MODELING AND SIMULATION OF AN

AUSTENITIZING FURNACE OPERATION

FOR CARBON AND LOW ALLOY STEELS

USING FINITE ELEMENT MODELLING

(MSE 504)

SUBMITTED BY:

Oluwasegun Richard AJAYI

Oluwasegunrich500@gmail.com

TO

Dr. P.O ATANDA

THE DEPARTMENT OF MATERIALS SCIENCE AND

ENGINEERING

FACULTY OF TECHNOLOGY

OBAFEMI AWOLOWO UNIVERSITY

ILE-IFE

Dec 20th, 2013

ABSTRACT

The effect of heat treatment operation (Austenitizing) on carbon and low alloy steels were

studied in this work using finite element (FEA) analysis and the results of the microstructural

morphology of the carbon and low alloy steels on cooling were also studied.

The implications of the heat treatment operation to temperatures of 910℃ of the steels and their

microstructures were evaluated. The austenitizing furnace design, Fig. 1, has a milled alumina-

silica brick, having maximum operating temperature of 1260℃ and thermal conductivity in the

range 0.1 to 0.2 𝑊 𝑚2 .K, back-up after the embedded heating element asbestos lining, glass

fibre insulation 0.03 to 0.06 𝑊 𝑚2 .K and an air-gap insulation so as to give an insulating effect

which necessitate a drastic thinning down of the silica brick thickness and glasswool fiber.

INTRODUCTION

Carbon is an interstitial impurity in iron and forms a solid solution with each of alpha α and δ

ferrites, and also with austenite γ. Plain carbon steels have been classified based on carbon

content of the steels. There are two sub-class namely:

1. According to the microstructure in annealed state:

Hypo-eutectoid steels: Microstructures of these steels contain varying proportions of

proeutectoid ferrite (or free ferrite) and pearlite. The amount of pearlite increases from

0% up to 100% as the carbon content of the steel increases to 0.77%

Eutectoid steel: This is steel with 0.77% carbon has 100% pearlite in microstructure.

Hyper-eutectoid steels: Microstructures of these steels contain proeutectoid cementite and

pearlite. The amount of free cementite increases up to a maximum of 22.7% as the carbon

of the steel is increased from 0.77% to 2.11%.

2. Though based on carbon content, but classified according to level of main mechanical

properties of practical importance.

Low carbon steels: have carbon up to 0.25%

Medium carbon steels: have carbon between 0.25% to 0.55%

High carbon steels; have carbon from 0.55% to a maximum of 2.11% but commonly up

to 15% maximum in commercial steels.

Austenitized steels have varying microstructure on cooling which influences, amongst all, their

mechanical properties such as improved strength, toughness, ductility and hardness. Thus, there

is great need for high performance austenitized steel. Austenitizing heat treatment is normally

carried out in an heat treatment furnace to temperature of 910℃. This paper analyzes the heat

flow patterns in the austenitizing heat treatment furnace with a view to achieving the desired

temperature at the core of the furnace.

The method used in this design and simulation problem is the Finite Element Analysis method.

The finite element method (FEM) is a numerical technique for solving problems which are

described by partial differential equations or can be formulated as functional minimization. A

domain of interest is represented as an assembly of finite elements.

FEA consists of a computer model of a material or design that is stressed and analyzed for

specific results. It is used in new product design, and existing product refinement. A company is

able to verify a proposed design will be able to perform to the client's specifications prior to

manufacturing or construction. Modifying an existing product or structure is utilized to qualify

the product or structure for a new service condition. In case of structural failure, FEA may be

used to help determine the design modifications to meet the new condition.

There are generally two types of analysis that are used in industry: 2-D modeling, and 3-D

modeling. While 2-D modeling conserves simplicity and allows the analysis to be run on a

relatively normal computer, it tends to yield less accurate results. 3-D modeling, however,

produces more accurate results while sacrificing the ability to run on all but the fastest computers

effectively.

METHODOLOGY

The austenitizing furnace design has a milled alumina-silica brick, having maximum operating

temperature of 1260℃ and thermal conductivity in the range 0.1 to 0.2 W m2 .K, back-up after

the embedded heating element asbestos lining, glass fibre insulation 0.03 to 0.06 W m2 .K and

an air-gap insulation so as to give an insulating effect which necessitate a drastic thinning down

of the silica brick thickness and glasswool fiber.

The different insulating materials with different thermal conductivity values (k-Values) where

selected in such a way as to keep the heating temperature at 1100℃ inside the furnace without

heat leakage out of the furnace.

In the finite element method (FEM) which is a numerical technique for solving problems of

partial differential equations can be formulated as functional minimization. A domain of interest

is represented as an assembly of finite elements. Approximating functions in finite elements are

determined in terms of nodal values of a physical field which is sought.

The objective of this work is to study, using finite element modeling, the heat flow patterns with

the aim of avoiding waste of construction material, selection of effective insulation and obtaining

an efficient heating system of the furnace to give the desired microstructure in the heat materials.

The heat equation is a parabolic partial differential equation PDE:

It describes the heat transfer process for plane and axisymmetric cases, and uses the following

parameters: Density ρ, Heat capacity C, Coefficient of heat conduction k, Heat source Q,

Convective heat transfer coefficient h, External temperature Text. The term h(Text – T) is a model

of transversal heat transfer from the surroundings, and it may be useful for modeling heat

transfer in thin cooling plates etc.

