The harsh environment of

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1 Vol., No. 5 AIST Transations Calibration of Thermal Models of Steel Continuous Casting Molds The harsh environment of ommerial steel ontinuous asting proesses makes taking measurements diffiult, expensive and limited with regard to the information gained. Computational models potentially offer deeper knowledge, but only if they an aurately predit the plant behavior. This reuires inluding and solving the euations whih govern all of the important physial phenomena. To ahieve reasonable speed while retaining auray, omputational models must be simplified and alibrated to math plant experiments, using parameters whih remain onstant over the range of proessing onditions of interest. Only after verifiation, alibration and validation an a model be used reliably as a preditive tool to investigative omplex proesses suh as ontinuous asting. Development of an aurate omputational model reuires verifiation, alibration and validation. Verifiation refers to mathing the model preditions exatly with the known analytial solution of a simple, well-defined test problem, in order to prove error-free programming of the hosen numerial methods, and to find reasonable hoies for mesh and time-step disretizations. Validation refers to mathing the model preditions with plant experiments to ensure that the euations being solved ontain the appropriate physis, and that the properties and onstants in those euations have good values. Calibration is usually needed to find values for those onstants to math the plant measurements and ahieve validation. These last two ativities generally reuire multiple iterations. This paper illustrates this ativity for the omputational model of heat transfer in ontinuous asting of steel, COND. The COND model has been suessfully applied to many ommerial asters in previous work, 6 and is desribed in detail else. This paper fouses on the alibration proedure to improve its auray. The proedure first involves a full 3D omputation of the mold to produe average results for a alibration domain. Input parameters to the COND model are defined and alibrated to math the average hot fae and thermoouple temperatures from the 3D model. Then, COND an be alibrated to math thermoouple measurements and heat flux measurements taken from plant operation. Finally, the model an be applied to gain new insights into the proess. A new methodology is presented to alibrate the D COND model with a full 3D finiteelement model of the mold. The thermoouple depth in the D model COND is offset to aount for both the 3D geometri effets and for the heat removed along the thermoouple wire by or air onvetion. With the offset, this simple D model an math losely with the 3D model. Coupled with models of solidifiation and interfaial phenomena, this modeling tool is applied to gain insights into many aspets of heat transfer in the proess. Authors Lane C. Hibbeler (left) (lhibbel@illinois.edu), Melody M. Langenekert, Junya Iwasaki, Inwho Hwang (hwang4@illinois.edu), and Brian G. Thomas (enter), professor, Department of Mehanial Siene and Engineering (bgthomas@ illinois.edu), University of Illinois at Urbana- Champaign, Department of Mehanial Siene and Engineering, Urbana, Ill., USA; and Ron J. O Malley (right), plant metallurgist (ron.omalley@ nuor.om), Nuor Steel Deatur LLC, Trinity, Ala., USA AIST.org September 3 Iron and Steel Tehnology-AIST Transations, September, 3 :9 99

2 3D Model of Mold: Calibration Domain The steady-state temperature distribution in the ontinuous asting mold is determined by solving the steady heat-ondution euation for temperature as a funtion of the three oordinate diretions, T(x,y,z): x k T x y k T k T + y + z z = k is the isotropi thermal ondutivity. (E. ) The temperature dependene of the thermal ondutivity of mold opper alloys of about.5%/ C has only a small effet on the typial mold temperature field. 