Numerical study of heat transfer in a multilayer wall

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2^ÈMECONFÉRENCE INTERNATIONALE SUR L’ÉNERGÉTIQUE APPLIQUÉE ET LA POLLUTION (CIEAP’2014)

Numerical study of heat transfer in a multilayer wall

Sofiane Boulkroune

^{1, 2}

, Mohamed Chaour

^1,2

, Mounira Bourebia

¹

, Djoubeir Debbah

²

, M.tayeb Abed ghars

¹

, kahalerras Mounir

¹

1Welding and NDT Research, Centre (CSC), B.P 64 Cheraga, Algeria (Algérie).

2Département de Génie Mécanique, Université Constantine 1, Constantine (Algérie).

Résumé

On propose une étude numérique, par différences finies, du transfert de chaleur dans un mur multicouche (trois couches) soumis à une condition de rayonnement sur le côté intérieur et prenant en compte les échanges de chaleur par conduction, convection sur ses deux faces. L’exploitation du code numérique est développée sur des cas relatifs au problème posé dans les fours. Les résultats numériques sont présentés sur des exemples de matériaux utilisés pour un four cubilot dans des conditions réelles de fonctionnement (flux, pertes convectives, etc.…). On analyse également, l’influence, sur le transfert de chaleur, de quelques paramètres clés du système comme le choix des matériaux, l’optimisation de leur épaisseur et également la nature variable du flux.

Mots clés : Transfert de chaleur, Cubilot, Isolation thermique.

Abstract

We proposed a study digital, by finite difference, heat transfer in a multilayer wall (three layers) subjected to radiation condition on the inner side and taking into account the exchange of heat by conduction, convection on both sides. The operation of the digital code is developed on cases related to the problem in the ovens. The numerical results are shown examples of materials used in a cupola furnace in real conditions of functioning (fluxes, losses convectives, etc). They also analyse, the influence, on the transfer of warmth, some key parameters of the system as the choice of materials, the optimization of their thickness and also the variable nature of the flow.

Keywords: Heat transfer, cupola, Heat Insulation.

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2 Nomenclature

T Temperature (°C)

e_i Thickness of the wall i(m), i=1,2,3 T_a Ambient temperature ( (°C), Ta =25°C Greek Symbols

Thermal conductivity of the material of each wall thermal i=1, 2,3 (W/m K)

Thermal Diffusivity (m³/s)

I

ntroduction:

The heat transfer is a process by which energy is exchanged in the form of heat between the body or circles with different temperatures. The heat can be transferred by conduction, convection or radiation. Currently we can see that the heat transfer is one of the physical phenomena the most studied. Several researchers have presented during these past two decades of work relating to the study of this phenomenon among them have can quote those Of N.

Berour [ 1] who has studied numerically the heat transfer torque combining radiation, conduction and convection for the semi-transparent, non-gray, doors at high temperature (application to glass furnaces). Another study carried out by K. Saito and Mr. Ohta [ 2] the phenomena of transfer of heat in the area pre hot of a cupola. The results show that the loading layer by layer allows to obtain a fusion more efficient load metal. H. Sun and al (3) have developed a mathematical model for a cupola to continuous casting based on both the balance of mass and heat. A numerical study of heat transfer in a multilayer wall to two or three layers has been studied by Y. Tamene and al (4). The objective of this work is to examine the effects of several parameters on the heat transfer in a wall multi layer subject to the real conditions of a cupola furnace.

2- MATHEMATICAL FORMULATION OF THE PROBLEM

Equations of thermal balance sheet write:

; , 0 , 1,2,3 (1)

initial conditions

.T T à t 0, l X l (2)

Boundary conditions

1∂ ₁

∂x 1 1 1 Φ X=0 (3)

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3- GEOMETRIC CONFIGURATION

The configuration considered is shown in Figure 1 it is the bottom area of a cupola; Fig.1a is a vertical furnace, so that a large metal tube called a ferrule, wherein the materials to be melted are in direct contact with the coke fuel. The steel shell is protected by the refractory and externally cooled by a water circuit run along the wall [5].

In our work it was considered that the area A of the cupola (fig.1, b) consisting of the molten cast iron with a temperature of 800 ° C is wrapped by three layers, the middle layer is made of brick, covered with a thickness e2 both sides by a concrete layer thickness e1 of internal and external thickness e3. The latter is subject to a condition variable flow. Exchange by convection with the surrounding environment are taken into account on both inner and outer surfaces.

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(b)

Figure 1: System Overview

(a): schéma représentatif d’un cubilot; (b) : studied configuration (1) Système de dépoussiérage.

