EFFECT OF THERMAL STRESS AND AXIAL LOAD ON COUPOLA FURNACE ... … · effect of thermal stress and axial load on coupola furnace metal components . 1 ejehson philip sule, 2. asha

International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016 21 ISSN 2278-7763

Copyright © 2016 SciResPub. IJOART

EFFECT OF THERMAL STRESS AND AXIAL LOAD ON COUPOLA FURNACE METAL COMPONENTS

1 EJEHSON PHILIP SULE, 2ASHA SATURDAY,3 EZEONWUMELU OGECHUKWU,4 ONUOHA EVARISTUS IROEME

[email protected],[email protected],[email protected],[email protected]

1,2,3,&4Scientific Equipment Development Institute SEDI,P. O .BOX 3205,Enugu ,Enugu State,

Nigeria

ABSTRACT

When an unrestrained metallic material is heated or cooled, it dilates in accordance with its characteristic coefficient of thermal expansion. But components that are restrained behave differently to thermal effects as a result of the restraining loads this could lead to permanent deformation of the surface due to rupture, wrinkles, crack, rumple etc. This study presents analysis of axial loading and thermal stresses in an internally heated Copula furnace component that is subjected to turbulent flow, and pulsating flow. The effect of flow Reynolds number on thermal stresses in the insulated component close to the chimney or exhaust channel ,the influence of hot fluid and axial load on components on the resulting thermal stresses in steel material owning to temperature gradient and with different diameters, and thickness to diameter ratios are covered in this study to examine the effects on thermal stresses and axial load. The amount of heat flux at the inner wall of the Component with regard to regular use and unfriendly heat dissipation creating severe temperature gradient on the inner and outer walls is also included in the study.

KEY WORDS: axial load, thermal stress ,temperature gradient, rumpling ,copula furnace part.

INTRODUCTION

The mechanical behavior of materials when subjected to thermal effects or thermal environment is a factor to into consideration when you are to design thermal machines or systems. Meeting the need for materials, which can function usefully at different temperature levels, is one of the most challenging problems facing some our technology. Some examples are the dilation effects like the strengthening of bridges on a hot day or the bursting of

water pipes in freezing weather and distortions set up in structures by thermal gradients. Sometimes-drastic changes in the properties of materials, such as tensile strength fatigue and ductility as for the metals could also result by the change in material temperature ,also this is not limited to the metals the plastics ,polymers or elastomers even composites exhibit such change in properties when subjected to thermal environment. The elements of mild steel component body expand with rising

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temperature. Such an expansion generally cannot proceed freely in a continuous medium, and stresses due to the heating are set-up. The difficulty is that operating conditions not only at elevated temperature levels, but frequently also at severe temperature gradients. Such temperature differentials may produce thermal stresses significantly high enough to limit the material life. Fatigue failure could also occur due to temperature fluctuations. Thermal cycling process which is the alternate heating and cooling of a material until they experience molecular reorganization which tightens or optimizes the particulate structure of the material throughout, relieving stresses and making it denser and uniform thereby minimizing flaws or imperfections. Miner postulated that when a component is fatigued, internal damage takes place and the nature of the damage is difficult to specify but it may help to regard the damage as the slow internal spreading of a crack, although this should not be taken too literally. He also stated that the extent of damage was directly proportional to the number of cycles for a particular stress level and quantified this by adding that “the fraction of the total damage occurring under one series of ycles at a particular stress level, is given by the ratio of the number of cycles actually endured (n) to the number of cycles (N) required to break the component at the same stress level” [3]

For example, thick-walled pipes subjected to internal heat flow are used in many applications. When a thick-walled cylindrical body is subjected to a temperature gradient, non-uniform

deformation is induced and thermal stresses are developed. The resulting thermal stresses add to the stresses resulting from internal and external pressures in the pipe material. One of the causes of thermal stresses in pipes is the non-uniform heating or cooling; such a situation that exists when for example pipes are welded, causing residual stresses. Nuclear engineering structures, military industries, chemical and oil industries, gun tubes, nozzle sections of rockets, composite tubes of automotive suspension components, launch tubes, landing gears, turbines, jet engines and dies of hot forming steels are typical examples.