7 This effet is readily inluded, but the governing euation for the alibration proedure is simplified here for onstant ondutivity: T x T T + + = y z (E. ) Boundary onditions inlude speified heat flux at the mold hot fae: T k = n k is the average thermal ondutivity, is the heat load that may vary with position and T/ n is the temperature gradient normal to the mold surfae. (E. 3) On the hannels, a onstant onvetion ondition is speified: T k = h T T n ( ) (E. 4) by defining the heat transfer oeffiient and sink temperature, T. The finite element method is used to solve these euations in the ompliated-shaped domain of the modern asting mold, owing to its aurate handling of arbitrary geometries. This work uses the ommerial finite-element software ABAQUS, 9 ombined with sripts written in Python ode to automate reation of the geometry, running of the analysis and post-proessing the results to extrat the parameters needed for the D COND model, as disussed later. The aim of this model is to enable the simple D model of the mold, COND, to ahieve the auray of a omplete 3D analysis of the multidimensional heat flow around the roots of hannels and thermoouple holes. The 3D model domain should reprodue the exat geometry of an appropriate periodi or symmetri portion of the mold geometry. The 3D model results an be used diretly to reveal loal heat transfer variations within this fundamental domain, suh as hot fae temperature variations around the mold perimeter between bolts. For the alibration of the D model, the 3D model results are spatially averaged over this symmetrially repeating domain, to extrat the average hot fae temperature T hot,3d, the average old fae temperature T old,3d, and the average temperature on the small surfae that ontats the thermoouple T TC,3D. These three temperatures are needed for the D model alibration. In addition, the 3D model results reveal insights into important mold temperature variations. Modern omputer platforms an solve this problem, even with very fine mesh resolution, with exeution times on the order of a few minutes. D Model of Mold Modeling heat transfer in ontinuous asting reuires aurate inorporation of the mold, interfae and solidifying shell. Away from the orners, many phenomena an be modeled reasonably well with a D assumption. The COND model is based on a D finite-differene solidifiation model of the shell, taking advantage of the large Pélet number that makes axial heat ondution negligible relative to heat transported by the moving steel. It inludes ondution and radiation aross the interfaial layers, aided by mass, momentum and fore balanes on the slag, whih are all solved analytially. For effiieny, heat ondution through the mold is modeled analytially. Axial heat ondution in the mold, whih is important near the menisus, is handled with a two-dimensional series solution.,,4 Through the thikness diretion, the oated opper plate is treated as a series of D thermal resistanes. The slot region is treated as a onvetion surfae in parallel with heat-ondution fins. Further details are given as follows. The mold in the COND model is envisioned as a retangular blok with retangular hannels, as shown in Figure. All hannels are idential Iron & Steel Tehnology A Publiation of the Assoiation for Iron & Steel Tehnology

3 Figure with depth, d ; width, w ; and pith, p. The hot side of the mold is supplied a heat flux, hot, from the interfae and solidifiation models, desribed else. Heat is extrated from the hannel surfaes via a onvetion ondition, h old (T old T ). The temperature distribution inside the mold is found by integrating diretly Euation and applying these two boundary onditions: T T hot T old T x d T ( x)= T + hot + h k old mold mold x w (E. 5) x is the distane away from the hot fae and d mold is the simulated mold thikness. Copper Mold p Coating layers are inluded by adding d oating /k oating resistors inside the parentheses. This gives a old fae temperature of T old = T(d mold ) = T + hot /h old and a hot fae temperature of T hot = T() = T + hot (/h old + d mold /h old ). The old side heat transfer oeffiient is adjusted to inlude sale deposits as another thermal resistane: dsale = + h k h old sale w (E. 6) D mold model. d mold Water Channel d d sale and k sale are the thikness and thermal ondutivity of any sale layers on the hannel sides and h w is the fin-enhaned heat transfer oeffiient of the nominal onvetion oeffiient h : a Nu = 5+. 