THERMAL RADIATION MODELLING OF DC SMELTING FURNACE FREEBOARDS

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1 THERMAL RADIATION MODELLING OF DC SMELTING FURNACE FREEBOARDS Q. Reynolds Mnte, Prvate Bag X3015, Randburg, 2125, South Afrca E-mal for correspondence: Abstract The problem of radaton heat transfer n a system of large numbers of surface elements was consdered. A numercal-mathematcal model detalng the radatve exchange between surfaces n a generalsed multple-surface shape model was constructed, developed, and tested to a satsfactory degree of complexty, at whch pont t was ncorporated nto a general-purpose computer program. Predctons by the model were compared to selected results from plot-scale DC arc furnace tests run at Mnte, to evaluate the sgnfcance of radaton heat transfer to the overall energy loss from the freeboard regons of such furnaces. Fnally, the model was used to examne a range of process and desgn varables, and scale-up ssues. Several nterestng aspects and phenomena come out of the exhaustve modellng wor, to hopefully ad the desgner of DC arc furnace freeboards n the future on both the plot and full ndustral scale. Keywords Modellng, Pyrometallurgy INTRODUCTION Exstng wor n the feld of heat transfer modellng of smeltng furnace behavour has been farly wdespread, treatng a great range of processes and furnace desgns. Much wor has been done n the feld of computatonal flud dynamc (CFD) modellng, wth partcular reference to dealng wth electromagnetcally drven hgh-temperature flows n the plasma arc regon of the furnace, and flow n the molten bath below t, as n Szeely et al (1983) and others. These models attempt to predct thermal and electrcal behavour of the electrc arc column and ts surroundngs by solvng the coupled partal dfferental equatons of heat and momentum transfer, and electromagnetcs numercally. However, the extent to whch radaton energy transfer s dealt wth s generally lmted to approxmate calculatons of drect radaton from the arc mpngng on the freeboard surfaces, as n Usho et al (1981), and whle t s often noted that the bath surface does transmt substantal amounts of thermal radaton to the other freeboard surfaces, ths factor s usually grossly neglected or over-smplfed. At best, the bath surface radaton s taen nto account by solvng for a small system of large, thermally unform surfaces as wth the approach taen by Holt & Baen (1993). Bowman (1994) documents expermental measurements of the behavour of such furnaces at full and substantal plot-plant scale, and Deneys & Robertson (1998) do the same n the laboratory, although agan radaton s neglected to some degree, wth only net energy loss numbers measured f at all. It s left to the researcher to nfer a mechanstc explanaton for the contrbuton of the varous components to the total energy losses. The development of a detaled model of the thermal radaton transfer from the molten bath surface to the upper sdewall and roof areas of the DC plasma-arc smeltng furnace s thus desrable. DEVELOPMENT OF THE MULTIPLE-REGION RADIATIVE EXCHANGE MODEL In the analytcal approach to surface radaton problems, one derves an energy balance on each of the surfaces partcpatng n the energy exchange n turn, thereby generatng a set of equatons (two for

2 each surface n the system for grey bodes) representng a total energy balance. These energy balance equatons are seen to contan terms pertanng to drect emsson of thermal radaton from the surface, ncdent radaton ether drectly from or reflected from other surfaces, and external sources or sns. Ths approach has been developed and presented by Hottel & Sarofm (1967) for all surfaces opaque and radatng as grey bodes, where a sngle value of the average hemsphercal surface emssvty, may be assgned to each surface s materal across the entre wavelength spectrum. Consder a partal enclosure of N dscrete surfaces, all of whch are absorbng, emttng, and reflectng radant energy between each other. Assumptons for the case of the grey body model are: - The