94 refractories WORLDFORUM 2 (2010) [2]

1 Introduction

The heat transfer analysis of multi-layer re-fractory concretes in both transient andsteady state conditions is particularly impor-tant for many pyro-processing industries.Knowing the temperature profile throughthe different layers is important for design

is generally applied to one or both sides byusing some simplified correlations to ac-count for wind and other flow effects.In many cases, simplifying assumptions aremade when undertaking a heat transferanalysis. Incorrect assumptions can lead topoor or the wrong selection of materialswhich in turn can lead to excess heat loss,refractory failure, overheating of vessels,too low shell temperatures or poor liningdesign with increased capital costs.Earlier research [1, 2] has found that thereis a significant difference between data-sheet thermal conductivity and publisheddata. The effect of higher material thermalconductivity and gaps between concretelayers are discussed. This paper discusses the problems associ-ated when undertaking heat transferanalysis, specifically, the effect of takingsimplified assumptions and the problem oflarge variations in refractory thermal con-ductivity values. The effect of refractorymaterial conductivity values and air gapsat the interface in a 1D analysis is provid-ed. It is shown that using a 1D heat trans-fer model to predict temperature profilesin refractory systems can result in seriouserrors.

and operational trouble-shooting. It is clearthat the design of refractory linings is be-coming increasingly important both struc-turally and in energy efficiency terms. Alsoindustry “fitness for service” (FFS) guidelinesfor pressure vessels require that the plant issafe for personnel and the public. FFS as-sessments will include refractory linings andthe practice of simply changing the refracto-ry design without proper engineering ap-proval could leave companies exposed. Heat transfer theory is generally well under-stood and it is possible to predict tempera-ture profiles under various conditions withreasonable accuracy, where accurate ther-mal property and convective / radiativeboundary conditions are known. Refractorylinings are generally composed of multiplelayers of varying insulating materials and adense abrasion resistant hot face layer. Forsteady conditions, when the layer is flat orthin (thickness < 5 % of the radius of curva-ture), conduction heat flow, Q, through eachlayer is well defined by Q = k /Δx A ΔTwhere k is the average thermal conductivityof the layer material, Δx its thickness, A thearea for heat transfer and ΔT the tempera-ture difference across the layer. Convection

Heat Transfer Design Considerations for Refractory Linings,Part 1

G. Palmer

This paper discusses the prob-lems associated when undertak-ing heat transfer analysis, specif-ically, the effect of taking simpli-fied assumptions and the prob-lem of large variations in refrac-tory thermal conductivity values.The effect of refractory materialconductivity values and air gapsat the interface in a 1D analysisis provided. It is shown that us-ing a 1D heat transfer model topredict temperature profiles inrefractory systems can result inserious errors.

Greg Palmer

Palmer Technologies Pty. Ltd.

Coorparoo DC, Queensland, Australia

Tony Howes

School of Engineering

The University of Queensland

4072 St. Lucia, Australia

Corresponding author: Greg Palmer

E-mail: Greg.Palmer@palmertechgroup.com

Keywords: Heat transfer, refractory linings,

design considerations

Received: 09.11.2009

Accepted: 11.11.2009

Ther

mal

con

duct

ivit

y [W

/m ⋅

K]

Density [kg/m2]

Fig. 1 Thermal conductivity of refractory versus density comparison from published data[5, 9]

refractories WORLDFORUM 2 (2010) [2] 95

2 Thermal conductivity measurement and estimation

Heat transfer analysis is one of the mostcommonly used tools in evaluating and de-signing refractory structures. The analysis isalmost always carried out using a 1D steadystate program assuming perfect conductionsthrough composite layers. This requires theuse of refractory thermal conductivity andthe most commonly used source are manu-facturer’s data sheets. Hence the accuracy ofreported thermal conductivity data and thevalidity of perfect conduction through com-posite layers are particularly important fordesigners. There are a number of methods for deter-mining thermal conductivity of refractorymaterials, for example, the hot wire method,calorimetry and laser flash thermal diffusivi-ty. The aim is not to discuss these techniquesbut rather to discuss variations on tempera-ture predictions between reported and pre-dicted thermal conductivity.

The most common method to determine re-fractory thermal conductivity has been thecalorimetry method which as been used formore than 60 years. It would be safe to saythat the hot-wire method is now more fre-quently used due to speed and cost.Thermal conductivity of refractory materialshas been studied both theoretically [3, 4]and practically [1, 5, 6, 7]. This research hasfound that the hot-wire method is well suit-ed for heterogeneous refractory materialsbut not well suited for non-isotropic materi-als like insulation fibreboard [8]. In 1988Crowley and Young [1] studied a number ofdifferent thermal conductivity test tech-niques and concluded that there were signif-icant differences between static and dynam-ic methods. It was also concluded that thedetermination of the thermal conductivity (k)using the comparative test1), which relates kto geometric bulk density2), was the mostconsistent and agreed closely with the hot-wire data. They also found that the thermal

conductivity for materials of similar densityand composition often had thermal conduc-tivities that differed from the published dataoften by as much as 50 %. A more recent analysis undertaken byAkiyoshi et al [5] investigated the relation-ship of thermal conductivity with volumetricbulk density3) and temperature for aluminaand fireclay refractories. The investigationused the hot-wire technique and the resultswere statistically analyzed using the leastsquares method. A correlation was develop-ed for fireclay and alumina refractories withvolumetric bulk density in the range of