5Re Pr b (E. 8) h w w = h + ( p w) hkmold tanh d p p h ( p w ) k mold (E. 7) The first term on the right-hand side aounts for the heat leaving the roots of the hannels, while the seond term aounts for the heat transferred through the lateral surfaes of the fins. This euation assumes a large number of retangular hannels that are very long in the asting diretion, and that heat loss into the baking plate or box is negligible. Of many empirial orrelations for the onvetion oeffiient, the fored-internal-flow orrelation of Sleiher and Rouse is hosen for its aurate fit with many measurements (about 7% average error): The Nusselt number, Nu = h D h /k ; Prandtl number, Pr = m p, /k ; and Reynolds number, Re = V D h /m are evaluated, respetively, at the temperature of the bulk, T ; the temperature of the hannel surfae, T old ; and the film temperature, Tfilm = ( T + Told ). The hydrauli diameter, defined as four times the ross-setional area divided by the perimeter, is D h = w d /(w + d ) for a retangular hannel, and a =.88.4/(4 + Pr) and b = /3 +.5exp(.6 Pr) are fitting onstants. The veloity, V, is found from the total flowrate in the plant and the total hannel area. The properties 4 vary with temperature ( C) as follows: k ( T)= T (E. 9) AIST.org September 3 3

4 m ( T )=. 6 r ( T ) r ( T)= T T p, ( T)= T T (E. ) (E. ) (E. ) Measurements available at most asters inlude thermoouple temperatures and the average heat flux, based on the mold flowrate and its temperature inrease. In the D COND model approximation, thermoouple temperatures, T TC, are obtained by evaluating Euation 5 at the appropriate distane beneath the hot fae, d TC : d TTC = T + hot + h old d k mold mold TC (E. 3) The inrease in temperature of the mold as it flows through the hannels is found by applying a heat balane on a differential slie through the and integrating over the working mold length: DT p ()= z wd V z hot ( z ) ( z ) ( z ) r p, z is the distane below the menisus. dz (E. 4) This assumes that all heat entering the mold is removed by the mold. This predition of mold temperature rise must be modified to aount for unused hannels when asting narrow slabs relative to the mold width and, if appliable, the fat that the hannels might not all have the same dimensions and pith: DT = DT w p slab wd A hannels (E. 5) w slab is the slab width and A hannels is the total ross-setional area of the hannels. After geometri alibration desribed in the next setion, a seond alibration/verifiation stage should be performed to ensure that this predition of the temperature rise mathes with the plant measurements. D Model Calibration Simplifying the mold geometry for the D model reuires areful definition of the dimensions in order to retain the thermal harateristis of the system. The geometri parameters in the D model desribed above are the simulated mold thikness, d mold ; the hannel width, w ; the hannel depth, d ; and the hannel pith, p. By hoosing these parameters arefully, the D model an attain the preditive apability of the 3D finite-element alulation mentioned previously. This setion presents the euations to aomplish this, whih have been implemented into the Python sript and are exeuted after post-proessing of the finite-element results, prior to running COND. Water Channel Geometry The hannels in the D model must have idential ross-setional area to the physial mold to maintain the mass flowrate of the ooling. To maintain the onvetion oeffiient in the hannels, the hydrauli diameter must be the same as well. For a single hannel, this reuires: wd A = atual, wd w + d D ( ) =, hatual (E. 6a) (E. 6b) A,atual and D h,atual are the ross-setional area and hydrauli diameter of the atual hannel. 4 Iron & Steel Tehnology A Publiation of the Assoiation for Iron & Steel Tehnology

5 These two euations are solved simultaneously to give: w d = A D ± ( A D ) A, atual, h, atual atual, h, atual atual, (E. 7) A Figure Physial Mold the smaller of the two roots is the hannel width and the larger root is the hannel depth. Note that both roots are positive beause A,atual and D h,atual are positive. If the mold has different types of hannels, whih is ommon around bolt holes, then the atual hannel area and hydrauli diameter should be their respetive averages for all N hannels aross the width of the repeating portion of the mold, modeled in the 3D alulation: N A, atual = A, atual, i N D = N i = D h, atual h, atual, i i = N (E. 8a) One-Dimensional Approximation Bolt y (E. 8b) Note that Euation 7 is not appliable if all hannels are round. An approximation that relaxes Euation 6b is used for this ase. 6 Speifially, setting w =.7 D produes