1966, No. 12 337

Continuous 'furnaces for rod materialU. H. Banga and W. Mesman

621.365.4

Furnaces in which products are subjected to heat treatment often have a temperaturegradient which makes it difficult to supervise and control the process. In this article theauthors show that continuousfurnaces can be designed in such a way that the temperature -'reached by the product is very closely defined. .

In many manufacturing processes a product has toto be subjected to one or more heat treatments. Thedegassing of thermionic valves, semiconductor diffu-sion processes and the soldering of components incircuits are examples from the electronics industry. Insome heat treatments the furnace is charged withbatches which go through a complete temperature cycle,each batch being heated to a certain temperature, per-haps kept there for a certain time, and then cooled.In another type of treatment the product is passed at acertain speed through a tubular or tunnel-shaped fur-nace which is kept at a constant temperature. Suchcontinuous furnaces mayalso be used for batch treat-ment of products. More often, however, products travelthrough the hot furnace in a constant stream. Duringtheir passage through the furnace they are heated to thetemperature at which they have to be processed whenthey emerge.

Temperature and power distributions

In many cases the temperature distribution in a con-tinuous furnace is such that the product reaches itshighest temperature somewhere inside the furnace.This applies particularly when the furnace consists ofa tube with a heater winding round it, whose turns havea constant pitch. The tube then has a temperaturedistribution along its length as illustrated by curve pin fig. la. When a product travels through such afurnace from left to right its temperature varies withposition as shown in curve q.In a case like the one illustrated here, it is difficult

to keep the heat treatment under exact control. Thisis because in the regulation of the temperature thereis an unavoidable delay between a change in furnacetemperafure and the corresponding change in thefinal temperature of the product. Moreover, it is diffi-cult to measure the temperature of the product in

Ir. U. H. Banga and W. Mesman are lVith Philips Research Lab-oratories, Eindhoven.

T

r

T

1

Fig. 1. Diagram showing the temperature distribution in a con-tinuous furnace (p) and in the material passed through the fur-nace, (q). Curves a are applicable if a heater winding of constantpitch is wound on the furnace tube, and curves b when the turnsare so arranged that the temperature inside the furnace is con-stant over the whole length.

motion. Another difficulty is that it is by no meansalways permissible to let the product reach a highertemperature in the furnace than the desired final tem-perature.The situation is much simpler if one ensures that the

furnace temperature remains constant over its wholelength. After entering the furnace the product then

338 PHILIPS TECHNICAL REVIEW VOLUME 27

increases steadily in temperature (fig. lb) and finally,jf the furnace is sufficiently long, it reaches the furnacetempérature. This can easily be measured and con-trolled: the furnace can be designed in such a way thatits temperature is virtually identical with that of theheater winding, so that it is sufficient to measure andregulate the temperature of the winding. Since thistemperature responds quickly to a change in themains voltage, for example, or in the ambient tempera-ture, the method gives a fast-acting control.

In the following we shall consider how a furnaceshould be designed in order to keep the temperaturethe same everywhere inside it, and how long the furnaceshould be in order to ensure that the product does infact reach the furnace temperature. We shall considerthe simplest form of furnace, namely a ceramic tubewith a heater winding wound round it, enclosed by acylindrical insulating sleeve (jig.2). We shall alsoconsider a simple shape for the product: this is takenas a cylindrical rod, and the rod is assumed to passthrough the furnace at a constant speed.

I H

t-----

Fig. 2. Continuous furnace for rod material. F furnace tube.H heater winding. I insulating sleeve. R rod passed through thefurnace at a speed v.

If the furnace temperature is to be the same over thewhole length, the heat generated, and hence also thepower supplied, should not be distributed uniformlyalong the length of the tube. The required distributtondepends on the dimensions of the furnace, on the re-quired temperature and also on the dimensions andmaterial properties of the rod and the speed at whichit is to travel through the furnace. The correct distribu-tion of the power can be obtained by making the pitchof the heater winding on the furnace tube depend onposition along the length of the furnace.

At the entrance, where the rod is still cold, morepower is needed for heating than further along in thefurnace. The proportion of the power per unit lengthwhich is effectively used, i.e. supplied to the rod, mayvary as a function of position as shown in fig. 3 by thecurve !JPu/!Jx; at places where the rod temperature isequal to the furnace température "effective" poweris no longer needed.

Heat losses

The heat lost through the insulating material is alsonot uniformly distributed over the length, even whenthe furnace temperature is the same everywhere insidethe tube. In this case the distribution is in fact uniformover the central part of the furnace, where the heatflow is almost radial, but there are extra heat lossesat the ends, and these losses increase with the diameter-to-length ratio of the furnace. The distribution of thepower loss per unit length may be as shown by curve!JPl/!JX in fig.3. The total power required per unitlength is given by

!JPt !JPu !JPl-=-+--.!Jx zlx L1x

If this quantity has been calculated as a function of xfor a given case, the power distribution correspondingto it can be realized by making the number ofturns perunit length proportional at each point to the value of!JPt/!Jx required at that point. If, for the case inquestion, a rod with the dimensions, material proper-ties and speed of travel which apply in the calculationis fed through the furnace then the ternperature of thefurnace will be the sarne over the whole length.

