Two modes of heat transfer mainly convection and radiation
are applied as boundary conditions in thermal structural analysis. Both convection (set by a surface film coefficient) and radiation (surface emissivity) can emit and receive thermal energy to and from the environment, but only radiation transfers thermal energy between disconnected bodies in the assembly. Normally when we run thermal-stress coupled analysis, we must have the same model in both thermal and stress analyses.
[0011] The thermal stress analysis is mostly performed by computer
implemented tools available such as ANSYS, NASTRAN etc. The component to be tested is modelled geometrically and the heat loads, temperature and boundary conditions are applied on it to conduct the FEM based stress analysis. The output gives the temperature or thermal stress at different points of the structure.
[0012] There are several methods available to simulate the
conduction and convection heat transfer on a FEA model of the structure in available FEA tools. These tools also include method to simulate radiation heat transfer between surfaces. The basis for thermal analysis in ANSYS is a heat balance equation obtained from the principle of conservation of energy. The finite element solution performed via ANSYS calculates nodal temperatures, and then uses the nodal temperatures to obtain other thermal quantities. The ANSYS program handles all three primary modes of heat transfer: conduction, convection, and radiation.

[0013] An ANSYS user has to specify convection as a surface load
on conducting solid elements or shell elements. The user also specifies the convection film coefficient and the bulk fluid temperature at a surface. ANSYS then calculates the appropriate heat transfer across that surface.
[0014] Radiation is a highly nonlinear mode of heat transfer. The
surface shown here as below:
A simplified form of the equation describing radiation from one surface to another is:
in which
a = Stefan-Boltzmann constant
Ai = Area of element-1
ei = Emissivity of surface-1 material
Fi-surface2 = View factor of element-1 with respect to surface-2
Fl-Surface2= Fla+ Flb+ F1c + F1c|+ F-|e
where Fix = View factor of element-1 with respect to element-x of surface-2 (Refer next slide)

Ti = Temperature of element-1
TSUrface2 = Average temperature of surface-2
[0015] The view factor between two surfaces as shown below with
normals Nj and Nj can be calculated as: i
i , , cosejCosei
^=^7^,1^,—^—
[0016] This method is suitable when radiation only occurs to space
and no surfaces are assumed to radiate between one another. In such cases where radiation occurs between surfaces of the structure, however, this radiation load is not sufficient.
[0017] ANSYS can solve radiation problems, in four ways:
- By using the radiation link element,
- By using surface effect elements between a surface and a point
- By generating a radiation matrix and using it as a superelement in a thermal analysis
- By using radiosity method.
[0018] Radiation Matrix method:

This method works for generalized radiation problems involving two or more surfaces receiving and emitting radiation. The method involves generating a matrix of form factors (view factors) between radiating surfaces and using the matrix as a superelement in the thermal analysis. One may also include hidden or partially hidden surfaces, as well as a "space node" that can absorb radiation energy.The Radiation Matrix analysis method consists of three steps: i) defining the radiating surfaces, ii) generating the radiation matrix and iii) using the radiation matrix in the thermal analysis.
[0019] Radiosity Method:
The Radiosity Solver method accounts for the heat exchange between radiating bodies by solving for the outgoing radiative flux for each surface, when the surface temperatures for all surfaces are known. The surface fluxes provide boundary conditions to the finite element model for the conduction process analysis in ANSYS. When new surface temperatures are computed, due to either a new time step or iteration cycle, new surface flux conditions are found by repeating the process. The surface temperatures used in the computation must be uniform over each surface facet to satisfy the conditions of the radiation model.
[0020] However the above methods of radiation analysis available
in present FEA tools such as ANSYS involve huge solution time to run the simulation and produce results. Also these methods are not suitable for structures with complex geometries. Existing techniques in Finite Element Analysis tool (example: ANSYS) to simulate radiation heat transfer are efficient neither in computational time nor in simulation efforts and are not capable of handling complex geometries.The present invention proposes a

new method of simulating radiation heat transfer for stress analysis in a cost effective, secure and environment friendly manner.
SUMMARY OF THE INVENTION
[0021] In view of the foregoing disadvantages inherent in the prior
arts, the general purpose of the present invention is to provide an improved combination of convenience and utility, to include the advantages of the prior art, and to overcome the drawbacks inherent therein.
[0022] In one aspect, the present invention provides a method of
simulating a radiation heat transfer between a first radiating surface and a second radiating surface of a structure in a finite element analysis. The method comprising making a Finite Element Model of the structure, determining an average temperature of the first radiating surface, defining a first node and transferring the average temperature of the first radiating surface to the first node, defining a second node and transferring the temperature of the first node to the second node, simulating the radiation heat transfer from the second node to the second radiating surface, determining an average temperature of the second radiating surface, defining a third node and transferring the average temperature of the second radiating surface to the third node, defining a fourth node and transferring the temperature of the third node to the fourth node, simulating the radiation heat transfer from the fourth node to the first radiating surface and performing the finite element analysis on the finite element model of the structure.
[0023] In another aspect of the present invention, further including