an error in the onvetion oeffiient of only %. The simulated hannel pith should be hosen to minimize the variations aused by different hannel sizes. Consider the umulative hannel ross-setional area plotted with distane along a symmetri portion of the mold width, shematially illustrated in Figure. The D model approximates this umulative area as a straight line with a slope that defines the simulated hannel pith, p : A umulative, simulated A, ( x)= p atual x (E. 9) The details of the atual umulative area funtion are speifi to an individual mold, but a simple leastsuares fit is suffiient to determine a good simulated pith. Next, the simulated mold thikness, d mold, should be hosen suh that the hot fae temperature mathes the 3D simulation under idential boundary onditions. Evaluating Euation 5 at the hot fae, mathing the result to the average hot fae temperature alulated with the 3D model, and rearranging, gives: Simulated hannel pith should math umulative hannel area. d k k = ( T, 3 T ) h mold hot D w old (E. ) Sine h old >> k mold, the seond term of Euation usually is negligible. To math the 3D alulation, the temperature dependeny of the properties and the sale layer are negleted during alibration, so Euations 6 and 7 simplify to: h h w h old = + ( p w) hk tanh d p p ( p w) k (E. ) Note that for some geometries, this alibration method auses the parameter d mold to be signifiantly larger than the distane between the hot fae and hannel roots, d old. The distane from the hot fae to the old fae temperature is found in the D model is defined as: d k k = d ( T 3 T )= T T ( ) mold mold old, D w hot, 3D old, 3D (E. ) AIST.org September 3 5 3

6 Depending on the hoie of T old,3d, the old fae temperature predited by COND an be hosen to math the root, average or other desired definition of old fae temperature. Defining the old fae temperature as the average root temperature over all hannels gives d' old lose to the physial distane between the hot fae and hannels. This alibration method enables the D model to math the hot fae and old fae temperatures alulated in the 3D model by hanging the hannel input geometry in a physially based manner. Thermoouple Hole Geometry The thermoouple temperature predited by the COND model may differ from the temperature predited by the 3D finiteelement model at the same loation. 6, Depending on the geometry, this error has been observed to exeed 5 C. This mismath is due to the inability of the D model to apture the effets of ompliated geometry near the thermoouple bore. However, this problem an be overome by hanging the loation of the simulated thermoouple. By moving the thermoouple point in the D model loser to the hot fae, the D model an reliably reprodue the hotter thermoouple temperature predited by the 3D model, regardless of heat flux, mold material and hannel behavior. By manipulating Euation 3, the simulated thermoouple depth in the alibrated D model should be: k k d TC = dmold ( TTC, 3D Tw)= ( Thot, 3D TTC, 3D ) (E. 3) This alibration of the thermoouple loation should be performed after the hannel geometry has been alibrated using Euations 7, 9 and. Even though the terms appear in Euation 3, d' TC is independent of heat flux, ondutivity and mold geometry. This observation is demonstrated later. Offset Methodology In the interest of a userfriendly model interfae, it is onvenient to express eah alibrated dimension as the blueprint value and an offset distane. This approah also illustrates the importane of the alibrations. For example, the mold thikness offset distane, d old, is defined as: Ddold = dold dold (E. 4) DdTC = dtc dtc (E. 5) Beause alibration is independent of heat load and mold properties, the offset alulation needs to be performed only one for a given mold geometry. Thermoouple Wire Heat Removal Measured thermoouple temperatures often read low due to ontat resistane between the thermoouple bead and the old fae the thermoouple is touhing. Heat is lost by ondution along the length of the thermoouple wires, espeially if they are long and well ooled. Assuming that the thermoouples behave as long, irular rod-fins, they extrat heat with a rate of: 4 = D hk T T TC TC TC ( ) (E. 6) D is the thermoouple diameter, k TC is the ondutivity of the thermoouple, h is the heat transfer oeffiient along the thermoouple wire to the surrounding