Fig. 2 Comparison of data sheet thermal conductivity and predicted thermal conductivity of dense and insulation castables

[W/m

⋅K]

[W/m

⋅K]

[W/m

⋅K]

[W/m

⋅K]

Fig. 3 Thermovision of furnace roof showing shelltemperatures

1) Using known standard materials and comparing temperature differentials across the standards2) Determined by sample measurement and weight3) Immersion technique4) P-Thermal is a1D transient heat transfer program developed by the authors

Temperature [°C]

Temperature [°C]Temperature [°C]

Temperature [°C]

96 refractories WORLDFORUM 2 (2010) [2]

550 kg/m3 and 3140 kg/m3 with porosity inthe range of 15 to 81 %.The relation for k in a range of refracto-ries is shown in equation 1.This equationwas reported to be valid for materials for25 °C ≤ T ≤ 1200 °C, 550 kg/m3 ≤ ρv ≤3140 kg/m3 and 36 mass-% ≤ Al2O3 ≤ 94mass-%. The work published by Crowley and Young[1] presents data suitable for comparisonpurposes. The field data published byCrowley and Young [9] was also comparedagainst the Akiyoshi et al. [5] correlationand is plotted in Fig. 1. This shows an ex-cellent correlation between refractory ther-mal conductivity measured by Crowley andYoung and Akiyoshi et al.Fig. 2 shows the difference between themanufacturer’s data sheet thermal conduc-tivity values and predicted thermal conduc-

show the difference between thermal con-ductivity values under perfect conductionsfor a one refractory layer system.The shell temperature was compared to a 1DP-Thermal4) [12] heat transfer model usingmanufacturer’s data sheet thermal conduc-tivity and the refractory thermal conductivitypredicted by equation 1 for a single insula-tion layer. Fig. 3 shows an infrared image of a furnaceroof with 150 mm thick insulation refractoryunder a 6 mm carbon steel shell. The tempe-ratures were taken shortly after start up andthe refractory lining had been completely re-placed. The shell temperature varies from149 °C (133 °C near the edge) to 160 °C.The 1D heat transfer model using the pre-dicted thermal conductivity data (equation1) is shown in Fig. 4. The 1D model for theone layer system is 156 °C which validatesthe refractory thermal conductivity valuespredicted by equation 1 (correlated to thehot-wire method). The 1D heat transfer model using the manu-facturer’s data sheet thermal conductivitypredicts a steady state shell temperature of121 °C. This is significantly less than whathas been measured from actual field data. Itis concluded that a 1D heat transfer modelusing the manufacturer’s data sheet thermalconductivity is likely to under-predict tempe-rature profiles in refractories systems by 20to 30 %. If the refractory thermal conductiv-ity values measured by the hot-wire tech-nique or calculated by equation 1 is used ina 1D perfect model then the shell tempera-ture can be predicted to within 5 % for aone layer system. It is concluded that corre-lations based on the hot-wire test can be

tivity using equation 1, for four different re-fractory castables. It can be seen there is asignificant difference between predicted anddatasheet thermal conductivity values, insome cases the error is greater than 50 %.This is in line with data published by Crow-ley and Young [1]. Published literature hasfound that the hot-wire method is an accu-rate and reliable [10, 11] method for deter-mining thermal conductivity of refractorymaterial. Thus it is concluded that correla-tions based on the hot-wire test can be usedto accurately predict refractory thermal con-ductivity. It is also concluded that manufac-turer’s datasheet thermal conductivity valuesin some cases can be very inaccurate for un-known reasons.

3 Analysis for a one layer system

An example for a furnace roof is used to

Fig. 4 P-thermal analysis of furnace roof using thermal conductivity calculated by equa-tion 1

Fig. 5 Thermovision of reactor shell showing a hot spot and surrounding shell temperature (~180 °C)

Tem

pera

ture

[°C]

Time [h]

(1)

refractories WORLDFORUM 2 (2010) [2] 97

used to accurately predict refractory thermalconductivity in a one layer refractory systemusing a 1D heat transfer model.