surfaces are grey and opaque (an acceptable approxmaton n the case of the solds and lquds dealt wth n smeltng furnaces), that s, that a fracton of any radaton ncdent on the surface s absorbed and the rest (1-) reflected, wth α ndependent of the wavelength of the rradaton. - Reflecton from the surfaces s dffuse, meanng that a beam s drecton once t leaves the surface s ndependent of ts drecton of ncdence upon the surface. Ths s generally the case for unpolshed, rough surfaces. In the enclosure, an energy balance over a sngle surface s obtanable: Fgure 1 - Energy balance over sngle grey surface Incdent radaton flux H from other parts of the system mpnges on surface. A porton of ths flux s reflected (R ), and ths radatve component s complemented by drect emsson from the surface E. Together, these two components gve the total radatve flux emsson from the surface, W. The dfference between H and W gves the net energy nput or output to the surface by means other than radaton, q net,. The energy balance s expressed as follows: W E + R R (1 α) H (1 ) H W E + (1 ) H (1) and also: q net W H R W E W W ( E W ) (2) Now an expresson for the ncdent radaton flux H s requred. Consder that there are N surfaces n the system, each emttng a flux W wth 1...N. For a gven, a certan fracton of the flux emtted from surface s seen by surface. The fracton s termed the vew factor and represents the geometrc attenuaton of radatve exchange occurrng between a par of surfaces due to ther relatve orentaton and shape. The defnton of the vew factor s most often represented as a double ntegral over the two partcpatng surfaces: F 1 A A, A cosθ cosθ da da π r 2 (3)

3 Here, r s the dsplacement vector between ponts on surfaces and, and θ and θ are the angles that r maes wth the normal vectors on and. Gven ths defnton t s seen that: A H N 1 A F W (4) snce all radaton ncdent upon surface orgnates from other surfaces n the system. Whch by substtuton from above s seen to yeld: W E 1 H N 1 A A F W N 1 F W (5) The system of equatons to be solved thus becomes: W E 1 q net, 1 N 1 F ( W E ) W (6) Each surface n the system s seen to requre the soluton of two equatons for two unnowns, the net emsson flux W (va the frst equaton, the W-equaton ) and the surface temperature T (nfluences E and n some cases q net,, va the second equaton, the T-equaton ). The surface type s defned by how q net, nfluences proceedngs. A set of 3 surface types are commonly encountered n furnace analyss, and are: - Cooled/heated element. Here, q net, taes the form U (T -T 0 ) where T 0 s the temperature of the coolng or heatng medum and U s the total energy transfer coeffcent between the surface and the medum. - Specfed flux element. Here q net, s a fxed, pre-specfed number. Ths element s useful for adabatc surfaces (q net 0) or for specfyng a fxed net flux such as from an arc source. - Specfed temperature element. Here T s a fxed, pre-specfed number. Ths ntroduces some dfferences nto the model formulaton, snce the T-equaton s replaced by the much smpler specfcaton, T T,spec. The numercal method appled to the soluton of the T- and W-equatons s to smply sweep through each of the surfaces n turn, calculatng new W values (usng values of T and W from the prevous teraton) usng the W-equaton, and then do the same for the T values usng the T-equaton. Iteraton over the par of nternal loops then occurs untl the maxmum change n estmated values between one step and the next s less than a certan small number. Snce the W-equaton s lnear n W, ts approxmate soluton at each teraton step s found by smply solvng for W n terms of the other W. For the T-equaton, a new estmate of T s generated by applyng the Newton-Raphson numercal method on T (snce, n general, frst and fourth powers of T are present, mang analytcal soluton tedous), unless the surface type s constant temperature, n whch case the temperature specfcaton s smply appled. Snce the equatons nvolved are all lnear or polynomal n nature, convergence usng ths method s sutably rapd.