medium at temperature T, and T TC is the thermoouple temperature. The heat transfer oeffiient should be around 5 kw/m² K for or. kw/m² K for air. The thermoouple temperature, T' TC, aounting for this heat loss, an be modeled using another heatondution resistor: d TTC = TTC + k gap gap TC (E. 7) T TC is the predited thermoouple temperature whih, for the D model, is from Euation 3, using the alibrated thermoouple depth, d' TC, from Euation and d gap and k gap are the size and thermal ondutivity of the gap between the thermoouple and the mold opper. and the thermoouple offset distane, d TC, is: 6 Iron & Steel Tehnology A Publiation of the Assoiation for Iron & Steel Tehnology 4

7 The gap ondutivity should be about.5 W/m K for a thermal paste, or about.4 W/m K for dry, still air. The gap size is typially on the order of.. mm, but an be treated as a alibration parameter to fore the models to math plant measurements. This approah of alibrating thermoouple temperatures has been demonstrated in reent works presented else.,3 Example Calibrations The alibration proedure presented in this work is demonstrated for two ommerial asting molds with ompliated mold geometries. Both are unoated thin-slab mold wide faes, one with and one without a funnel. Four ases, summarized in Table, are onsidered to prove the method for different geometries and proessing onditions. Mold A is,986 mm wide, 95 mm long and 4 mm thik. It has a retangular array of mold bolts at 8 mm in the width diretion and 33 mm in the asting diretion, exept for the top and bottom row of bolts. There are three rows of thermoouples at 5 mm, 355 mm and 55 mm below the top of the mold, spaed at 8 mm in the width diretion, diretly between bolt olumns. The alibration domain models a typial thermoouple in the middle row of thermoouples, extending to its four nearest bolts. The periodi nature of this mold geometry allows use of the fundamental alibration domain, shown in Figures 3 5. As seen in Figure 3, the hannels immediately adjaent to the bolt olumns urve around the bolt holes; exept for these regions, the hannel pith is 7.7 mm. Eah fundamental domain has six 6-mm-deep ball-end-milled hannels, whih run almost the entire length of the mold between any two adjaent olumns of bolt holes. The two hannels diretly adjaent to a olumn of bolt holes are 6 mm wide, while the standard hannels are 5 mm wide. Mold B is,86 mm wide,, mm long and 8 mm thik. It has a funnel that is 75 mm wide with a 6-mm-wide inner flat region. The funnel tapers from a 3.4-mm rown to an 8-mm rown at mold exit. This mold has a retangular array of mold bolts at.5 mm in the width diretion and 5 mm in the asting diretion. There is a thermoouple hole drilled into every bolt hole, exept for the topmost row and outermost olumns of bolts. The hannels onsist of banks of 8 ball-end-milled hannels, 5 mm aross, 5 mm deep and mm pith, between two bolt olumns, with gun-drilled -mm irular hannels immediately adjaent to the bolt holes. The alibration domain models a typial thermoouple outside of the funnel region, and inludes one irular hannel and nine ball-end-milled hannels. 3D Model Results The 3D model of the mold ontains the exat geometry of a portion of the mold geometry, hosen here as the fundamental domain shown in Figure 3, for ase. The three proess parameters input to this model are simply: Table Simulation Parameters and Results Case Case Case 3 Case 4 Mold A 3D A D A 3D A D B 3D B D B 3D B D Thermal ondutivity k (W/m K) Heat flux (MW/m²) Water HTC h (kw/m² K) Water temperature T w ( C) Hot fae temperature T hot ( C) Mold thikness d mold (mm) Cold fae temperature T old ( C) Distane to old fae d old (mm) Cold fae offset d old (mm) Thermoouple temperature T TC ( C) Distane to thermoouple d TC (mm) Thermoouple offset d TC (mm) AIST.org September 3 7 5