4 Analysis for a two layer systemwith and without air gaps

Due to the fact that small air gaps exist be-tween refractory composite layers a 1D mod-el was developed which included an air gapat the interface between the two concretelayers in order to study the effect of data-sheet thermal conductivity on lining temper-ature profiles. Previous research has shown that two re-fractory conditions are existing, the first isthe green state when the concrete is firstcast [13]. In this condition the bonding be-tween the two concrete layers is most likelyto be well bonded. The second and most im-portant condition for designers is the firedstate when the concrete has dried and gapscan exist at the interface. The heat transfer for a two layer system(shell, insulation and hot-face) was evaluat-ed by analyzing a reactor vessel. The originalrefractory lining is composed of 150 mmKastolite 2300LI and 100 mm 1800 gradehot-face. The reactor operates at a tempera-ture of 1250 °C. Fig. 5 shows the shell temperatures for a re-actor which had a hotspot in one area. Theshell temperature away from the hotspotwas approximately 180 °C. After the hotspotwas repaired the shell temperature was mo-nitored using welded thermocouple wire.The temperature varied from 160 °C to180 °C. The temperature profile was calcu-lated using a 1D heat transfer model (with-out an air gap) using both Akiyoshi (eqn 1)and manufacturer’s data sheet k values. Thetemperature profile using k calculated fromequation 1 is shown in Fig. 6. This predicts ashell temperature of 209 °C. Repeating the analysis using the manufac-turer’s data sheet k values has a tempera-ture profile as shown in Fig.7. This predicts ashell temperature of 195 °C which is higherthan the measured shell temperature by ap-proximately 15 °C.The analysis is repeated again using theAkiyoshi k values (equation 1) with an airgap. The temperature profile with air gap of~10 W/m2 K at the interface is shown inFig. 8. In this case the predicted shell tem-perature is 181 °C which is within the meas-ured shell temperature range.

Fig. 6 1D heat transfer temperature profile using k from equation 1 with no air gap

Fig. 7 1D heat transfer temperature profile using k from the manufacturer’s data sheet

Fig. 8 1D heat transfer temperature profile using k from equation 1 with an air gap

Tem

pera

ture

[°C]

Tem

pera

ture

[°C]

Tem

pera

ture

[°C]

Time [h]

Time [h]

Time [h]

98 refractories WORLDFORUM 2 (2010) [2]

It is concluded that the effect of a gap inthe order 1 mm at the interface betweenthe concrete layers is important andshould be taken into consideration whendesigning refractory linings.

5 Conclusions

It is concluded that the current designprocedure of using a 1D heat transfermodel to predict temperature profiles inrefractory systems can result in serious er-rors and the use of simplified forced con-vection coefficient equations can lead toerrors of 25 % or more. The analysis andhistorical data shows that manufacturer’spublished thermal conductivity values canbe very inaccurate for unknown reasons.The error in the manufacturer’s thermalconductivity can be by as much as 50 %.Research by others has shown that corre-lations based on the hot-wire test can ac-curately predict refractory thermal con-ductivity. It has been found that usinghot-wire thermal conductivity data withan interface air gap is an accurate methodfor predicting temperature profiles in re-fractory systems.

[8] Wulf, R.; Barth, G.; Gross, U.: Intercomparison of

insulation thermal conductivities measured by

various methods. Int. J. Thermophys. 28 (2007)

1679–1692

[9] Crowley, M.S.; Young, J.S.: Evaluation of thermal

film coefficients in furnace walls. Proc. Int. Forum

on Advances in Refractories Technology, Cincin-

nati, 1988. Am. Ceram. Trans. 42-4 (1988) 547–

556

[10] Nunes dos Santos, W.: Advances on the hot wire

technique. J. Eur. Ceram. Soc. 28 (2008) 15–20

[11] Aksel'rod, E.I.; Vishnevskii, I.I.: Use of the hot

wire method for measuring the thermal con-

ductivity of lightweight, fiber, and powder re-

fractory materials. Thermal Engng. (1984) [4]

49–53

[12] Palmer, G.B.; Howse, T.: Calculation of transient

and steady state heat transfer in refractory li-

nings under various conditions. Refractory Ap-

plication and News 12 (2007) [1]

[13] Palmer, G.B.; Ellis, R.E.: Behaviour of monolithic

refractory and its importance in design of re-

fractory structures. Refractory Application and

News 12 (2007) [6]

References

[1] Crowley, M.S.; Young, J. S.: Thermal conducti-

vity of monolithic refractories. Ceram. Bull. 67

(1988) [7]

[2] Hemrick, J.G.; Charles, W.K. jr.; Andrew, A.W.;

Mattison, K.F.: Thermal conductivity of alumi-

na measured with three techniques. J. Testing

and Evaluation 31 (2003) [4]

[3] Allen, A.W.; Heat transfer mechanisms in re-

fractory materials. Refractory Applications

and News 10 (2005) [1]

[4] de Sylos Cintra jr., J.; Nunes dos Santos, W.:

Numerical analysis of sample dimensions in

hot wire thermal conductivity measurements.

J. Eur. Ceram. Soc. 20 (2000) 1871–1875

[5] Akiyoshi, M.M.; da Silva, A.P.; da Silva, M.G;

Pandolfelli, V.C.: Impact of thermal conducti-

vity on refractories. Am. Ceram. Soc. Bull. 81

(2002) [3]

[6] Akiyoshi, M.M.; Pereira, R.; da Silva, A.P.; Pan-

dolfelli, V.C.: Effect of alumina content, poro-

sity and temperature on the thermal conduc-

tivity of refractories. Am. Ceram. Soc. Bull. 82

(2003) [6]

[7] Hemrick, J.G.; Loveland, E.: Technique develop-

ment for large sample thermal conductivity me-

asurement. Proc. UNITECR 2005, pp. 846