4 Vew Factors The general radatve model as formulated above maes no assumptons as to the shape of the surface elements used to construct the system. Any such elements can be used, provded the vew factors F can be calculated. Consderng a general 3-dmensonal surface n space, the best and smplest way to approxmate that surface wth a collecton of smpler surfaces s to use flat trangular polygons. Ths s the hgherdmensonal analogue to approxmatng a 2D curve wth a seres of straght-lne segments. Just as any curve, contnuous or not, can be approxmated to any level of detal by usng approprately szed lne segments, so any 3-dmensonal surface can be smlarly approxmated usng plane trangle segments. The use of a trangular surface element as the base prmtve for constructon of 3-dmensonal systems n whch radaton exchange s occurrng therefore allows for the greatest flexblty n terms of the geometry of sad systems. It also smplfes the calculaton procedure for the vew factors, snce only one general type of geometrc arrangement need be consdered. Dervaton of the general trangle-trangle vew factor s performed wth the ad of vector mathematcs and results n a sngle-ntegral expresson, whch s evaluated numercally for all surface pars n the model. Occluson by convex parts of the 3D model s also taen nto account by a shadowng algorthm. Attenuaton Model For Gas And Partcles In The Freeboard In the freeboard space between surfaces n the model, gases wll generally emt and absorb radaton, and cold feed dust and fume wll absorb and scatter radaton. The alteraton of ntensty of a beam of radaton passng through an absorbng and scatterng partculate medum s shown, agan n Hottel & Sarofm (1967), to be: I I 0 exp[( K a, p K s, p ) L] (7) An ntegral term (the source term due to scatterng nto the beam of radaton) has been neglected here for smplcty. The equaton above may be ncorporated nto the vew factor expresson for a gven par of trangles, mang the assumpton that the beam length L s a constant for the par of surfaces n queston: F exp[( K a, p K s, p ) L]. F (8) where the overbar ndcates that the contrbuton of scatterng and absorbng materal has been taen nto account. The overbarred vew factors are then used n place of the normal vew factors n the multple surface radaton model. Radaton from and to gases n the freeboard space s dealt wth va the calculaton or measurement of gas emssvty and absorbtvty for a partcular composton of gas at a partcular temperature and pressure. Dealng wth radatve exchange n the presence of gas volumes s n general a consderably more complex problem than nter-surface radaton (detal scales approxmately wth volume versus the current treatment, whch scales approxmately wth area). Certan smplfcatons can be made n cases where the entre volume may be treated as sothermal but the complexty s stll great. However, calculaton of gas radaton propertes usng the Wde-Band model of Edwards (1981) demonstrates that, for the CO-rch atmosphere typcally encountered n smeltng furnace freeboards, the contrbuton of the gas volume to the radatve energy exchange s neglgbly small (of the order of 5% or less). Scatterng and absorbton by suspended partcles may be charactersed by the sze range that the partcles fall nto. Large partcles, whose characterstc dmenson s very much larger than the wavelength of the ncdent radaton, exhbt scatterng accordng to geometrc reflectons of the

5 ncdent beam. Small partcles, wth characterstc dmenson much smaller than the ncdent radaton wavelength, exhbt electromagnetc scatter or refracton. Partcle effects can vary from neglgble to qute sgnfcant, so drect calculaton of the attenuaton factors produced by fume and dust loadng wthn the freeboard space s calculated n advance, usng theory developed n Hottel & Sarofm (1967). Data Vsualsaton Usng VRML Due to the dffculty nherent n descrbng modellng results n three dmensons as s the case here, a dsplay format was chosen to facltate quc and easy assmlaton of a large quantty of data both geometrc (the shape of the surface on whch the calculatons are beng performed) and quanttatve (data at varous ponts on the surface such as temperatures or energy fluxes). The Vrtual Realty Modellng Language (VRML) has exsted as a standard for the presentaton of 3- dmensonal, nteractve data snce the ncepton of the VRML 1.0 standard n VRML prescrbes a format for fles wrtten n ASCII text that may be nterpreted and dsplayed as a 3-dmensonal, nteractve world by a sutable pece of software (a VRML browser). Varous nodes smlar n functonalty to subroutnes and functons n conventonal programmng languages allow the specfcaton of