8 Figure 3 Figure 4 Mold temperatures ( C) in mold alibration domain from 3D model (ase ). Hot fae temperatures ( C) in mold alibration domain from 3D model (ase ). Figure 5 Mold temperatures ( C) from 3D model near thermoouple (ase ). The mold ondutivity, k. A uniform heat flux to the hot fae,. A uniform hannel onvetion oeffiient, h, and temperature, T w. The finite element model predits hot fae temperatures ranging from 43.8 to 5. C with an average hot fae temperature T hot,3d = 48 C, average old fae temperature T old,3d = 96.6 C, (taken at the hannel roots), and thermoouple temperature T TC, 3D = 46 C. The alulated temperature ontours for ase are shown in Figures 3 5. These results show that the highest hot fae temperature in this mold geometry, found opposite the bolt nearest to the thermoouple, is about 7 C hotter than the minimum temperature around the mold perimeter. It is not known if this hot fae temperature variation is signifiant for longitudinal rak formation. Geometri Calibration of COND With 3D Model Euation 7 gives the alibrated hannel width and depth as mm and mm, respetively. Figure 6 shows the determination of the hannel pith as 8.5 mm (average hannel area of 8.6 mm² divided by the least-suares slope of mm²/mm). Using Euation, the effetive heat transfer oeffiient is then kw/m² K, so Euation gives the alibrated mold thikness as 35. mm. Using 8 Iron & Steel Tehnology A Publiation of the Assoiation for Iron & Steel Tehnology 6

9 Figure 6 y Determination of the D hannel pith. idential boundary onditions and these alibrated geometries in COND gives a hot fae temperature of 48. C, whih mathes well with the 3D model. Using a thermoouple depth of 6.5 mm as alulated by Euation 3 instead of the nominal 8 mm (offset of.48 mm), the COND thermoouple temperature is 46.7 C, whih again mathes well with the 3D model. Using a old fae depth of 4.6 mm instead of the nominal 4 mm (offset of.6 mm), the COND predition exatly mathes the 3D model old fae temperature of 96.6 C. Table shows the results of implementing this alibration proedure for different geometries and different proessing parameters. Repeating the alibration proedure after hanging the boundary onditions and thermal ondutivity for mold A (ase ) gives very similar alibrated geometries. For mold B, the alibrated hannel is 5.84 mm wide and 3.7 mm deep, with a pith of.63 mm. Again, repeating the alibration proedure with different thermal loading onditions and material properties, produes nearly idential alibrated distanes for the same mold geometry. The thermoouple offsets of.3 and.43 mm reported here are nearly the same as the.4 mm offset that was alulated in previous work. 6 More areful alulation of the average temperatures would likely produe alibrated distanes that are even more similar. Nevertheless, the alibration proedure outlined here is independent of boundary onditions, and only needs to be performed one per mold geometry. Heat Transfer Calibration of COND With Plant Data One the mold geometry has been properly alibrated, the mold heat removal predited by COND should be alibrated to math plant measurements. Previous work 6 details this proess for a wide variety of onditions for mold B. For example, onsider asting a.45%c steel at 4.5 m/minute: the plant measures.55 MW/m² and COND alulates.54 MW/m² after alibration. Figure 7 shows that the COND preditions of thermoouple temperatures, one alibrated for geometri effets, math well with the maximum of the plant measurements at all thermoouples. The thermoouple alibration proedure was performed only one in this ase, assuming perfet ontat (d gap = ), and was applied to all thermoouples in the simulated mold. Intermittent nonzero ontat resistane is believed to explain why some of the plant thermoouples give lower temperatures. AIST.org September 3 9 7

10 Figure 7 Calibrated COND mathes plant thermoouple measurements. 6 Example Appliation: Effet of Mold Wear on Sale Formation After it has been alibrated both geometrially with the 3D model and thermally with plant measurements, as desribed in the previous setion, the aurate D model is ready to apply to investigate a variety of heat transfer phenomena. As a simple example appliation, the COND model that was alibrated and validated in this work for mold A was applied to study the formation of sale as the mold wears. Sale is assumed to form when the in the hannels is first able to boil, whih is assumed to be a possibility when the surfae temperature of the root of the hannel the alibrated old fae temperature exeeds the boiling temperature. The boiling temperature in C depends on the pressure as follows: 4 T boil = ( 75 6 p) log. (E. 8) p is the loal pressure in the ooling hannels in MPa. As the distane to the hannels dereases with mold wear, the mold hot fae temperature dereases, but the old fae temperature inreases, for