calculation and application of a view factor.
[0024] In yet another aspect of the present invention, the average
temperature of the first radiating surface and the second radiating surface is determined by simulating a convection heat transfer between the first radiating surface and the first node and between the second radiating surface and the third node respectively.
[0025] In another aspect of the present invention, the transferring of
the temperature of the first node to the second node and from the third node to the fourth node is performed using a unidirectional element.
[0026] In yet another aspect of the present invention, wherein
simulating of the radiation heat transfer from the second node to the second radiating surface and from the fourth node to the first radiating surface is performed by a method including radiation modeling between a point and a surface.
[0027] In another aspect the present invention provides a system for
simulating a radiation heat transfer between a first radiating surface to a second radiating surface of a structure in a finite element analysis. The system comprises an FE module for making a Finite Element Model of the structure, a module for determining an average temperature of the first and the second radiating surface, a node defining module for defining a first node, a second node, a third node, a fourth node, a module for transferring the average temperature of the first and the second radiating surfaces to the first node and the third node respectively, a module for transferring the temperature of the first and the third node to the second and the fourth node respectively, a module for simulating the radiation heat transfer from a node to the radiating surface and a module for performing the finite

element analysis on the finite element model of the structure.
[0028] These together with other aspects of the invention, along
with the various features of novelty that characterize the invention, are pointed out with particularity in the claims annexed hereto and forming a part of this disclosure. For a better understanding of the invention, its operating advantages and the specific objects attained by its uses, reference should be had to the accompanying drawings and descriptive matter in which there are illustrated exemplary embodiments of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0029] The advantages and features of the present invention will
become better understood with reference to the following more detailed description taken in conjunction with the accompanying drawings in which:
[0030] FIG. 1 illustrates a flowchart of a method of thermal analysis
using Finite Element Method (FEM);
[0031] FIG. 2 illustrates a flowchart of a method of simulating
radiation heat transfer in a Finite Element Analysis, according to one embodiment of the present invention;
[0032] FIG. 3 illustrates a schematic diagram of radiation heat
transfer between the first surface and the second surface, according to one embodiment of the present invention;
[0033] FIG. 4 illustrates the example of two concentric cylinders
used for simulating radiation heat transfer using three different methods,

according to one embodiment of the present invention;
[0034] FIG. 5a illustrates the temperature contours obtained in the
three methods at transient condition, according to one embodiment of the present invention;
[0035] FIG. 5b illustrates the temperature contours obtained in the
three methods at steady state condition, according to one embodiment of the present invention;
[0036] FIG. 6a illustrates the transient response of the outer cylinder
node obtained in the three methods in transient condition, according to one embodiment of the present invention; and
[0037] FIG. 6b illustrates the transient response of the inner cylinder
node obtained in the three methods in transient condition, according to one embodiment of the present invention.
[0038] Like reference numerals refer to like parts throughout the
several views of the drawings.
DETAILED DESCRIPTION OF THE DRAWINGS
[0039] In the following description, for purposes of explanation,
numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without these specific details.

[0040] As used herein, the term 'plurality' refers to the presence of
more than one of the referenced item and the terms 'a', 'an', and 'at least' do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced item.
[0041] The terms 'structure' or 'component' may be used herein
interchangeably and refer to convey the same meaning.
[0042] In an exemplary embodiment, the present invention provides
a method of simulating radiation heat transfer between two radiating surfaces. The method of the present invention may be used for mass implementation and used in an easy, cost effective, environment friendly and productive way.
[0043] It is to be understood that the improvements of the present
invention are applicable to any of a number of methods of simulating radiation heat transfer between two radiating surfaces other than those which are specifically described below. Such methods will be readily understood by the person of ordinary skill in the art, and are achievable by causing various changes that are themselves known in state of the art.
[0044] The trademarks, software names, etc used in the present
description are property of the respective owner companies and used herein for illustrative purposes only. The applicant does not claim any rights on such terms.
[0045] Reference herein to "one embodiment" or "another
embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase "in one

embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Further, the order of steps in process flowcharts or diagrams representing one or more embodiments of the invention do not inherently indicate any particular order nor imply any limitations in the invention.
[0046] Referring to FIG. 1 that illustrates a flowchart of a method
100 of thermal analysis using Finite Element Method (FEM) as per the prior art. The method starts with step 110 in which a geometric model of the structure whose stress analysis is to be performed, is made. The geometric model may be in 2-D or 3-D based on the shape of the structure. The model will have the same dimensions and shape like the original structure. The dimensions may be scaled in some cases. Several softwares are available to make the geometric model of the structure or component. The geometric model of the structure may be made in CAD (Computer Aided Design) software and then imported in the FEA software for analysis. The FEA software also provides the facility to make the geometric model in addition to the analysis.
[0047] In step 120 the geometric model is divided into a finite
number of elements or cells, each element or cell hereafter referred as a 'finite element'. The shape and size of the finite element depends on the geometry of the modelled structure. The finite elements may be solid elements for volumes or continua, shell or plate elements for surfaces and beam or truss elements for one-dimensional structure objects. The geometry of each finite element is defined by nodal points, for example, a brick or hexahedral element comprising eight corner nodes. Generally these finite elements are deformable under loading. More number of finite

elements may be made in specific portions of the structure which seem crucial in the design process.
[0048] Next in step 130 the boundary conditions in terms of
temperature are applied to the FE model. Similarly thermal loads are applied to the boundary on the edges, surfaces etc. The boundary condition and loads such as heat transfer coefficient, temperature, heat flux etc are applied on the nodes or surfaces of the finite elements.
[0049] In step 140 the properties of the materials are defined for the
model. The thermal properties like the thermal conductivity, density, specific heat are defined. If the structure includes portion made of different materials then different properties are defined accordingly. After dividing the geometric model into finite elements, applying boundary conditions and loads, and defining the material properties, the model may be referred as finite element model (FE model).
[0050] Now the finite element analysis is conducted in step 150 to
obtain the results. The results may include temperature distribution depicting the temperature at each node of the finite element model of the structure as a function of time. This temperature distribution is depicted as a thermal graph of the structure. The temperature distribution may also be shown as a video showing the temperature at geometric points on the surface as a function of time. It is then used to verify and make changes in the design of the structure for its desired performance.
[0051] Referring to FIG. 2 that illustrates a flowchart of a method 200
of simulating a radiation heat transfer between a first radiating surface and a second radiating surface of a structure in a finite element analysis, according to one embodiment of the present invention. Also referring to FIG. 3 that

illustrates a schematic diagram of radiation heat transfer between first surface to second surface, according to one embodiment of the present invention. The method 200 starts with step 210 of making a Finite Element Model (FE Model) of the structure, the Finite Element Model includes at least on element and a plurality of nodes. The making of the Finite Element Model comprises making a geometric model of the structure, dividing the geometric model into a plurality of finite elements, applying boundary conditions, applying loads and assigning a value of material property to the structure. The FE model is ready for the FE analysis.
[0052] Next step 220 is of determining an average temperature of
the first radiating surface S1. In step 230 a first node N1 is defined and the average temperature of first radiating surface is assigned to the first node N1. In one embodiment of the present invention, the average temperature of the first radiating surface S1 is determined by simulating a convection heat transfer between the first radiating surface S1 and the first node N1. The transferring of the average temperature of the first radiating surface S1 to the first node N1 may also be done by other methods known in prior art.
[0053] In step 240 a second node N2 is defined. The temperature of
the first node N1 is transferred to the second node N2. In one embodiment of the present invention the transferring of the temperature of the first node N1 to the second node N2 may be performed by using a unidirectional element. Other methods known in prior art may also be used to transfer the temperature of the first node N1 to the second node N2.
[0054] Step 250 is simulation of the radiation heat transfer from the
second node N2 to the second radiating surface S2. In one embodiment

the simulation of radiation heat transfer from the second node N2 to the second radiating surface S2 is performed by a method including radiation modeling between a point and a surface. The simulation of radiation from a node to surface is known in prior art, so that method is used for this. Thus the radiation heat transfer from the first radiating surface S1 to the second radiating surface S2 is done by using the above steps.
[0055] Now in next step 260 an average temperature of the
second radiating surface S2 is determined. In step 270 a third node N3 is defined and the average temperature of second radiating surface S2 is assigned to the third node N3. In one embodiment of the present invention, the average temperature of the second radiating surface S2 is determined by simulating a convection heat transfer between the second radiating surface S2 and the third node N3. The transferring of the average temperature of the second radiating surface S2 to the third node N3 may also be done by other methods known in prior art.
[0056] In step 280 a fourth node N4 is defined. The temperature of
the third node N3 is transferred to the fourth node N4. In one embodiment of the present invention the transferring of the temperature of the third node N3 to the fourth node N4 may be performed by using a unidirectional element. Other methods known in prior art may also be used to transfer the temperature of the third node N3 to the fourth node N4.
[0057] Step 290 is simulation of the radiation heat transfer from the
fourth node N4 to the first radiating surface S1. In one embodiment the simulation of radiation heat transfer from the fourth node N4 to the first radiating surface S1 is performed by a method including radiation modeling between a point and a surface.