dfferent 3-dmensonal shapes, or more abstract enttes and propertes such as colour, nterpolaton sequences or Internet hyperlns. An mportant geometry node s the IndexedFaceSet node, whch allows the specfcaton of an object constructed of or approxmated by arbtrary polygonal surfaces, wth the only prerequste beng that the component surfaces are flat. Each of the surfaces n the object may be assgned a unque colour and other propertes, mang ths node partcularly useful for the dsplay of complex 3-dmensonal data such as the results of the radatve exchange model. MODEL COMPARISON AGAINST EXISTING PILOT PLANT DATA After verfcaton of the numercal model aganst smple cases for whch analytcal solutons exst, the effectveness of the model n predctng the thermal behavour of DC smeltng furnace freeboard regons was evaluated. Several comparsons were performed between model predctons and actual plant data from recent large-scale plot plant projects at Mnte. The furnaces used at Mnte for the most part follow a generc axsymmetrc desgn, wth a cylndrcal shell topped wth a truncated concal roof and a flat plug at the centre. The sngle graphte electrode enters through the plug secton. Sgnfcant dfferences between desgns usually nvolve refractory choce and layout, and sde-wall coolng methods. Fgure 2 - Schematc of DC arc furnace freeboard as used n radatve exchange models

6 For the purposes of modellng the varous cases examned, several varables and condtons were specfed, along wth the geometry of the system. In a furnace freeboard such as s shown above, energy s added to the freeboard by the surface of the hot molten slag bath, and s removed from the sdewall, concal roof and plug va externally cooled refractory layers. The electrode s generally not cooled n any way wthn the freeboard space and therefore may be assumed to be adabatc, reradatng all of the energy mpngng on t. The net energy transfer models for the respectve areas of the furnace were specfed as follows: Slag bath Constant temperature elements Sdewall Specfed heat transfer coeffcent elements Concal roof Specfed heat transfer coeffcent elements Plug Specfed heat transfer coeffcent elements Electrode Adabatc elements In order to evaluate the heat transfer coeffcent for the elements requrng such numbers, a smplfcaton s ntroduced. Assumng that the refractory layers on the sdewalls, roof and plug are thn n comparson to other dmensons of the furnace, whch s generally the case, and mang the approxmaton that conducton through the refractory s essentally one-dmensonal from nsde to out: d d (9) 1 r, n s, n U n r, n s, n hc, n for each surface element n. Ths gves the overall heat transfer resstance between the hot-face surface of the refractores (whch s partcpatng n the radatve exchange model) and the coolng medum, generally ndustral water at 25 O C. d r and r, and d s and s are the thcnesses and thermal conductvtes of refractory lnng and outer steel shell respectvely, and h c s the heat transfer coeffcent between the shell and the coolant. Snce the coolng method used s nvarably forced convecton at hgh coolant flowrates, and the thcness of steel used n the outer shell s small, the frst term domnates the above equaton and allows t to be smplfed even further: U n d r, n r, n (10) Specfcaton of surface emssvtes for the varous surfaces n the freeboard regon s made possble wth the ad of the observaton that all surfaces acqure over the course of a project a layer of varable thcness consstng of splashed or condensed process materal. The only excepton to ths s the electrode, whch s n constant moton and wears bac from the arcng tp at an apprecable rate. Ths accreton layer s usually too thn to sgnfcantly affect the value of U n, but t does modfy the surface emssvty of surface element n to that of the process materal. Although lterature values for surface emssvtes of typcal process materals found n smeltng furnaces are hard to come by, results from the calbraton of pyrometer nstruments used on the plant floor at Mnte suggest that 0.7 s a very good estmate for hot or molten slag materal of wdely varyng types. Emssvty of the electrode s taen at 0.3, a lterature value for graphte. Data from fve plot projects were used n the comparson. Cases 1 and 2 concerned Cobalt removal from slags, Cases 3 and 5 were nvolved wth the producton of Ferroncel from laterte ores, and Case 4 dealt wth the producton of Znc from slags by fumng. Slag temperatures ranged from 1400 to 1700 O C, and refractory desgn vared maredly from case to case. Data was taen from a sutable seres of operaton perods representng a steady-state condton, for each case.