a given heat flux. Using Euation 8 with the COND results, the ritial peak heat flux into the mold at whih boiling and sale deposits ould form an be identified. At the example operation pressure of. MPa, the ritial old fae temperature is 84.3 C, and the ritial loal heat flux drops from 5.5 to 3.68 MW/m with just 4 mm of mold wear. Sale layers serve to inrease mold temperature: speifially, COND predits that a 5-µm-thik sale layer will inrease both hot fae and old fae surfae temperatures by more than C. Some worn molds have been observed to operate with higher average heat removal, and the smaller resistane to heat flow from the thinner mold is insuffiient to explain this. 6 The appliation here suggests that sale formation assoiated with the mold wear ould be a possible explanation. Iron & Steel Tehnology A Publiation of the Assoiation for Iron & Steel Tehnology 8

11 Figure 8 Critial heat flux for sale formation dereases as mold wear inreases. Sale formation problems an be minimized by maintaining high-purity uality, keeping high veloity, and areful design of hannels and delivery system to avoid pressure drops. Note also that thinner molds tend to have lower temperatures, whih helps to prevent sale formation with a lower old fae temperature. However, sine the heat transfer from the shell into the mold depends on the interfaial gap resistane assoiated more with hot fae temperature, the net effet on overall heat transfer depends on the mold flux behavior. 6 The results here suggest that molds should be paired as mathing sets, wear should be regularly monitored and hannels should be arefully inspeted for sale formation. Conlusions This work has derived and demonstrated a method for imparting the auray of a 3D mathematial model of mold heat transfer into a D model of the ontinuous asting proess. Speifially, the hannel geometries and thermoouple position are hanged slightly from their respetive blueprint values to ompensate for multidimensional heat transfer. The alibration proedure was demonstrated to be independent of proess onditions, so it needs to be performed only one per mold geometry. One this geometri alibration is performed, the shell-mold interfaial parameters in the fast D model an be alibrated to math plant data, and then the model an be applied to aurately investigate various aspets of heat transfer in the ontinuous asting proess. An example appliation is provided to show that a sale layer is more likely to form for older, thinner molds. The 3D models used in this work show the variation of mold surfae temperature due to the geometri features of the mold. Future work is needed to uantify the allowable variability in mold surfae temperature to avoid defets in the ast steel. Aknowledgments The authors gratefully aknowledge the finanial support of the member ompanies of the Continuous Casting Consortium at the University of Illinois at Urbana-Champaign, and the National Siene Foundation (Grant CMMI 9-38 REU). AIST.org September 3 9

12 Referenes. Y. Meng and B.G. Thomas, Heat Transfer and Solidifiation Model of Continuous Slab Casting: COND, Metallurgial and Materials Transations, Vol. 34B, No. 5, 3, pp M.R. Ridolfi, B.G. Thomas, G. Li and U. Della Foglia, The Optimization of Mold Taper for the Ilva-Dalmine Round Bloom Caster, La Revue de Metallurgie CIT, Vol. 9, No., 994, pp J. Sengupta, M.K. Trinh, D. Currey and B.G. Thomas, Utilization of COND at ArelorMittal Dofaso s No. Continuous Caster for Crater End Determination, AISTeh Conferene Proeedings, Vol. II, 9, pp G. Li, B.G. Thomas, B. Ho, G. Li and N. Youssef, COND User Manual, CCC Report, University of Illinois, July Y. Meng and B.G. Thomas, Simulation of Mirostruture and Behavior of Interfaial Mold Slag Layers in Continuous Casting of Steel, ISIJ International, Vol. 46, No. 5, 6, pp B. Santillana, L.C. Hibbeler, B.G. Thomas, A. Hamoen, A. Kamperman and W. van der Knoop, Heat Transfer in Funnel Mold Casting: Effet of Plate Thikness, ISIJ International, Vol. 48, No., 8, pp I.V. Samarasekera and J.K. Brimaombe, The Thermal Field in Continuous-Casting Molds, Canadian Metallurgial Quarterly, Vol. 8, No. 3, 979, pp S. Chenna Krishna, N. Supriya, Abhay K. Jha, Bhanu Pant, S.C. Sharma and Koshy M. George, Thermal Condutivity of Cu-Cr-Zr-Ti Alloy in the Temperature Range of K, ISRN Metallurgy, Vol., Artile ID 58659, 4 pages,. 