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Heat Mass Transfer (2015) 51:787–794DOI 10.1007/s00231-014-1454-6

ORIGINAL

The role of leak air in a double‑wall chimney

Klaus Lichtenegger · Babette Hebenstreit · Christian Pointner · Christoph Schmidl · Ernst Höftberger

Received: 21 October 2013 / Accepted: 22 October 2014 / Published online: 31 October 2014 © Springer-Verlag Berlin Heidelberg 2014

led to the environment, as well as a combustion air supply. Traditionally the combustion air is directly taken from the room where the heating appliance is located.

During the last decades building shells got much tighter, advancing in the direction of passive houses. Therefore building shells of modern houses are often too tight to ena-ble enough air supply through leakage. Consequently, mod-ern stoves are constructed room sealed with separate air supply in order to enable the operation of stoves in air-tight buildings. A separate inlet for the supply air, connected to a duct, enables the air to stream directly from the external to the stove, eliminating the need to use air from the room. An additional advantage of room-sealed stoves is the decou-pling of controlled domestic ventilation and combustion air supply.

One possibility to arrange the air supply is using a dou-ble wall chimney, as sketched in Fig. 1. This arrangement is favorable for simple installation without the need for a separate opening, but it also faces some problems: Due to preheating of the air, the buoyant force reduces the natural draft of the chimney—an effect which can be significantly reduced by proper insulation.

In an Austrian research project conducted in coopera-tion with an industrial partner, different annular gap setups of metallic chimney systems for room sealed stoves (both log wood and pellet stoves) of a nominal load up to 10 kW have been investigated [2]. Different insulation setups were tested to understand the mechanisms of air preheating and pressure drop in the chimney system:

• double-wall chimney without insulation• double-wall chimney with insulated liner• double-wall chimney with insulated case• double-wall chimney with insulated liner and insulated

case

Abstract In modern buildings with tight shells, often room-independent air supply is required for proper opera-tion of biomass stoves. One possibility to arrange this sup-ply is to use a double-wall chimney with flue gas leaving through the pipe and fresh air entering through the annu-lar gap. A one-dimensional quasi-static model based on balance equations has been developed and compared with experimental data. Inclusion of leak air is crucial for repro-duction of the experimental results.

1 Introduction

The efficient use of biomass will be essential to achieve the transition to a lifestyle based on renewable resources. This is particularly true for heating purposes both on large and small scale. In order to reach the European 20-20-20 goals [1], about half of the demand for renewable energy will have to be covered by biomass. More than half of this amount will presumably be used in domestic small-scale combustion systems.

Approximately 1 million biomass stoves are sold in Europe per year; the total number of installed biomass stoves is estimated to 25 millions. Each stove has to be equipped with a chimney, through which the flue gases are

K. Lichtenegger (*) · B. Hebenstreit · C. Pointner · C. Schmidl · E. Höftberger Bioenergy 2020+, Gewerbepark Haag 3, 3250 Wieselburg-Land, Austriae-mail: klaus.lichtenegger@bioenergy2020.eu

B. Hebenstreit Energy Engineering, Department of Engineering Sciences and Mathematics, Luleå University of Technology, 971 87 Luleå, Sweden

788 Heat Mass Transfer (2015) 51:787–794

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In addition to the measurements, a mathematical model has been developed which has been briefly described in [3] and is discussed in more detail in the current article.

A reference model for the single-wall case is described in Sect. 2, the model for the double-wall setup is described in Sect. 3. Comparison to experimental data follows in Sect. 4. The results and possible extensions of the model are discussed in Sect. 5.

2 Modelling of the single‑wall case

To set up the notation and in order to have a reference sys-tem at hand, we first briefly describe the modeling of a single-walled chimney system, allowing for an insulating layer. The system is discretized by introducing Ncyl slices, as sketched in Fig. 2.

The model is one-dimensional, making use of the wealth of heuristic relationships for heat and mass trans-fer established in engineering [4]. A summary of the geo-metric and physical quantities characterizing the single- as well as the double-wall system is given in Table 1; we also employ average values like ρ(k)

p = 12(ρ

(k)p,in + ρ

(k)p,out) or

T(k)g = 1

2(T

(k)gl + T

(k)gu ).