7 Table 1 Results of comparson of model wth expermental results Project Regon Predcted W/m 2 Measured W/m 2 PILOT CASE 1 Upper sdewall Flat Roof Concal Roof PILOT CASE 2 Upper sdewall Concal Roof PILOT CASE 3 Upper sdewall Concal Roof PILOT CASE 4 Upper sdewall Concal Roof PILOT CASE 5 Upper sdewall Concal Roof For the most part, the results agree farly well wth the model predctons, especally so gven the state of uncertanty nherent n measurements from an ndustral plot plant and the assumptons necessary for the formulaton of the model results. The correct qualtatve trends are also predcted by the model, gvng hgh energy fluxes n regons where hgh ones are measured, and low predctons n regons of low measured flux. Several dscrepances do appear n the results of ths comparson. It seems that the hgher the energy transfer through the furnace wall, the more the model over-predcts the energy flux occurrng n that regon. Ths s partcularly notceable n the refractory regons closest to the molten slag bath, whch suggests a possble explanaton for the dfference. Snce these regons are physcally closest to the molten slag (and any splashng that may result from moton of the plasma arc and sold feed materal), t s hghly probable that a frozen sull of slag and unreacted feed materal may freeze or accrete to ther surfaces, offerng a sgnfcant energy transfer resstance on that porton of the wall. Ths would cause lower energy flux measurements than would be expected from the refractory desgn of the sdewall alone. For most of the cases the dscrepancy n results between model and plot data may be explaned by the presence of a nomnal layer of frozen materal, 2 7 cm thc, n the lower sdewall regon of the furnace. Slag sulls have ndeed been observed on the sdewalls of furnaces at Mnte, and thcnesses n the range 2 5 cm are common. Qualtatve Evdence To Support The Bath Radaton Mechansm Interestng expermental evdence obtaned durng a recent plot campagn at Mnte further corroborates the clam that radaton from the hot bath surface, rather than the contrbuton from the actual plasma arc column tself, s the most sgnfcant factor n freeboard energy losses from furnaces of ths scale. In ths project, a water-cooled copper bloc (a copper fnger cooler ) approxmately 20cm x 20cm x 50cm n dmensons was bult nto the upper sdewall brcwor, just below the juncton of the concal roof and the cylndrcal crucble. The bloc was bult nto the wall such that ts front 20cm x 20cm face was very close to, f not drectly exposed to, the freeboard volume, to act as an energy flux sensor. Snce copper conducts thermal energy far better and faster than the refractores, an examnaton of the transents that occur n the measurement of energy losses from ths bloc when for some reason the power n the furnace s shut down for a sgnfcant perod of tme can gve nsght as to the mechansm of radaton energy loss occurrng. If the freeboard losses are as a result of drect radaton from the plasma arc, one would expect the copper fnger losses to drop off very rapdly, snce the net energy flux mpngng on the face of the cooler wll have made an abrupt step change down to zero. If, on the other hand, the losses are due to radaton from the molten bath, one would expect the copper fnger losses to drop off far more slowly, snce the energy source drvng the freeboard energy losses n ths case s stll present, even though the actual furnace power s off.

8 Furnace Power, W Cu Fnger Cooler Energy Losses, W Furnace Power Copper Fnger Losses Tme, s Fgure 3 - Copper fnger cooler transent n response to power outage 0 As can be seen clearly n fgure 3, at ths pont n the project, after havng run stable for several hours, the furnace power s shut down for around twenty-fve mnutes (at 600s on the graph). The transent trend of the copper cooler energy loss exhbts no sudden drop at all over ths entre perod, contnung n fact to rse, presumably as the dust and fume clear out of the freeboard space n the absence of feed and arc, and enable the cooler face to more clearly see the bath surface. It would therefore appear that freeboard energy losses, at least on typcal plot-scale furnaces, are domnated by radaton from the hot, molten bath surface. EFFECT OF VARIABLES ON THE MODEL The fully developed surface re-radaton model was used n a detaled examnaton of the effects of DC-arc furnace desgn and process varables on the thermal behavour. The approach conssted of comparng the behavour to a common base case whle varyng each examned varable n solaton. Ths base case furnace desgn follows closely the desgn of the large-scale 5.6MVA plot plant furnaces used at Mnte, wth a furnace vessel approxmately 2m n dameter and 2.5m hgh. Some examples, and dscusson, follows. Effect of scale The effect of scalng up the dmensons of the furnace freeboard geometry (note that refractory desgn remans the same as the freeboard s scaled up) s neglgbly small ndeed. An order-of-magntude varaton n furnace sze, from 1m dameter to 12m, produces dfferences n surface temperatures and energy fluxes n all regons that are small enough to be attrbuted to numercal naccuraces. Ths effect s llustrated n fgure 4.