9. ABAQUS 6. User Manuals, Dassault Simulia In., Providene, R.I.,.. C.A. Sleiher and M.W. Rouse, A Convenient Correlation for Heat Transfer to Constant and Variable Property Fluids in Turbulent Pipe Flow, International Journal of Heat and Mass Transfer, Vol. 8, No. 5, 975, pp M.M. Langenekert, Influene of Mold Geometry on Heat Transfer, Thermoouple and Mold Temperatures in the Continuous Casting of Steel Slabs, M.S. thesis, University of Illinois at Urbana-Champaign,.. L.C. Hibbeler, S. Kori, K. Xu, B.G. Thomas and C. Spangler, Thermomehanial Modeling of Beam Blank Casting, Iron & Steel Tehnology, Vol. 6, No. 7, 9, pp L.C. Hibbeler, B.G. Thomas, R.C. Shimmel and G. Abbel, Thermal Distortion of Funnel Molds, AISTeh Conferene Proeedings, Vol. I,, pp NIST Webbook, Appendix To alulate the umulative hannel area, the following euation defines the area of a semiirle of diameter d as a funtion of distane along the diametrial edge, for x d: d x x x x Ax ( )= aros d d d d 4 (E. 9) F Nominate this paper Did you find this artile to be of signifiant relevane to the advanement of steel tehnology? If so, please onsider nominating it for the AIST Hunt-Kelly Outstanding Paper Award at AIST.org/huntkelly. This paper was presented at AISTeh 3 The Iron & Steel Tehnology Conferene and Exposition, Pittsburgh, Pa., and published in the Conferene Proeedings. Iron & Steel Tehnology A Publiation of the Assoiation for Iron & Steel Tehnology

13 AIST Transations seeks to publish original researh artiles fousing on sientifi or tehnial areas relevant to the iron and steel ommunity. All artiles are peer-reviewed by Key Reviewers prior to publiation. The sope of the Transations spans all fields of iron and steel manufaturing, from extrative metallurgy to liuid metal proessing, asting, thermomehanial proessing as well as oating, joining/welding and mahining. Artiles related to struture and properties, i.e., haraterization, phase transition, hemial analysis and testing of reep, orrosion or strength are aepted. In addition, papers on proess ontrol, testing and produt performane are also enouraged. The Transations will publish papers on basi sientifi work as well as applied industrial researh work. Papers disussing issues related to speifi produts or systems an be onsidered as long as the struture follows a sientifi investigation/disussion, but not for the aim of advertising or for the purpose of introduing a new produt. Papers should be no longer than 5, words, or pages inluding figures. Papers will either be aepted unonditionally, onditionally based on reviewers omments, or rejeted. The review proess should be ompleted in less than two months. Upon aeptane, authors will be asked to omplete a form to transfer opyright to AIST. A PDF proof of the aepted manusript will be sent eletronially to the author(s) approximately one month prior to publiation for final approval. Reprints of published manusripts an be ordered through AIST. Please ontat me with any uestions regarding AIST Transations. Sridhar Seetharaman AIST Transations editor, assoiate professor, Carnegie Mellon Center for Iron and Steelmaking Researh, Pittsburgh, Pa., USA , sridhars@andrew.mu.edu To submit a manusript for onsideration, an eletroni opy (saved as an MS-Word doument) should be sent to: AIST Transations sridhars@andrew.mu.edu AIST Transations are indexed through Chemial Abstrats Servie, Columbus, Ohio. AIST Transations Key Reviewers Professor Chris Pistorius Carnegie Mellon University, Pittsburgh, Pa., USA Professor Hatem S. Zurob MMaster University, Hamilton, Ont., Canada Dr. P. Kaushik senior researh engineer, ArelorMittal Global R&D Steelmaking Proess Researh, East Chiago, Ind., USA Professor Patriio F. Mendez Department of Chemial and Materials Engineering, University of Alberta, Edmonton, Alta., Canada Professor Lifeng Zhang Shool of Metallurgial and Eologial Engineering, University of Siene and Tehnology Beijing, Beijing, China Dr. Fred B. Flether prinipal researh engineer, ArelorMittal Global R&D Researh and Development, Coatesville, Pa., USA Dr. Stefanie Sandlöbes sientist, Max-Plank-Institut für Eisenforshung GmbH, Düsseldorf, Germany Dr. Il Sohn assoiate professor, Neo- Metallurgial Proessing Lab, Department of Materials Siene and Engineering, Yonsei University, Seoul, Korea AIST.org September 3 3