Some of the relevant quantities are also displayed in Fig. 3. We introduce the abbreviations

(1)(αA)(k)wpi = α

(k)wpiA

(k)wpi, (αA)(k)wpo = α(k)

wpoA(k)wpo,

(2)

(αA)(k)wp = 2π�h(k)

ln

dwpi+2xst,pdwpi

�st+

lndwpo

dwpi+2xst,p

�ins

−1

Fig. 1 Sketch of the double-wall chimney setup The flue gas exits through the inner pipe, while fresh air enters through the annular gap. Insulat-ing layers, if present, are placed outside of the steel pipes, according to the four combinations listed in Sect. 1

Fig. 2 Scheme of discretization (sketched for the single-walled chimney system)

789Heat Mass Transfer (2015) 51:787–794

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for the coefficients of convective and conductive heat trans-fer to, from and through the pipe wall. The coefficients αwpi and αwpo are determined from the Nußelt numbers, which depend on the properties of the gas flow, characterized by Reynolds and Prandtl number.

Pressure in the chimney is determined to a large extent by buoyancy; in addition dynamic pressure and friction

have some influence. Calculation of the static pressure pstat is done using Bernoulli’s equation

(3)pstat(h)+ ρ(h)

v2(h)

2︸ ︷︷ ︸

dynamic pressure

+ g

∫ H

h(ρa − ρ(z)) dz

︸ ︷︷ ︸

buoyancy

− qfric,p(h)︸ ︷︷ ︸

friction

= pa,

Table 1 Geometric and physical quantities used to describe the single-wall (sgl.) and double-wall (dbl.) chimney system

In the symbol list, subscripts k and superscripts (k) which indicate the kth cylinder slice have been omitted. An abbreviation like Twp[i/o] means that both Twpi and Twpo are used to describe the system

Symbol Quantity (and definition, if applicable) sgl. dbl.

dwpi Inner pipe wall diameter√ √

x[st/ins],p Thickness of steel/insulation layer in pipe wall√ √

dwpo Outer pipe wall diameter, dwpo = dwpi + 2(xst,p + xins,p)√ √

dwgi Inner gap wall diameter√

x[st/ins],g Thickness of steel layer in gap wall√

dwgo Outer gap wall diameter, dwgo = dwgi + 2(xst,g + xins,g)√

Apipe Area of pipe section, Apipe =π4d2wpi

√ √

Agap Area of annular gap section, Apipe =π4(d2wgi − d2wpo)

√

�h Height of the cylinder slice√ √

Awp[i/o] Area of inner/outer pipe wall barrel, A(k)wp[i/o] = πdwp[i/o]�hk

√ √

Awg[i/o] Area of inner/outer gap wall barrel, A(k)wg[i/o] = πdwg[i/o]�hk

√

�[st/ins] Thermal conductivity of steel/insulating material√ √

cp(T) Specific heat capacity of air or flue gas at temperature T√ √

Tp[l/u] Temperature of flue gas at lower/upper boundary of the pipe slice√ √

Twp[i/o] Pipe wall temperature at inner/outer surface√ √

Tg[l/u] Temperature of air at lower/upper boundary of the gap slice√

Twg[i/o] Gap wall temperature at inner/outer surface√

pp,[in/out] Pressure of flue gas entering/leaving the pipe slice√ √

ρp,[in/out] Density of flue gas entering/leaving the pipe slice√ √

vp,[in/out] Velocity of flue gas entering/leaving the pipe slice√ √

mp,[in/out] Mass flow for pipe, m(k)p,[in/out] = Apipeρ

(k)p,[in/out]v

(k)p,[in/out]

√ √

pg,[in/out] Pressure of flue gas entering/leaving the gap slice√

ρg,[in/out] Density of flue gas entering/leaving the gap slice√

vg,[in/out] Velocity of flue gas entering/leaving the gap slice√

mg,[in/out] Mass flow for gap, m(k)g,[in/out] = Apipeρ

(k)g,[in/out]v

(k)g,[in/out]