[0058] At step 300 the finite element analysis on the finite element
model of the structure is performed and the results are obtained.
[0059] In one embodiment of the present invention the first node,
the second node, the third node and the fourth node are representative nodes and extra nodes different from the plurality of nodes of the Finite Element Model of the structure.
[0060] In another embodiment, the present invention provides a
system for simulating a radiation heat transfer between a first radiating surface to a second radiating surface of a structure in a finite element analysis. The system comprises an FE module for making a Finite Element Model of the structure, the Finite Element Model includes a plurality of nodes, a module for determining an average temperature of the first and the second radiating surface, a node defining module for defining a first node, a second node, a third node, a fourth node, a module for transferring the average temperature of the first and the second radiating surfaces to the first node and the third node respectively, a module for transferring the temperature of the first and the third node to the second and the fourth node respectively, a module for simulating the radiation heat transfer from a node to the radiating surface and a module for performing the finite element analysis on the finite element model of the structure.
[0061] The system may be implemented as a independent tool for
executing the method 200 or it may be made as a part of existing FEA tools. The modules described such as FE module, node defining module and other modules may be made as a part of program and may aid in performing the corresponding steps of the method 200.

[0062] The system may include a main memory for storing
computer readable code for a finite element analysis application module, at least one processor coupled to the main memory, such that the processor executes the computer readable code in the main memory to cause the application module to perform operations of the method 200. The system is implemented as software installed on a computer system which may include a main memory, preferably random access memory (RAM), and may also include a secondary memory. The secondary memory may be hard disk drive, removable storage drives, like a floppy disk drive, a magnetic tape drive, an optical disk drive, a CD drive, a USB memory etc.
[0063] For validating the method 200 of the present invention an
example of two concentric cylinders is taken as shown in FIG. 4. The two concentric cylinders 'outside cylinder' and 'inside cylinder' have convection and radiation as heat transfer. The convection is on the outer circumferencial boundary of the 'outer cylinder', between the inner surface of 'outer cylinder' and outer surface of 'inner cylinder', and in the central portion of the 'inner cylinder'.
[0064] A FE model is made by dividing the cylinders into finite
elements as shown. A set of boundary conditions are applied. Radiation along with free convection boundary conditions are applied between the two cylinders.
[0065] After making the model and applying boundary conditions
and load, a FE analysis is conducted with three methods:
i) Radiosity Method

ii) Radiation Matrix method
iii) Method 200 of the present invention.
[0066] The mission starts from Steady State IDLE and accelerates
to takeoff in 10 seconds, stabilizing at takeoff for 15 minutes. The results obtained from all the methods are compared.
[0067] Referring to FIGs. 5a and 5b which illustrates the
temperature contours obtained in the three methods at transient condition and at steady state condition respectively, according to one embodiment of the present invention. The temperature contours were obtained at transient state after 10 seconds from all the three methods viz Radiosity, radiation matrix and the method 200 of the present invention. It can be seen from the FIG. 5a that all three temperature contours looks very same. Similarly temperature contours were obtained at steady state condition after 900 seconds from all the three methods. It may be observed from FIG. 5b that all three temperature contours looks very same. This validates that the method 200 of the present invention gives the same results given by the Radiosity and Radiation matrix method.
[0068] FIGs. 6a and 6b illustrate the transient response of the outer
cylinder node and inner cylinder node obtained in the three methods in transient condition, according to one embodiment of the present invention. It can be seen from both the graphs that the 'new method' which is the method 200 of the present invention gives the results same as the other two methods Radiation Matrix and the Radiosity method.
[0069] From the above example analysis and the results obtained it
may be concluded that the method 200 of the present invention is