9 Effect of Scalng on regon energy fluxes Energy flux, W/m Sdewall Concal Roof Flat Roof Scale factor Fgure 4 Graph showng effect of changng the furnace scale Effect of attenuaton factor The effect of attenuaton of radatve energy n the freeboard space by an nterposng medum can be pronounced. Wth the caveat that ths s a very smplstc model n terms of ts ablty to deal wth absorpton, emsson and scatterng by dust and fume n the gas space, several nterestng effects appear as the attenuaton factor ncreases from zero n both the ndustral and plot-scale results. The bul effect of an ncrease n attenuaton factor s to lower the energy flux receved by all freeboard surfaces, as the attenuatng medum ntercepts more and more of the thermal radaton n the freeboard space. A more subtle effect s an ncrease n the spread of surface temperatures nsde the furnace gas space, wth the ranges growng to span an order of magntude or more n some cases. The most notceable area exhbtng ths behavour s the upper sdewall. The presence of an attenuatng medum s thus a double-edged sword to some degree, offerng decreased net energy losses from the furnace freeboard whle ncreasng the chance of fracture and spallng due to very large thermal gradents n contguous refractory zones. Attenuaton n the freeboard space can also produce a scale-dependent effect that may cloud the ssue of accurate scale-up calculatons. It s seen from fgure 5 that whle the re-radant energy losses from the plot-scale case (a 2m dameter furnace) are stll very sgnfcant at a factor of , a smlar factor n the larger ndustral-scale case (a 12m dameter furnace) would lead to almost complete attenuaton of all re-radant energy, and very good sheldng of the freeboard surfaces by the attenuatng medum. A drect measurement (by samplng or otherwse) of the dust and fume loadng nsde the freeboard space on the plot scale s thus consdered to be of consderable value when the tme comes to scale to an ndustral desgn.

10 Sdewall energy flux - % of value at Attenuaton factor0 % Industral (12m) Plot (2m) Attenuaton factor, m -1 Fgure 5 - Graph showng effect of furnace sze on the attenuaton of radaton Effect of changng U-values Alterng the heat transfer coeffcent value on any of the cooled surfaces n the freeboard model produces a pronounced effect on both the temperature and energy flux dstrbuton wthn the furnace. The surface whose U-value s changed experences the most dramatc change, generally decreasng n temperature and ncreasng n energy flux as U s ncreased. The effect on the remanng surfaces n the model s generally to decrease margnally n both energy flux and temperature. Usng a more conductve wall desgn on the upper sdewall or roof regons would allow all regons n the furnace freeboard to operate cooler, at the expense of greater total energy losses and hgher sustaned energy fluxes. Effect of furnace dameter Reducng the furnace dameter, wth all other dmensons fxed, results n a drop n both surface temperatures and energy fluxes n all regons, wth the decrease acceleratng as the dameter decreases. The results would seem to suggest that ths effect becomes very sgnfcant at dameters smaller than 1.5m for ths partcular case. Effect of sdewall heght Increasng the heght of the furnace sdewall secton exposed to the freeboard space s seen to decrease the temperatures and energy fluxes n all regons. The effect s small, however, wth net energy fluxes through the freeboard regons decreasng only 5 10% at most. Snce the net surface area ncreases lnearly wth ncreasng sdewall heght, the net energy loss wll also ncrease. Effect of roof angle The roof angle (vared by varyng the heght of the roof plug above the surface of the slag bath, and measured from the horzontal) produces several nterestng effects. The gross effect s a decrease n surface temperatures and energy fluxes n all regons as the roof angle ncreases, although ths may also be attrbuted to the ncrease n total roof surface area ncurred by the method of alterng the angle. A secondary effect concerns the spread of temperatures on the upper sdewall and roof. As the angle ncreases from zero, the spread of temperatures n both these regons appears to go through a mnmum around 40 o, wth the maxmum and mnmum temperatures gettng farly close to the average. Identfyng ths mnmum would prove useful n terms of mnmsng the temperature varance across a contguous regon of refractory (such as the roof or sdewall sectons) n order to mnmse the thermal stresses n these areas.