The transfer of heat in a solid occurs in virtue of heat conduction alone for time periods longer than phonon relaxation time. This does not have any macroscopic levels of movement in the solid body such as non-uniform electrons motion. At the surface o f a body, heat transfer can occur in three ways: heat conduction, convection, or radiation. The heat exchange in the case of convection occurs by virtue of the motion of non-uniformly heated fluid or gas contiguous with the body. Convective heat transfer is the sum of the heat carried by the fluid. Heat exchange by means of electromagnetic waves takes place between bodies separated by a distance in the case of radiation. The pipe flow subjected to conjugate heating, where heat conduction in the solid interacts with convection heat transfer in the fluid, situations that result in large temperature gradients finds wide applications in engineering disciplines. This is due to the fact that the thermal loading can have a

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significant effect on the thermal resistance of the pipe. Examples of systems, in which the conjugate heat transfer exists, include heat exchangers, geothermal reservoirs, marine risers, sub-surface pipelines engineering structures, refrigeration ducts and nuclear reactors. Based on the conditions of flow and heat transfer, the temperature gradients resulting in pipes differ. The effect of thermal cycling on a material cannot be undermined because of its importance to the design and manufacturing engineer. When a material is subjected to a temperature gradient it tends to expand differentially, during this process thermal stresses are induced. The source of heat that causes the thermal gradient may be friction as in the case of brake.

FLUID FLOW

The characteristic that distinguishes laminar from turbulent flow is the ratio of inertial force to viscous force, which can be presented in terms of the Reynolds number. Viscosity is a fluid property that causes shear stresses in a moving fluid, which in turn results in frictional losses. This is more pronounced in laminar type of flow; however, the viscous forces become less important for turbulent flows. The reason behind this is due to that in turbulent flows random fluid motions, superposed on the average, create apparent shear stresses that are more important than those produced by the viscous shear forces. The eddy diffusivities are much larger than the molecular ones in the region o f a turbulent boundary layer removed from

the surface (the core region). Associated with this condition, the enhanced mixing has the effect of making velocity, temperature and concentration profiles more uniform in the core. As a result, the velocity gradient in the surface region, and therefore, the shear stress, is much mlarger for the turbulent boundary layer than for the laminar boundary layer. In a similar manner, the surface temperature, and therefore, the heat transfer rate is much larger for turbulent flow than for laminar flow. Due to this enhancement of convection heat transfer rate, the existence of turbulent flow can be advantageous in the sense of providing improved heat transfer rates. However, the increase in wall shear stresses in the case of turbulent flow will have the adverse effect of increasing pump or fan power requirements. On the other hand, the conductive heat transfer becomes more important in laminar flow than the turbulent flow.

SCOPE

Investigating the thermal stresses in internal heated steel component when they are subjected to different flow conditions and it covers both the steady and the unsteady types of flow. But thermal recycling as well as fatigue could not be far from this work. Since the temperature of the solid-fluid boundary depends on the fluid properties, the effect of the fluid Prandtl number on thermal stresses is investigated. In actual practice, the temperature and heat flux distributions on the boundary depend strongly on the thermal properties and the flow characteristics of the fluid as well as on

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the properties of the wall. In order to account for this effect, different pipe wall materials are considered. Similarly, the temperature level and the temperature gradients within the solid are highly influenced by the amount of heat flux supplied at the outer wall of the pipe, therefore, different heat flux levels are used in the study to examine the effect of heat flux on thermal stresses in pipes.The study parameters also include the change of thermal stresses with the pipe dimensions. Different pipe diameters, thickness to diameter ratios and length to diameter ratios are also employed in the study.

AIMS AND OBJECTIVES

This work is aimed at show casing the effect of axial load and thermal stress on a component of a cupola furnace with CAE using Solid Works 2013,this can be employed to estimate the service life of a copula furnace since the steel shell whether lagged with bricks or not are subjected regularly to thermal stress and fatigue.

a.

b.