√

ma2p Mass flow of leak air from ambient to pipe√

ma2g Mass flow of leak air from ambient to annular gap√

mg2p Mass flow of leak air from annular gap to pipe√

αwp[i/o] Coefficient of convective transfer to/from the inner/outer pipe wall√ √

αwg[i/o] Coefficient of convective transfer to/from the inner/outer gap wall√

εwpo Coefficient of emission of the outer pipe wall√ √

εwg[i/o] Coefficient of emission of the inner/outer gap wall√

ψwp[i/o] Coefficient of friction of the inner/outer pipe wall√ √

ψwg[i/o] Coefficient of friction of the inner/outer gap wall√ √

Ta Ambient temperature√ √

pa Ambient air pressure√ √

�pp Pressure deficit in pipe, �pp = pa − pp√ √

�pg Pressure deficit in gap, �pg = pa − pg√

ρa Ambient air density√ √

σp Porosity of pipe wall√ √

σg Porosity of gap wall√

790 Heat Mass Transfer (2015) 51:787–794

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where qfric(h) denotes the pressure loss due to fric-tion in [h, H]. We introduce the pressure difference

�pp(h) := pa − pstat(h)discretization

−→ �p(k)p . For the discre-

tized version of the friction term, we make the ansatz

with the dimensionless friction number ψ(k)wpi, which is cal-

culated from the roughness rwpi and the Reynolds number Rek according to

The pipe wall is modelled as homogenously porose. For the volume flow of leak air we use the ansatz

(4)

q(k)fric,p : = qfric,p(hk)− qfric,p(hk−1)

= ψ(k)wpi

12ρ(k)p

(v(k)p

)2

dwpi�hk ,

(5)1

�

ψ(k)wpi

= −2 log10

2.51

Rek

�

ψ(k)wpi

+rwpi

3.71 dwpi

.

(6)V(k)a2p ≡

m(k)a2p

ρ(k)p

= σpA(k)wpi + A

(k)wpo

2�p(k)p

Velocities follow from the continuity equation, which, for the (quasi)stationary case simplifies to div j = 0. Including leak air, one arrives at

Temperatures are calculated from the energy balance. The description of heat transfer is simplified by using arith-metic means instead of the logarithmic temperature differ-ences. Thus one obtains a formally linear system of equa-tions. The systematic error introduced by this procedure is small and can be further reduced by increasing the number of cylinder slices.

The main contributions are convective heat transport by the flue gas and convective/conductive heat transfer through the wall. Two smaller contributions are heat from friction and radiation. For the heating due to friction we make the ansatz

in order to be consistent with (4). Energy loss to the ambi-ent via radiation is given by

The factorization performed to formally linearize this term, which improves the numerical properties of the system. For the (quasi)stationary setup, one obtains the energy balance

with the matrix

(7)ρ(k)p =

pa −�p(k)p

RN2Tkp

with RN2=

R

µN2

.

(8)v(k)p,out =

1

ρ(k)p,out

(

v(k)p,inρ

(k)p,in + m

(k)a2p

)

.

(9)Q(k)fr = ψ

(k)wpi

π

8ρ(k)p

(

ρ(k)p

)3dwpi �hk

(10)

Qradp2a = σSBεwpoAwpo

(

T3wpo + T2

wpoTa + TwpoT2a + T3

a

)

︸ ︷︷ ︸

=:�p2a

(Twpo − Ta

).

(11)

C1 ·

Tpu

Twpi

Twpo

=

�

cp�Tpl

�mp,in −

(αA)wpi2

�

Tpl + cp(Ta)ma2pTa + Qfrwpi

(αA)wpi2

Tpl�(αA)wpo +�p2a

�Ta

Fig. 3 Some quantities used to characterize a single cylinder slice in the single-wall case

(12)C1 =

cp�Tpu

�mp,out +

(αA)wpi2

− (αA)wpi 0

−(αA)wpi

2(αA)wpi + (αA)wp − (αA)wp

0 − (αA)wp − (αA)wp + (αA)wpo +�p2a

.

with a porosity coefficient σp. This coefficient is initially unknown and can be estimated by comparing the simu-lation results with experimental data. Leak air through the stove can be modelled in an analogous way as V = σstove Astove�p

(k=1)p . For the present simulation this

contribution has been neglected by setting σstove = 0m3/s

m2 Pa.