comparable in terms of accuracy with the existing FEA methods. In addition to this, the method 200 has the following advantages:
Significant cycle time reduction (~ 85%)
This method is suitable to simulate radiation in all the engineering applications where radiation needs to be modelled like aerospace, automobile etc.
- Ease of building the model.
- The method accounts for temperature dependent emissivity, and improves the accuracy.
- The method is capable of handling large & complex models even with low configuration machines.
- This method can be implemented in any FEA tool or computational software or code for simulating the radiation heat transfer from one surface to another.
[0070] It is to be noted that the present invention uses the radiation
analysis methods available in the FEA software tool ANSYS and the method 200 of the present invention may also be implemented easily in ANSYS, however the method of the present invention may be implemented in other FEA tools by making changes to suit the corresponding FEA tool. The method of the present invention may be implemented as an step in any existing FEA tool or may be developed as a part of a new independent FEA tool or any software which needs to simulate the radiation heat transfer between two radiating surfaces in an easy, cost effective, environment friendly and productive way.
[0071] In other instances, well-known methods, procedures, and
steps have not been described herein, so as not to obscure the particular

embodiments of the present invention. Further, various aspects of embodiments of the present invention may be made using various systems and methods.
[0072] Although a particular exemplary embodiment of the invention
has been disclosed in detail for illustrative purposes, it will be recognized to those skilled in the art that variations or modifications of the disclosed invention, including the rearrangement in the steps of the method, changes in steps, variances in terms of devices may be possible. Accordingly, the invention is intended to embrace all such alternatives, modifications and variations as may fall within the spirit and scope of the present invention.
[0073] The foregoing descriptions of specific embodiments of the
present invention have been presented for purposes of illustration and
description. They are not intended to be exhaustive or to limit the invention
to the precise forms disclosed, and obviously many modifications and
variations are possible in light of the above teaching. The embodiments
were chosen and described in order to best explain the principles of the
invention and its practical application, to thereby enable others skilled in
the art to best utilize the invention and various embodiments with various
modifications as are suited to the particular use contemplated. It is
understood that various omissions, substitutions of equivalents are
contemplated as circumstance may suggest or render expedient, but is
intended to cover the application or implementation without departing from
the spirit or scope of the claims of the present invention. , .

We Claim:
1. A method of simulating a radiation heat transfer between a first radiating
surface and a second radiating surface of a structure in a finite element
analysis, the method comprising steps of:
- making a Finite Element Model of the structure, the Finite Element Model including at least one element and a plurality of nodes;
- determining an average temperature of the first radiating surface;
- defining a first node and transferring the average temperature of the first radiating surface to the first node;
- defining a second node and transferring the temperature of the first node to the second node;
- simulating the radiation heat transfer from the second node to the second radiating surface;
- determining an average temperature of the second radiating surface;
- defining a third node and transferring the average temperature of the second radiating surface to the third node;
- defining a fourth node and transferring the temperature of the third node to the fourth node;
- simulating the radiation heat transfer from the fourth node to the first radiating surface; and
- performing the finite element analysis on the finite element model of the structure.
2. The method according to claim 1, further including calculation and
application of a view factor.
3. The method according to claim 1, wherein the average temperature of the
first radiating surface and the second radiating surface is determined by

simulating a convection heat transfer between the first radiating surface and the first node and between the second radiating surface and the third node respectively.
4. The method according to claim 1, wherein transferring of the temperature of the first node to the second node and from the third node to the fourth node is performed using a unidirectional element.
5. The method according to claim 1, wherein simulating of the radiation heat transfer from the second node to the second radiating surface and from the fourth node to the first radiating surface is performed by a method including radiation modeling between a point and a surface.
6. The method according to claim 1, wherein the first node, the second node, the third node and the fourth node are representative nodes.
7. The method according to claim 1, wherein the first node, the second node, the third node and the fourth node are extra nodes different from the plurality of nodes of the Finite Element Model of the structure.
8. The method according to claim 1, wherein making the Finite Element Model comprising:

- making a geometric model of the structure;
- dividing the geometric model into a plurality of finite elements;
- applying boundary conditions;
- applying loads; and
- assigning a value of material property to the structure.

9. A system for simulating a radiation heat transfer between a first radiating surface to a second radiating surface of a structure in a finite element analysis, comprising:
- an FE module for making a Finite Element Model of the structure, the Finite Element Model includes a plurality of nodes;
- a module for determining an average temperature of the first and the second radiating surface;
- a node defining module for defining a first node, a second node, a third node, a fourth node;
- a module for transferring the average temperature of the first and the
second
radiating surfaces to the first node and the third node respectively;
- a module for transferring the temperature of the first and the third node to the second and the fourth node respectively;
- a module for simulating the radiation heat transfer from a node to the radiating surface; and
- a module for performing the finite element analysis on the finite element model of the structure.