Fig 1.(a) and (b) pictoral view of a working copula furnace with a rumpled or wrinkled part

MODELING

Fig 2. Section Of The A Cylindrical Shell Of Cuopular Furnace

𝑟0 = 𝑜𝑢𝑡𝑒𝑟 𝑡𝑎𝑑𝑖𝑢𝑠 𝑚,

𝑟𝑖 𝑖𝑠 𝑖𝑛𝑛𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 ,

𝐿 , 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎 𝑐𝑦𝑙𝑖𝑛𝑑𝑟𝑖𝑐𝑎𝑙 𝑠ℎ𝑒𝑙𝑙 ,

𝑡 𝑖𝑠 𝑡𝑟ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠ℎ𝑒𝑙𝑙

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𝑞 𝑖𝑠 ℎ𝑒𝑎𝑡 𝑓𝑙𝑢𝑥 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑜𝑛 𝑡ℎ𝑒 𝑖𝑛𝑛𝑒𝑟 𝑤𝑎𝑙𝑙 𝑜𝑓 𝑡ℎ𝑒 𝑠ℎ𝑒𝑙𝑙 ,

𝑢 , 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑜𝑤 𝑜𝑓 ℎ𝑜𝑡 𝑔𝑎𝑠 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛

BOUNDARY CONDITIONS

The boundary conditions for the conservative equations of flow involving fluid and solid are:

A. At pipe axis:

Radial gradient of axial velocity and temperature are set to zero, while the radial

velocity is taken as zero, i.e.:

𝜕𝑈𝜕𝑟

(𝑌, 0) = 0, 𝜕𝑇𝜕𝑟

(𝑌, 0) = 0 and 𝑉(𝑌,𝑂)=O

B. At inner solid wall (r = rj, where r; is pipe inner radius):

No-slip condition is assumed

𝑈(𝑌, 𝑟𝑖)

𝑉(𝑌, 𝑟𝑖) = 0

C. At outer surface of the pipe (r = r0, where r0 is pipe outer radius): Uniform heat flux is assumed, i.e.:

𝑟 = 𝑟0

0 ≤ 𝑥 ≤ 𝐿 D. A t solid-fluid interface, i.e.:

𝑟 = 𝑟0

0 ≤ 𝑦 ≤ 𝐿

�̇�𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 = 𝐾𝑠𝑜𝑙𝑖𝑑𝜕𝑇𝑠𝑜𝑙𝑖𝑑𝜕𝑟

= 𝐾𝑓𝑙𝑢𝑖𝑑𝜕𝑇𝑓𝑙𝑢𝑖𝑑𝜕𝑟

𝑇𝑆𝑜𝑙𝑖𝑑 = 𝑇𝑓𝑙𝑢𝑖𝑑

E. The flow is assumed to be at uniform temperature, i.e.:

𝜕𝑇𝜕𝑟

(0, 𝑟, 𝑡) = 0

The type of flow is specified based on the considerations made:Turbulent flow:A unidirectional flow with uniform inlet speed is assumed.

THERMAL STRESSES RELATIONS

In the solid, the governing heat conduction equation for the steady-state cases (applicable for fully developed laminar and turbulent flow situations) is:

1𝑟𝜕𝜕𝑟�𝑟 𝜕𝑇

𝜕𝑟�+ 𝜕2𝑇

𝜕𝑌2= 0 [1]

and for the transient case (pulsating flow):

𝜕𝑇𝜕𝑡

= 𝑥 �1𝑟𝜕𝜕𝑟�𝑟 𝜕𝑇

𝜕𝑟� + 𝜕2𝑇

𝜕𝑌2� [2]

The relation between thermal stress and strain follows the thermoelasticity

formulae i.e.:

𝜀𝜃 = 1𝐸�𝜎𝜃 − 𝑣�𝜎𝑟 + 𝜎𝑦�� + 𝛼𝑇

[3]

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𝜀𝑟 = 1𝐸�𝜎𝑟 − 𝑣�𝜎𝑦 + 𝜎𝜃�� + 𝛼𝑇