For the steady state case, the elliptic version of the heat equation,

2.1 Finite Element Modeling

The finite element modeling involves forming a variational formulation of the finite element

equations to give the governing equation The heat equation is a parabolic partial differential

equation (PDE) but the equation used was the elliptic heat transfer equation with no phase

change. Let us consider an isotropic body with temperature dependent heat transfer. A basic

equation of heat transfer has the following appearance:

Here qx, qy and qz are components of heat flow through the unit area; Q = Q(x, y, z, t) is the

inner heat generation rate per unit volume; ρ is material density; c is heat capacity; T is

temperature and t is time. According to the Fourier’s law the components of heat flow can be

expressed as follows:

where k is the thermal conductivity coefficient of the media. Substitution of Fourier’s relations

gives the following basic heat transfer equation:

The equation used was the elliptic heat transfer equation with no phase change and boundary

condition was incorporated.

-div(k * grad(T) = Q + h * (T ext – T)

where T is temperature; k= thermal conductivity; Q= heat source; h= convective heat coefficient

and Text= ambient temperature.

Boundary conditions: T=25℃ on the outside shell, T= 1100℃ on inside of furnace. The furnace

is shown in Figs.1-5 and meshed. Inserting the boundary conditions and the partial differential

equation in each element, the solutions were obtained as shown in Fig 5-9.

To summarize in general terms how the finite element method works, the main steps of the finite

element solution procedure are shown below;

Discretize the continuum. The first step is to divide a solution region into finite elements.

The finite element mesh is typically generated by a preprocessor program. The

description of mesh consists of several arrays main of which are nodal coordinates and

element connectivities.

Select interpolation functions. Interpolation functions are used to interpolate the field

variables over the element. Often, polynomials are selected as interpolation functions.

The degree of the polynomial depends on the number of nodes assigned to the element.

Find the element properties. The matrix equation for the finite element should be

established which relates the nodal values of the unknown function to other parameters.

For this task different approaches can be used; the most convenient are: the variational

approach and the Galerkin method.

Assemble the element equations. To find the global equation system for the whole

solution region we must assemble all the element equations. In other words we must

combine local element equations for all elements used for discretization. Element

connectivities are used for the assembly process. Before solution, boundary conditions

(which are not accounted in element equations) should be imposed.

Solve the global equation system. The finite element global equation system is typically

sparse, symmetric and positive definite. Direct and iterative methods can be used for

solution. The nodal values of the sought function are produced as a result of the solution.

Compute additional results. In many cases we need to calculate additional parameters.

For example, in mechanical problems strains and stresses are of interest in addition to

displacements, which are obtained after solution of the global equation system.

2.2 FINITE ELEMENT MODEL OF THE AUSTENITIZING FURNACE

Flow Chart Of The Finite Element Analysis Using PDETOOL

Fig. 1: Sectional View Of The Austenitizing Furnace With different k-Values

Fig. 2. Austenitizing furnace with boundary descriptions.

Fig. 3. Austenitizing furnace with label descriptions.

Fig. 4. Meshing of the Austenitizing Furnace within refractory lining for FE analysis.

Fig. 5. The Austenitizing Furnace in the PDE specification mode to define heat modelling.

3. RESULTS AND DISCUSSION

3.1 Results

The results of the modeling are found in Figs. 5-10 below, Figs. 5 and 6 show the temperature

profiles in the austenitizing furnace with the milled alumina-silica brick, asbestos lining and

glass fibre insulation. The figure shows the temperature in the austenitizing pot at 1100℃. This

temperature falls to about 500℃ from 700℃ in the refractory lining and from 500℃ to 300℃ in

the air-gap. The temperature in the asbestos lining fell from 300℃ to 100℃.

Fig. 7 shows the heat flux occurring in the austenitizing furnace with the milled alumina-silica

brick, asbestos lining and glass fibre insulation incorporated in the refractory lining. The heat

flux inside the furnace is about 110 W/m2. The heat flux was observed to be highest in the

refractory lining about 520W/m2 falling in the air-gap and further still in the asbestos and glass

wool.

The heat flux in the refractory outlining the airgap as well was observed to be 1000C as in the

asbestos and glass-wool. Figs. 8a and b show heat flux in the salt bath furnace with no air-gap

insulator. The heat flux in the refractory lining and asbestos was observed to be 3000C. In the

glass wool it was observed to be 2000C. Figs. 9a and b show the temperature gradients in the

furnace incorporated with air-gap insulator. They show a very high temperature gradient in the

air-gap insulation. Figs.10a and b shows temperature gradients in the furnace without air-gap

insulation to be highest in the glass wool insulation. .

Fig.5: The Austenitizing furnace showing the temperatures profiles from the pot to the shell. The

temperature at the shell falls to 25℃ and the inside temp.1100℃

Fig.6: A 3-Dimensional presentation of the Temperature profiles in the furnace.

Fig.7: The austenitizing Furnace with refractory lining showing Heat flux from the heating coils

through the refractory insulation to the shell. We could see that the majority of the heat is

retained in the refractory bricks. The heat flux inside the furnace is constant because it is not

expected to fluctuate after reaching the desired temperature.

Fe–Fe3C phase diagram,

Several of the various microstructures that may be produced in steel alloys and their relationships

to the iron–iron carbon phase diagram are now discussed, and it is shown that the microstructure

that develops depends on both the carbon content and the heat treatment.

List of codes

Appendix I. Nomenclature

A surface area [m2]

p Cˆ heat capacity per unit mass [J/kg/K]

k thermal conductivity [W/m/K]

Hˆ enthalpy per unit mass [J/kg]

L length of one-dimensional system [m]

m number of temporal intervals [dimensionless]

n number of spatial intervals [dimensionless]

q heat flux [W/m2]

t time [s]

T temperature [K]

Tref thermodynamic reference temperature [K]

x spatial coordinate [m]

y spatial coordinate [m]

z spatial coordinate [m]

thermal diffusivity [m2/s]

fluid density [kg/m3]