11 Effect of emssvty The grey-body surface emssvty of the refractory regons of the furnace has a large mpact on the thermal behavour of the furnace freeboard. As the emssvty drops, the surface temperatures and net energy fluxes n all regons drop wth t, acceleratng as the emssvty approaches zero. The emssvty of the varous surfaces wthn the furnace freeboard space s dffcult to enforce as a desgn varable. It wll rather tend to be a functon of the type of refractory used to lne that porton of the vessel (whch s most lely to be chosen for propertes other than ts emssvty), as well as a functon of the process tself. After prolonged operaton one mght reasonably expect to see much of the furnace nteror coated wth at least a thn layer of process materal, potentally alterng ts emssvty consderably. Effect of slag surface temperature Unsurprsngly, the temperature of the surface of the slag bath n the furnace has an enormous mpact on the thermal behavour, snce ths surface s ultmately the source of all energy n the freeboard reradaton model. As the slag temperature ncreases, the surface temperatures and the energy fluxes n all regons follow t almost lnearly. CONCLUSIONS The development and use of a general model of thermal radaton nterchange from surfaces has been successful to some degree n explanng the energy dstrbuton and thermal behavour of the freeboard regon n the DC plasma arc furnace. Comparson to data from the 1-2MW scale ndcates that radaton from the hot, open bath s the prncpal source of energy loss from ths regon, not the plasma arc column. Changng varous desgn and process varables n the model was seen to produce nterestng and occasonally unexpected results n the thermal behavour of the freeboard space. REFERENCES Bowman, B., 1990, Effects on furnace arcs of submergng by slag, Ironmang and Steelmang, No. 2. Bowman, B., 1994, Propertes of arcs n DC furnaces, In: Electrc Furnace Conference Proceedngs. Brent, A., 1989, A computatonal analyss of heat transfer and flud flow n plasma meltng furnaces, PhD Thess, Unversty of Mnnesota. Deneys, A.C. & Robertson, D.G.C., 1998, Flud Flow Phenomena n a Laboratory Scale DC Arc Furnace for Slag Cleanng, Iron and Steel Socety Techncal Paper. Edwards, D.K., 1981, Radaton Heat Transfer Notes, Hemsphere. Gu, L., Jensen, R., & Baen, J.A., 1993, Metal vapour nfltraton n argon arcs used for heatng lqud metal, In: Electrc Furnace Conference Proceedngs. Holt, N.J. & Baen, J.A., 1993, Transferred Argon Arc Reactor Wth Emphass On Radaton Heat transfer, In: Electrc Furnace Conference Proceedngs. Hottel, H.C. & Sarofm, A.F., 1967, Radatve Transfer, McGraw-Hll. Sawc, A. & Krouchnn, A.M., 1998, Modellng of the cylndrcal part of the effectve arc n steelmang AC arc furnaces, Eletrowarme Internatonal, December. Shams, M.R.R.I., 1994, Turbulent flud flow modelng to predct the heat transfer n the plasma furnace, PhD thess, Indan Insttute of Technology. Szeely, J., McKellget, J. & Choudhary, M., 1983, Heat-transfer flud flow and bath crculaton n electrc-arc furnaces and dc plasma furnaces, Ironmang and Steelmang, No. 4. Usho, M., Szeely, J., & Chang, C.W., 1981, Mathematcal modellng of flow feld and heat transfer n hgh-current arc dscharge, Ironmang and Steelmang, No. 6.

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