[4] 𝜀𝑦 = 1

𝐸�𝜎𝑦 − 𝑣(𝜎𝑟 + 𝜎𝜃)� + 𝛼𝑇

[5] 𝜀 is turbulent dissipation variable ( 𝑚2 𝑠2⁄ ),𝜀𝑣 , tangential strain 𝜀𝑟 radial strain 𝜀𝑥 axial strain 𝜎𝑣effective stress (Pa) 𝜎𝑢 tangential stress (Pa) 𝜎𝑟 radial stress (Pa) 𝜎𝑦 axial stress (Pa) T ;temperature at a grid point K turbulent kinetic energy generation variable (𝑚2 𝑠2⁄ ) 𝐾𝑓=thermal conductivity of the fluid W/mk 𝐾𝑠 = thermal conductivity of the solid W/mk P Pressure Pa Pr laminar prantl number Prt turbulent prantl number q heat flux Re laminar Renolds number Ret=turbulent Renolds number R radial coordinate m

Solving the above equations for a hollow cylinder results in [83]:

𝜎𝜃 =𝐸𝛼

(1−𝑣)𝑟2� 𝑟

2−𝑟𝑖2

𝑟02−𝑟𝑖2∫ 𝑇. 𝑟𝑑𝑟 +𝑟0𝑟𝑖

∫ 𝑇. 𝑟𝑑𝑟𝑟𝑟𝑖

−

𝑇. 𝑟2� [6]

𝜎𝑟 = 𝐸𝛼(1−𝑣)𝑟2

� 𝑟2−𝑟𝑖2

𝑟02−𝑟𝑖2∫ 𝑇. 𝑟𝑑𝑟𝑟0𝑟𝑖

−

∫ 𝑇. 𝑟𝑑𝑟𝑟𝑟𝑖

� [7]

𝜎𝑦 = 𝐸𝛼(1−𝑣)

� 2𝑟02−𝑟𝑖2

∫ 𝑇. 𝑟𝑑𝑟𝑟0𝑟𝑖

− 𝑇�

[8]

The effective stress according to Von-Mises theory [84] is:

𝜎𝑣 = �𝜎𝜃2 + 𝜎𝑟2 + 𝜎𝑦2 −

�𝜎𝜃𝜎𝑟 + 𝜎𝜃𝜎𝑦 + 𝜎𝑟𝜎𝑦��12� [9]

TURBULENT FLOW

The mean flow equations are simplified after the consideration o f Boussinesq approximations. In cylindrical polar coordinates the conservation equations are written.

Continuity:

𝜕𝑈𝜕𝑦

+ 1𝑟𝜕𝑦𝜕𝑟

(𝑉𝑟) = 0 [10]

MOMENTUM

1𝑟𝜕𝜕𝑟

(𝑟𝑉𝑈𝜌) + 𝜕𝜕𝑌

(𝜌𝑈2) = −𝑑𝑃𝑑𝑌

+1𝑟𝜕𝜕𝑟�𝑟(𝜇 + 𝜇𝑡)

𝜕𝑈𝜕𝑟� [11]

ENERGY

1𝑟𝜕𝜕𝑟

(𝑟𝑉𝑇𝜌) + 𝜕𝜕𝑌

(𝜌𝑈𝑇) =1𝑟𝜕𝜕𝑟�𝑟 � 𝜇

𝑃𝑟+ 𝜇𝑡

𝑃𝑟𝑡� 𝜕𝑇𝜕𝑟� [12]

where Pr and Prt are bulk and turbulent Prandtl numbers respectively. In order to determine the turbulent viscosity and the Prandtl number, the k-e model is used. The constitutive equations for the turbulent viscosity are as follows:

𝜇𝑡 = 𝐶𝜇𝐶𝑑𝜌𝐾2

𝜀 [13]

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where k and 𝜀 are the turbulent kinetic energy generation and the dissipation variable respectively. The transport equation for k is:

1𝑟𝜕𝜕𝑟

(𝑟𝑉𝐾𝜌) + 𝜕𝜕𝑌

(𝜌𝑈𝐾) =

𝜇𝑡 �𝜕𝑈𝜕𝑟�2

+ 1𝑟𝜕𝜕𝑟�𝑟 �𝜇 + 𝜇𝑡

𝑃𝑟𝑡� 𝜕𝐾𝜕𝑟� −

𝜌(𝜀 + 𝐷𝜀) [14]

𝐷𝜀 = 2(𝜇 𝜌⁄ )�𝜕𝐾𝜕𝑦�2 [15]

𝜀 attains zero at x = 0.The transport equation for 𝜀 is:

1𝑟𝜕𝜕𝑟

(𝑟𝑉𝜀𝜌) + 𝜕𝜕𝑌

(𝜌𝑈𝜀) =

𝐶𝜀1𝜌𝜀𝐾𝜇𝑡 �

𝜕𝑈𝜕𝑟�2

+ 1𝑟𝜕𝜕𝑟�𝑟 �𝜇 +

𝜇𝑡𝑃𝑟𝑡� 𝜕𝜀𝜕𝑟� − 𝐶𝜀2

𝜌𝜀2

𝐾+ 2𝜇𝜇𝑡

𝜌�𝜕

2𝑊𝜕𝑟2

�2

[16]

In order to minimize computer storage and run times, the dependent variable at the walls were linked to those at the first grid from the wall by equations, which are consistent with the logarithmic law of the wall. Consequently, the resultant velocity parallel to the wall in question and at a distance xi (where x+ < 2) from it corresponding to the first grid node was assumed to be represented by the law of the wall equations [85], i.e.:

𝑉0𝐶𝑑𝐶𝜇𝐾1 2⁄

𝜏𝑤𝑎𝑙𝑙 𝜌⁄=

1𝐾𝐼𝑛 �𝑒�𝐶𝑑𝐶𝜇�

1 2⁄𝐾1 2⁄ 𝑦1

𝜌𝜇� [17]

𝐾 = 0.417 𝑎𝑛𝑑 𝑒 = 9.37

from which the wall shear stresses were obtained by solving the momentum

equations.The constants used in the transport equations are:

𝐶𝜇 = 0.5478,𝐶𝑑 = 0.1643 , 𝐶𝜀1= 1.44 ,𝐶𝜀2= 1.92 ,𝑃𝑟𝑘= 1.0 ,𝑃𝑟𝜀 = 1.314

𝑅𝑒𝑡 = 𝐾2

(𝜇 𝜌⁄ )𝜀 [18]

𝜇=fluid dynamic viscosity 𝜏𝑤𝑎𝑙𝑙 = 𝑤𝑎𝑙𝑙 𝑠ℎ𝑔𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠 𝑃𝑎 𝑣 = 𝑝𝑜𝑖𝑠𝑠𝑜𝑛′𝑠𝑟𝑎𝑡𝑖𝑜𝑛 𝜇𝑡= fluid dynamic turbulence viscosity 𝜌 =density of fluid 𝜌𝑠𝑜𝑙𝑖𝑑=density of the solid THE FLUID AND SOLID TEMPERATURE FIELDS The interior wall temperature at a given axial plane is calculated

𝑇𝑤 = 2∗𝑇𝑓𝑤∗𝑇𝑠𝑤𝑇𝑓𝑤+𝑇𝑠𝑤

[19]

𝑇𝑚𝑒𝑎𝑛=mean temperature 𝑇𝑠𝑜𝑙𝑖𝑑=solid side temperature 𝑇𝑓𝑙𝑢𝑖𝑑=fluidside temperature ANALYSIS WITH CAE

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The CAE analysis is done to verify effect of axial load and thermal stress in relation to the thickness of the coupola furnace component which is uninsulated however this does not mean that the internally insulated parts are not affected but this infect is gradual and minimal as it depends on the type of insulation i.e type of bricks used.

`ASSUMPTIONS

The following assumption are made

1. No slip on the hot gas stream flow

2. No friction on application of the axial load

3. The hot stream has a constant temperature

4. The material is isotropic 5. The temperature difference is

constant. 6. Flow is turbulent nor

pulsating

MESH PROPERTIES

TABLE1 properties of the mesh of the parent model

Total Nodes Aspect Ratio

Jacobian Points

18097 91.5 4 Points Total Elements

Mesh Type Element Size

8929 Solid Mesh 35.852 mm

Table 2. MATERIAL PROPERTIES

OF THE MODEL

Name: AISI 1035 Steel (SS)

Model type: Linear Elastic Isotropic

Default failure criterion: Max von Mises Stress

Yield strength: 282.685 N/mm^2 Tensile strength: 585 N/mm^2 Elastic modulus: 205000 N/mm^2 Poisson's ratio: 0.29 Mass density: 7850 g/cm^3