Although it is a simple matter to calculate the heatloss occurring at places where the heat flow can betaken as radial, this is not so simple for the extralosses at the ends. A good approximation can be ob-tained, however, by means of an electrical analoguein the form of a resistance network [11.

_X

Fig. 3. Power required per unit length of furnace as a functionof position x in the furnace. LlPu/L1x effective power. LlPl/Llxpower to make up for the heat loss. LlPt/L1x total power.

1966, No. 12 CONTINUOUS FURNACES 339

The magnitude of the heat loss is readily controlledwithin very wide limits by the choice of the insulatingsleeve. A thick sleeve gives a small heat loss; a disad-vantage of operating a furnace in this rather economi-cal way is, however, its high thermal capacity, whichcauses a considerable lag in response to temperaturecontrol. This means that when the conditions arechanged (e.g. the speed of travel or thickness of therod) fairly severe temporary variations in temperaturemay occur. To keep these within bounds, a relativelyhigh heat loss therefore has to be accepted.

Calculating the temperature distribution in the rod

In order to calculate the distribution of the effectivepower it is necessary to know the temperature distri-bution in the rod. We shall therefore calculate thisdistribution, working on the assumption that the out-side wall ofthe furnace tube has a uniform temperatureTs. In general, the thermal conductivity of the furnacetube is high enough to allow the inside wall tempera-ture also to be taken as equal to Ti. We further assumethat the heat transfer between the inside wallof thefurnace and the rod takes place solely by radiation.Two more approximations are introduced which relateto heat transport in the rod: we assume that the ther-mal conductivity of the material is high enough togive a uniform temperature over the cross-section;on the other hand we neglect the thermal conductivityin the axial direction compared with the heat transportdue to the movement of the rod.

The température T; of the rod material will now bea function of the location x in the furnace, the speed vof the rod, the diameters D, and D, of rod and furnace,and the properties of the relevant materials.

For the calculation of TT we consider a section offurnace and rod of length zlx (fig. 4). In a state oftemperature equilibrium the heat AH; radiated fromthe furnace wall to the rod will be eq ual to the heatLlH2 transported by the movement of the rod. Thesequantities are given by the following eq uations:

LlH1 = nDrcrr (Tr4-Tr4) zl x,

dT~LlH2 = -,tnDr2 s v - zl,x ,

dx

Here Crr is a coefficient determining the heat exchangeby radiation between the furnace wall and the rod:

where Cz is the Stefan-Boltzmann radiation constant,(cz = 4.96 X 10-8 kcaljm 2 deg- h), and Er and Er are theemissivities of furnace wall and rod respectively [2l.

IIIIII

I :

m~,: l :I ~M I

I II I

--Tc

0, {

~I I

~x

Fig. 4. Section of length Llx of rod and furnace. t'IHl heat flowfrom furnace wall to rod. LlH2 heat transport due to the move-ment of the rod.

Further, s is the specific heat capacity of the rod mater-ial (normally measured in kcal/rnêdeg).

Eq uating (1) and (2) and integrating with respectto x gives:

1=r.n:log + 2 are tan TrfTr = xjç, . (4)

1 - TrfTf

(I)

where the characteristic quantity ç, which has thedimension of length, contains all the geometric andmaterial parameters:

(4a)(2)

This relation between the dimensionless variablesTr/Tf and xjç, shown graphically in fig.5, may beused with any configuration to calculate the theoretical

(3) [1] See e.g. V. Paschkis and J. Persson, Industrial electric fur-naces and appliances, Jnterscience Publ., New York, 1960;G. Liebmann, Resistance-network analogues with unequalmeshes or subdivided meshes, Brit. J. appl. Phys. 5, 362-366,1954; M. J. Laubitz, Design of gradientless furnaces, Can.J. Phys. 37, 1114-1125, 1959.

[2] See H. Gröber, S. Erk and U. Grigull, Die Grundgesetzeder Wärrneübertragung, Springer, Berlin, 1963, page 368 etseq.

