附录
Heat Transfer During the Rolling Process
1 WORKPIECE TEMPERATURE CHANGE IN HOT STRIP MILL
After reheating a slab to a desired temperature, it is subjected to rolling. A rolling cycle in a typical hot strip mill includes the following main steps:
1、Descaling of the slab prior to flat rolling by using high-pressure water descaling system in combination, in some cas, with edging.
2、Rough rolling to a transfer bar thickness which may vary from 19 to 40 mm. The rough rolling is usually accompanied by edging and inter pass descaling.
3、Transfer of the transfer bar from roughing mill to a flying shear installed ahesd of finishing mill. The shear is usually designed to cut both head and tail ends of the bar.
4、Descaling of the transfer bar prior to entering the finishing mill.
5、Finish rolling to a desired thickness with a possible u of interstand descaling and strip cooling.
法拉第常数
6、Air and water cooling of the rolled product on run-out table.
7、Cliling of the rolled product.appear是什么意思
Various types of heat transfer from the rolled workpiece to its surrounding matter occur during the rolling cycle. Some of the lost heat is recovered by generating heat inside the workpiece during its deformation.
The main components of the workpiece temperature loss and gain in hot strip mill are usually identified as follows:南非总统祖玛
1、loss due to heat radiation,
2、loss due to heat convection,
3、loss due to water cooling,
4、loss due to heat conduction to the work rolls and table rolls,
5、gain due to mechanical work and friction.
The analytical aspects of the components are briefly described below.
2 TEMPERATURE LOSS DUE TO TADIATION
Two methods have been employed to derive equations for temperature loss due to radiation.
In the first method, the temperature gradient within the material is assumed to be negligible. The amount of heat radiated to the environment is then calculated using the Stefan-Boltzmann law:
d q
r =S dt
T
T
A
a
r
kewpie
)
(4
4-
ξ
Where
r
A—surface area of body subjected to radiation, m2;]
d q'
r
—amount of heat radiated by a body,J;
S—Stefan-Boltzmann constant;
familiar用法
T—temperature of rolled material at time,K;
Ta—ambient temperature,K;
t—time,s;
ξ—emissivity.
The amount of heat lost by a body d q''
r
is give by:
d q''
r =dT
cV
r ρ
Where c—specific heart of rolled material, J/（kg·K）;
Vr—volume of body subjected to radiation, m3
惊喜的英文单词
ρ—density of rolled material, kg/m3。
The rate of temperature loss ar can be calculated by considering the heat balance
condition d q
r =d q''
r
, and Eqs.1-1 and 1-2: ar=)
(4
4
a
r
r T
T
msftcV
A
S
dt
dT
-
=
ρ
ξ
Equations for the rate of temperature loss due to radiation which have been obtained by reducing some of the known equations to a compatible form with an assumption that Ta<T are summarized in Table 1-1. In the derivation of the equations, the dependency of the parameters S、ξ、ρand c on temperature is not taken into account. However, the variations
of the constants with temperature may be significant and,therefore, the final from of 1-3 will depend on the average values lected for the constants.
The temperature loss c T ∆ during radiation time tr can be calculate by intergrating the differential equation:
r T ∆=⎰tr
r dt a 0 The cond method of calculating temperature loss due to radiation takes into account the heat transfer along the thickness of the material. If z is the distance from the center of the body toward its surface, then from a Fourier equation we obtain:
22dz
T d a dt dT = Where a —thermal diffusivity of rolled material ,m2/s
The differential equation 1-5 can be solved numerically by the method of finite differences.
The goal of the calculations is to establish a relationship between the average temperature of the material Tave which would affect the rolling deformation process and the material surface temperature Tsurface which could be measured.
3 TEMPERTURE LOSS DUE TO CONVECTION
ohm
In the hot strip mill, heat transfer by convection is related to the motion of air surrounding a workpiece. This motion continuously brings new particles of air into contact with the workpiece. Depending upon whether this internal motion is forced, or free, the heat transfer is referred to as either forced or free convection. The latter is a usual ca in the hot strip mills.
A key factor in the calculation of temperature loss due to convection is to determine the heat transfer coefficient, which depends on the material temperature, ambient temperature, material specific heat and density, and the dynamic viscosity of the air flow and its characteristic, i.e., free, enforced laminar, turbulent, etc. The known mathematical interpretations of this relationship are too c
ontroversial to be recommended for practical calculation. A connsus among some rearch workers is that the temperature loss due to
convection cv T ∆ should be expresd as a certain percentage of the temperature loss due to radiation:
cv T ∆=cv k （r T ∆）
Here cv T ∆ is the ratio between the temperature loss due to convection and radiation and varies between 0.01 and 0.22 according to different studies.
4 TEMPERATURE LOSS DUE TO WTER COOLING
weariness
The temperature loss due to water cooling can be calculated by assuming that conduction plays a major role in heat transfer from a workpiece to water. Therefore, when water contacts one side of the workpiece continuously across its width, the amount of heat passing through the outer surface of the workpiece may be expresd by the formula:
a
t T T kb q w w w πω)(2'-= Where k —thermal conductivity of the surface layer, W/（m·K ）；
'w q —amount of heat passing through outer surface of the workpiece,J;
b —water contact length, m;
w —workpiece width, m;
Tw —water temperature, K;
tw —water contact time,s.
The amount of heat relead by a workpiece is given by:
)(''d w T cV q ∆=ρ
Where v —volume of workpiece cooled by the water,m3;
d T ∆—temperatur
e loss due to water cooling, K.
From the heat balance condition 'w q =''w q ,Eqs.1-7 and 1-8, and taking into account that tw=vbeagle
b where V —workpiece velocity, m/s
and
h
V bw 1≈ We obtain that the temperature loss due to water cooling is equal to
d T ∆=av
b T T ch k w πρ)(2- The amount of heat absorbed by cooling water may be expresd as:
''w q =)(w w w w T V c ∆ρ
Where w ρ——density of water ，kg/m3；
w c ——specific heat of water ，J/（kg·K ）；
Vw ——volume of water absorbing heat ，m3；
From hert balance ''w q =''w q , Eqs.1-8, 1-11, and 1-12, and also taking into account that
hv
d V V w = Wher
e d —water flow per unit o
f strip width, m3/（m·s ）.
We obtain the following formula for the temperature ri of water:
w T ∆=a
bv T T h c k w w w πρ)(2- Equation 1-11 does not show an explicit dependence of the temperature loss on the flow rate and pressure of cooling water. The flow rate and pressure, however, may substantially affect the thermal conductivity k of the surface layer that parates the body of workpiece from cooling water. Indeed, the surface layer consists of scale and boiled water, which work as a thermal barrier. This barrier will be weakened to a greater degree with increa of both the flow rate and pressure of cooling water.
5 TEMPERATURE LOSS DUE TO CONDUCTION TO WORK ROLLS
Temperature loss due to heat conduction to the work roll can be calculated if it is assumed that two bodies of uniform unitial temperature T and Tr are presd against each other and that, at the interface, considered to be plane, there is contact resistance formed by oxide layer.