Shear modulus: 80000 N/mm^2 Thermal expansion

coefficient: 1.1e-005 /Kelvin

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MODELS

Fig3. 3-D model of the cone shell

Fig4. 3-D mesh of the model

i.

ii.

iii.

iv. fig.5, (i) to (ivi) deform models of the cone part

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Fig 6.deformed rumple cone part of the cupola furnace due to exial laod and regular heating TABLE3. Simulated Results Axial Load = 1800N 𝑇𝑖=internal wall temperature =1900k 𝑇𝑜=outer surface temperature =400k

S/N THICKNESS mm

Von Misers Stress

N/mm2 Node: 16081

Strain Element:

4597

Deformation mm

Node: 1912

1 24 4317.35 0.012558

3.55025

2 20 4251.1 0.0120281

3.44285

3 16 4222.11 0.0129057

3.43544

4 12 4542.29 0.0160067

3.38356

5 8 4039.12 0.0115654

3.29209

6 4 4260.11 0.011131

1.96201

GRAPH

Fig 7. Stress development on the

material with application of axial load and temperature gradient

Fig 8. Strain development on the

material with application of axial load and temperature gradient

4000

4200

4400

4600

0 10 20 30

Von

Mis

ses s

tres

s,M

Pa

Thickness ,t,mm

effect of change in thickness ,t,mm

00.005

0.010.015

0.02

0 10 20 30

Stra

in

Thickness,t,mm

Strain on the component

0

1

2

3

4

0 10 20 30

Disp

lace

men

t,mm

Thickness,t,mm

linear defomation

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Fig 9.Linear deformation development

on the material with application of axial load and temperature gradient

DISCUSSION This study reveals the effect of thermal stress on the cone model and the rumple effect is more visualized than in data form, see fig 5,iv and fig 6 ,there is a clear similarity between the pictorial view and the simulated model. The value of the maximum stress is used to predict the furnace column shell model life based on fatigue analysis. Thermal stress has more effect on service life of a cupola furnace than mechanical stress. Hence ,the material do not show distinct variation on linear displacement of the component as a whole, but the software was able to show clearly the rumpling of the material owning to the temperature gradient since ductility of a material increase with increase in temperature in a thermal environment, the axial load on the has to compress as the material fails under thermal environment. The table 3. shows that the Von Misses stress increase as the thickness decreases under the same thermal condition and axial load. Thus, to withstand axial load under severe thermal conditions, thicker materials should be used with or without insulations especially areas from charging door and above, but in general,coupola furnace component need to be limned internally with insulating bricks to maximize the

performance and efficiency and as well as extend the life of the metal parts due to thermal recycling as foundry operation is regular. Therefore, effect of thermal stress on metallic material like mild steel is minimized when they are lagged internally. CONCLUSION Axial load and thermal stress has a significant effect on failure of copula furnace parts. Proper Insulation minimize or eliminate these effects resulted from temperature difference (gradient). The rumple and wrinkles observed is as a result of thermal stress on the constrained cone part by axial load,this effect due to severe temperature difference is minimized by adapting thicker materials or insulating their inner walls with good insulating bricks. REFFERENCES

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2. L. Bauwens, “Oscillating Flow

of a Heat-Conducting Fluid in a Narrow Tube”, J. Fluid Mech., Vol. 324, pp. 135-161, 1996.

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3. Miner, M. A., Cumulative damage in fatigue transactions ASME, 67, 1945.

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“Interaction of a Steady Approach Flow and a Circular Cylinder Undergoing Forced Oscillation”, Journal of Fluids Engineering, Vol. 119, pp. 808-813, 1997.

5. Z. Guo and H. Sung,

“Analysis of the Nusselt Number in Pulsating Pipe Flow”, Int. J. Heat Mass Transfer, Vol. 40, No. 10, pp. 2086-2489, 1997

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8. O.A. Amas, and M.A.

Ebadian, “Convective Heat Transfer in A Circular Annulus

with Various Wall Heat Flux Distributions and Heat Generation”, Journal of Heat Transfer, Vol. 107, pp. 334-337, 1985.

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EFFECT OF THERMAL STRESS AND AXIAL LOAD ON COUPOLA FURNACE ... … · effect of thermal stress and axial load on coupola furnace metal components . 1 ejehson philip sule, 2. asha