340 PHILlPS TECHNICAL REVIEW VOLUME27

1,-----~------_r----~~------.__.r,.1r,

ÎA I

t------ ----------- a1g------- ----:~~----~----a/g4-------~~~1

2 4

Fig. 5. Heating of rod material in a continuous furnace withuniform temperature Tr. The graph shows the ratio of the rodtemperature Te to Tr as a function of the dimensionless quantityx/I;, in which the characteristic quantity I; includes all the geo-metric and material parameters involved in the calculation.At the entrance (x = 0) the temperature of the material is 0 OK.It has virtually reached the furnace temperature after coveringa distance a. If the rod is introduced into the furnace at roomtemperature To the heating process begins at the point correspond-ing to To/Tr. For example, point A corresponds to To/Tf = 0.2.The material then reaches the temperature Tr after travelling adistance a'.

temperature gradient in a rod whose initial tempera-ture is 0 "K, which enters a furnace in which the temper-ature is uniformly Tr. It can be seen that the rod hasvirtually reached the furnace temperature after travel-ling a distance a corresponding to

a/ç = 7.

In normal conditions the rod will enter the furnaceat room temperature (300 OK), and the curve shouldthen be used from the corresponding point onwards.If, for example, the furnace temperature is 1500 "K,the heating of the rod begins at Tr/Tr = 0.20. Accord-ing to fig. 5 this corresponds to x/ç ~ 0.8 (point A).In this case the rod will therefore have virtuallyreached the furnace temperature after travelling a dis-tance a' corresponding to a' fÇ = 6.2.

Power requirements

The useful heat flow required per unit length inorder to raise the rod to the appropriate temperatureduring its passage through the furnace, LJHl/LJx, isfound directly from eq. (1) (or eq. (2)). We,now writethis equation in the form:

~~l = nDrcrrTr4 { 1 - (~r}. (6)

Converting the heat flow into electrical power (1 kcal/h= 1.16 W) we find from this the useful electric powerper unit length, for which we can write:

LJpu { (Tr)4}LJx = C 1- Tr '

with

With the aid of (7) and (4) -- or fig. 5 -- we can nowagain show the dimensionless quantity

LJPufLJx C

as a function of x/ç (fig. 6). From this graph the re-quired effective power per unit length can be derivedfor all configurations as a function of the length co-ordinate of the furnace.

-r !; = 1,16rrOrCfrr,"g= o: sv

16 Cfr r,3

~ t--!:-- 2 4 6_x/g 8

Fig. 6. Distribution of useful power per unit length, required togive the furnace a uniform temperature. The graph gives curvesof dimensionless quantities in which C and ,I; include all thegeometric and material parameters.

(5)The total effective power required could be calculated

by integrating the curve in fig. 6 from the point cor-responding to the temperature Tro at which the rodenters the furnace. It is easy to see, however, thatthis power (the heat transported per second by themoving rod) is given by:

1.16Pu = - nDr2 sv (Tr-Tro) watt. (8)

4

The total power required is found by adding the pow-er loss to P« As already mentioned, an electrical ana-logue can be used for accurately calculating the latterpower and its distribution over the length of thefurnace. The heater coil now has to be wound on thefurnace tube with a number of turns per unit lengthwhich is proportional to the total power required per

, unit length.

Furnace measurements

(7)

We have used the foregoing calculations i,n the designof a furnace for heating magnet steel in rod form(diameter Dr = 14 mm). The rod had to travel at aspeed v of 3.6 m/h through a furnace with an insidediameter Dr of 40 mm, and had to be heated from roomtemperature, 300 "K, to 1200 "K. Further data are

IS = 845 kcal/ma deg, sr = 0.3 and Sr = 0.38. Usingeq. (3) we calculate Crr = 1.45 kcal/me deg+h. Thecharacteristic quantity ç is thus 0.106 m. Theheating of the' rod begins at Tr/Tr = 0.25, which is(7a)

1966, No. 12 CONTINUOUS FURNACES 341

seen from fig.5 to correspond to xl; = 1. The rodwill therefore reach the furnace temperature aftertravelling a distance 6; = 0.64m.The furnace built was 1.40metres long. Fig. 7 shows

the calculated rod temperature as a function of dis-

n n~I/rxx x0

x

IV

1200T

t 800

400

20 40 60 80 100 120 140cm-x

Fig. 7. Axial temperature distribution for a rod of magnet steelwith a diameter of 14mm, travelling at a speed of 3.6 m/h througha furnace in which the temperature is everywhere 1200 "K, Thesolid curve indicates the calculated temperature; the crosses aretemperatures measured at the rod with a thermocouple. The circlesindicate the temperature of the heater winding. The trianglesindicate the temperature measured at two points on the insidewall of the furnace.

tance inside the furnace.The useful power can be calculated with the aid of

eq. (8), and is found to be 470W. The distribution ofthis power over the length should follow a curve asshown in fig. 6. The curve LJPu/LJx in fig. 8 gives thisdistribution on the appropriate scales.The insulating sleeve had an outside diameter of

11 cm. The heat conductivity coefficient of the insu-lating material depended on temperature to a fairlyconsiderable extent, being 0.035 kcal/m deg h at100°C and 0.257 kcal/mdeg h at 900°C. For thisreason, in the calculation of the heat losses the sleevewas divided into three shells, in each of which the

1500wim

I

Î'\

~x ~fl~\.r-.I---

20 40 60 80 100 120 140cm--..x

Fig. 8. Distributions of effective power P« and the power lossPI which are required to give the furnace discussed in this articlea uniform temperature.

temperature was assumed to be constant. This gave aheat loss of 840 W. The extra losses at the ends, whichwere determined with an electrical analogue, were35 W, so that the total heat loss was 875W. The distri-bution over the length of the furnace is shown by thecurve LJPI/LJx in fig. 8.