(2) Cheminée.

(3) Gueulard.

(4) Chargement.

(5) Arrosage.

(6) Garnissage.

(7) Colonne du cubilot.

(8) Charges métallique.

(9) Charges coke + castine.

(10) Boîte à vent.

(11)Regard de surveillance.

(12) Tuyères.

(13) Laitier.

(14) Trou de coulée.

(15) Chenal de coulée.

(16) Sole.

(17) Trou de décrassage.

(18) Creuset de fonte.

(19)Porte d’allumage.

(20) Goulotte de récupération des eaux de refroidissement.

(21) Bac à crasse.

(22) Portes de défournement

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3 4-RESULTATS ET DISCUSSION

The working of numerical code was accomplished in following conditions:

e1=1 cm, e2=20 cm, e3=1 cm, h 1=10 W/m

²

°C, h 2 = 100 W/m

²

°C, h I = 106 W/m

²

°C;

Tf1 = 20 °C, Tf 2 = 800 °C, FI = 500 W/m

²

The materials are considered for central brick wall, the mortar for the two outer and inner layers

On numerical plan, the number of step used in every coat is the following: N1 = 8 , N2 = 20 , N3 = 8 .

In this work, we limited our analysis to a steady flow, the influence of thickness on the thermal behavior of the multilayer.

In Figures 2, 3 and 4 shows the influence of the thicknesses of the different layers on the inner wall temperature. It is noted that the internal temperature drops to approximately 3 ° C and a degree, respectively if the triple thickness of the core layer (brick) and the first layer (mortar).

The thickness of the third layer (mortar) has very little influence the internal temperature (less than a variation degree).

We proposed a flow variable which gives the pace represented on figure 5. We note that the temperature is inversely proportional with the flow, or an increase in the flow causes the decrease of the internal temperature of the wall.

0 20 40 60 80 100

765 770 775 780 785 790 795 800 805

Température(°C)

Temps(Heure)

e1=0.01 e1=0.02 e1=0.03

Figure 2: Evolution of the internal temperature as a function of the thickness of the first layer in mortar

0 20 40 60 80 100

760 765 770 775 780 785 790 795 800 805

Température(°C)

Temps(Heure)

e2=0.1 e2=0.2 e2=0.3

Figure 3: Evolution of the internal temperature as a function of the thickness of the intermediate wall brick

0 20 40 60 80 100

765 770 775 780 785 790 795 800

Température(°C)

Temps(Heure)

e3=0.01 e3=0.02 e3=0.03

Figure 4: Evolution of the internal temperature as a function of the thickness of the outer layer in mortar

0 20 40 60 80 100

760 765 770 775 780 785 790 795 800 805

Température(°C)

Temps(Heure)

FI=0 W FI=300 W FI=400 W FI=500 W FI=600 W

Figure 5: Evolution of the internal temperature of the wall as a function of the flow

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4 CONCLUSION

In this work, we have proposed a thermal model of transitional prediction of the distribution of the temperature of a multilayer wall subjected to thermal conditions variables, or it is question of a flow variable and transfers of thermal convective to the inside and outside. The numerical results show that it is possible to select and optimize the materials comprising the multilayer wall according to the objectives set in terms of internal temperature and result in terms of energy and power consumption..

REFERENCES

[1]. N. Berour, " Modélisation du transfert de chaleur par rayonnement, conduction et convection : application aux fours verriers ", UHP - Université Henri Poincaré, 2005.

[2]. K. Saito, M. Ohta, " Influence of shape of charged metal and charge composition upon heat absorption by metallic charge in the preheat zone of Cupola ", Imono A. vol. 60, N° 5.pp.307-312, 1988.

[3]. H.H. Sun, C.C. Kong, H.H. Wu, "Mass and heat transport in a coke fueled shaft furnace", Canadian Metallurgical Quarterly, Vol 45,N°4.pp.395-408, December 2006.

[4]. Y. Tamene, S. Abboudi, C.Bougriou, " Simulation des transferts thermiques transitoires à travers un mur multicouche soumis à des conditions de flux solaire et de convection ", Revue des Energies Renouvelables, vol.12 N°1.pp.117-124, 2009.

[5]. L. Chazé, R. Sanz, " Fusion de la fonte au cubilot ", Revue de Techniques de l’Ingénieur, M₁.765 P.2, 1997.

[6]. T. Stolarski, S. Makasone, S. Yoshimoto

" Engineering Analysis with ANSYS Software ", Tokyo university of science, Tokyo, Japon.2006.