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Simulation of the variation in temperature in a material without and with default

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Simulation of the variation in temperature in a material without and with default

K.Gherfi, M.Chaour, S.Boulkroune Welding and NDT Research Centre (CSC)

BP 64 CHERAGA-ALGERIA

kaddour.gherfi@gmail.com,chaourmed@yahoo.fr,sofiane25000dz@yahoo.fr

Abstract—In this article our principal study is the simulation of the variation in temperature in a solid material in absence and in presence the default, in particular a fracture on the level of surface of material, and to see how the default influences on heat transfer in a solid. The simulation is made by FLUENT software which permits us to solve the energy equation by finite volumes method.

Keywords—heat transfer; simulation; material; default I. INTRODUCTION

The heat transfer domain is a vast domain, it includes three great domains: conduction, convection and radiation, in this study we fix our work on conduction.

Conduction is the mode of heat transfer existing in a given medium without there being apparent displacement of matter.

It is what occurs in particular in a homogeneous solid medium (metal, wall), but which also takes place in the motionless fluids.

Conduction cannot exist that if there are variations in temperatures i.e. if the variation in temperature is not null. In the contrary case the medium is in thermal equilibrium and no heat transfer can occur. So that is variation in temperature exists, it needs an external action for the system to be able to maintain the temperatures conditions given to the limits of the system [1].

Among the problems which they exist in materials, there are the fractures, for that we tried in this paper to make a simulation of the heat transfer in a material without and with fracture, because modeling fracture in engineering materials has been the focus of research for many years [2]

II. GEOMETRICAL CONFIGURATION

The studied configuration is presented on“Fig. 1” and “Fig.

2”, it acts of a rectangular material (three dimensions) without and with a surface fracture.

We suppose that this material is iron with the following properties:

Material density = 7860 kg/m3 Specifique heat = 440 J·kg-1·K-1 Thermal conductivity = 80,2 W·m-1·K-1

Flow (q)

T=300 K T=300

K

T=300 K T=300

K

T=300 K

Fig. 1. Geomerical without fracture

Flow (q)

T=300 K

T=300 K T=300

K

T=300 K

T=300 K

Fig. 2. Geomerical with fracture

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III. MATHEMATICAL FORMULATION

The formula called the heat tansfer equation is shown below (in one dimensional case). [3]

2 0

2 

 

 

X T t

T (1)

In our case we have tree dimensional the heat transfer equation becomes:

2 0

2 2 2 2

2 

 





 

Z T Y

T X

T t

T (2)

With

T: la température (temperature) t: Time

α=λ/ρCP:

ρ: Material density λ: Thermal conductivity CP: specific heat

We apply a flow of heat on the superior face of the two materials (without and with fracture) and we see the temperature profiles in the two parts.

The equation of flow is the following form:

Y q T

 

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The value of appling flow is : q = 3000 w/m2

On the level of the others faces we suppose the boundary conditions such as the temperature is constant T = 300K.

IV. NUMERICAL METHOD

we used our simulation by the software FLUENT, the governing eauqtions were discretized by the finite volume method on a staggered mesh and the SIMPLE algorithm was used for the treatment of velocity-pressure coupling. In this work , we will use second Order Upwind scheme, because it requires less computing time and provides better stability of the numerical solution and results close to the exact solution.

Although certain restrictions on mesh configuration had to be imposed to avoid locking, these restrictions were less severe than those of the equivalentfinite element meshes. Numerical calculation with meshes consisting of triangular cells showed excellent agreement with analytical results. Meshes consisting of quadrilateral finite volume (FV) cells displayed too stiff behavior, indicating a locking phenomenon.[4]

V. RESULTS AND DISCUSSION

The objective of our numerical simulations is for studying the temperature profile in the materials without and with defaults.

A. Material Without Default

Fig. 3. Mesh of material without fracture

Fig. 4. Mesh of material with fracture

Fig. 5. Temperature profile in a material without default (plan 1).

Fig. 6. Temperature profile in a material without default (plan 2).

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According to“Fig. 5”and“Fig. 6”, in two different planes, we note that the temperature profile has a gradual and uniform distribution descending from the surface to the center of the material due to the limit conditions at the surface (T = 300K), and for “Fig .7” We also note that the temperature is maximum and stable whenever we approach the center of the material in the plane (X, Z).

B. Material With Default

According to “Fig. 8” and “Fig. 9”, we note that the temperature profile has a gradual and uniform distribution descending from the surface, but when we get closer to the center we see that the distribution is disturbed and the maximum temperature concentrated at the fracture, and for the

“Fig. 10”, We note that there is drop in temperature at the crack due to the temperature difference between the material and the default (fracture).

VI. CONCLUSION

The results of our simulation of the temperature variation in a material without and with default, showing that the fractures cause problems of heat distributions in heat transfer domain, especially in the heat exchanger, because that the heat transfer in material is different when there is no continuity of medium that is to say there is a void that is the fracture.

Fig. 7. Temperature profile in a material without default (plan X,Z).

Fig. 9. Temperature profile in a material with default (plan 1).

Fig. 8. Temperature profile in a material with default (plan X,Z).

Fig. 10. Temperature profile in a material with default (plan 2).

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REFERENCES [1] J.Brau, 2006, INSA de Lyon.

[2] Michael Meyn, Sebastian Kilchert,Stefan Hiermaier, “3D modeling of fracture in brittle isotropic materials using a novel algorithm for the determination of the fracture plane orientation and crack surface area”, 2012, Finite Elements in Analysis and Design.

[3] Pawet Kopyt*, Malgorzata Celuch-Marcysiak*, "On the influence of mesh refinement and non-uniformity on the solution of the heat transfer equation in coupled EM-thermal analysis", vol. 2, N P. 578-581, Product Type: Conference Publication Date of Conference: 17-19 May 2004 IEEE.

[4] I. Bijelonjaa, I. Demirdzicb, S. Muzaferijab, "Afinite volume method for incompressible linear elasticity", Comput. Methods Appl. Mech. Engrg.

195 (2006) 6378–639.

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