To find the distribution of the turns of the heaterwinding we must now determine the total power re-quirement per unit length from the sum of'the ordinatesof the two curves in fig. 8. This sum is plotted infig. 9.The extra losses at" the ends are assumed here to beconstant over a small distance in order to arrive at apracticable distribution of the turns.

In accordance with the distribution given by fig. 9, aheater winding of 136 turns was used, with a total

;500~p.<:IX

t1000

n

~\

~t X

-.i'----_ f

".

2000Wim

500

20 40 60 80 100 120 140cm_x

Fig. 9. Distribution of the total power required over the lengthof the continuous furnace described. If the heater windings aredistributed in such a way that the number of turns per unit lengthat each point is proportional to the corresponding power re-quired per unit length, the temperature inside the furnace iscompletely uniform.

resistance of 15 Q. The temperature distribution inthis furnace was measured by a thermocouple whichtravelled along with the rod. The crosses in fig. 7 in-dicate a number of measured points. The temperatureof the winding at various points was also measured(denoted by circles). The triangles give the temperatureat two places on. the inside wall of the furnace. (At theentrance to the furnace the inside wall will have a some- .what lower temperature than the outside wall, owingto the heavy flow of effectiveheat through the furnacewall which occurs here.)

Bearing in mind that various approximations andsimplications were made in the calculations, the agree-ment between measurement and calculation can beconsidered satisfactory.· The actual distance which

342 PHILlPS TECHNICAL REVIEW VOLUME27

the rod has to travel before reaching the final temper-ature is somewhat greater than calculated: this isprobably due to the difference in temperature betweenoutside and inside wall - we took this difference tobe zero - and to the fact that the emissivities er and er,which we assumed to be constant, in reality decreasewith rising temperature.In conclusion, it should again be pointed out that.a

furnace, calculated and constructed on the principledescribed here, shows the required temperature dis-tribution only when the rod passed through it has thedimensions, properties and rate of travel used in thecalculation. Any departure from these quantities mayresult in a different temperature distribution. Forexample, the effect of reducing the speed is to increasethe temperature at the entrance end of the furnace.Calculations of these effects are rather complicatedand can best be carried out by using a computer. By thesame means, various refinements can be introducedinto the calculation. It is possible, for example, to take

into account the temperature difference between theoutside and inside walls of the furnace tube, and alsothe conduction and convection part of the heat transferbetween furnace wall and rod. The heat transport due toconduction along the axis oftherod, which weassumedto be negligible compared with the heat transportdue to the forward movement, can then be taken into. account as well. In many cases, however, such an elab-orate treatment is not necessary and an approximatecalculation gives sufficiently accurate results.

Summary. In continuous furnaces with a heater winding ofconstant pitch the temperature distribution may make it diffi-cult to supervise and control the heat treatment of productspassing through the furnace. This is much easier if the furnacehas a uniform temperature over its whole length. This requires awinding of non-constant pitch. On the basis of a simple furnaceand a product of simple form - a rod - a calculation is made ofthe required input power distribution over the length of the fur-nace. This distribution depends on the diameter of the rod, theproperties of the material and the speed at which the rod travelsthrough the furnace. An experimentally determined temperaturedistribution showed good agreement with the calculated distri-bution.

A sensitive torque meter for high frequencies

An instrument for dynamic torque measurementshas recently been developed at Philips Research Labor-atories; unlike existing mechanical meters, this in-strument has a good high-frequency sensitivity. It con-sists basically of a shaft of magnetostrictive material(permaUoy), which is clamped at one end, the torque tobe measured being applied at the other end (fig. 1).The shaft is encircled by a coil through which an alter-nating current flows; this induces an alternating axialmagnetic field in the shaft, and as long as there is notorque exerted on the shaft; the magnetic inductionremains purely axial. When the shaft is twisted by theapplication of a torque, stress anisotropy occurs, andas a result of this the magnetic induction acquires atangential component (Bt). An alternating voltage cannow be measured between the two ends of the shaft,

621.317.799:531.232

~------{/l---------,E

Fig. 1. Principle of the torque meter. A shaft of magnetostrictivematerial. I current through coil. H alternating field. B magneticinduction, Box its axial component and Bt its tangentialcomponent. T torque. E output voltage.