Flue gas densities are calculated from the ideal gas equation,

This equation is formally linear (and thus can be solved by simple matrix inversion). However, some of the ele-ments of C1 and of the inhomogenity depend directly or indirectly on the unknown temperatures (Tpu, Twpi, Twpo). In addition, the equations for the cylinder slices are cou-pled, since for example T (k)

pu = T(k+1)pl and v(k)p,out = v

(k+1)p,in .

Thus obtaining the final solution requires an iterative approach, during which also velocities, pressure values,

791Heat Mass Transfer (2015) 51:787–794

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leak air mass flow and heat transfer coefficients are re-calculated several times. The boundary values Ta, pa, T

(1)pl

and v(1)pl are obtained from experiment (but see Sect. 5 for remarks on this issue).

3 Modelling of the double‑wall case

The modelling of the double-wall case is in principle simi-lar to the single-wall case, but more complex; in particular the pressure conditions are complicated. Most additional quantities are defined analogously to the ones in the single-wall case, with subscripts g denoting the annular gap. For example, the pressure loss due to friction in the pipe (4) is supplemented by a similar term for pressure loss in the annular gap,

The flow of leak air from ambient to the pipe, V (k)a2p, is

replaced by the two volume flows

Calculation of velocities from the continuity equation takes the form

(13)q(k)fric,g =

(

ψ(k)wpo

dwpo+

ψ(k)wgi

dwgi

)

1

2ρ(k)g

(

v(k)g

)2�hk ,

(14)V(k)a2g = σg

A(k)wgi + A

(k)wgo

2�p(k)g ,

(15)V(k)g2p = σp

A(k)wpi + A

(k)wpo

2

(

�p(k)p −�p(k)g

)

.

Radiation is formally linearized by employing the prefactors

with the first expression taking into account reflection and re-absorption within the annular gap. The characteristic quantities are listed in Table 1, some are also sketched in Fig. 4.

The main obstacle in setting up a consistent model is the heat transfer from and to the annular gap. The problem of the asymmetrically heated annular gap is not fully solved yet [5]. As an approximation, the expres-sions for an annular gap with thermal insulation have been used, but this introduces a systematic error, which is a serious source of uncertainty for the results of the model.

The energy balance leads to the equation

(16)v(k)p,out =

1

ρ(k)p,out

(

v(k)p,inρ

(k)p,in + m

(k)g2p

)

,

(17)v(k)g,out =

1

ρ(k)g,out

(

v(k)g,inρ

(k)g,in − m

(k)g2p + m

(k)a2g

)

.

(18)

�p2g =σSBAwpo

1εwpo

+AwpoAwgi

(1

εwgi− 1

)

(

T3wpo + T2

wpoTwgi + TwpoT2wgi + T3

wgi

)

,

(19)

�g2a = σSBεwgoAwgo

(

T3wgo + T2

wgoTa + TwgoT2a + T3

a

)

,

Fig. 4 Some quantities used to characterize a single cylinder slice in the double-wall case

792 Heat Mass Transfer (2015) 51:787–794

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with the matrix

(20)C2 ·

TpuTwpiTwpoTglTwgiTwgo

=

�

cp�Tpl

�mp,in −

(αA)wpi2

�

Tpl +12cp(Tg)mg2pTgu + Qfr

wpi(αA)wpi

2Tpl

(αA)wpo2

Tgu�

cp(Tgu)mg,in −(αA)wpo+(αA)wgi+cp(Tg)mg2p

2

�

Tgu + cp(Ta)ma2gTa + Qfrgap

12(αA)wgiTgl�

(αA)wgo +�g2a

�Ta

(21)C2 =

C(2)11 − (αA)wpi 0 − 1

2cp(Tg)mg2p 0 0

−(αA)wpi

2C(2)22 − (αA)wp 0 0 0

0 − (αA)wp C(2)33 −

(αA)wpo2

−�p2g 0

0 0 − (αA)wpo C(2)44 − (αA)wgi 0

0 0 −�p2g − 12(αA)wgi C

(2)55 − (αA)wg

0 0 0 0 − (αA)wgi C(2)66

,

a characteristic example, some simulation results for the uninsulated setup are compared to experimental data in Figs. 5 and 6. The calculations have been performed with leakage rates of σp = 0.0000

m3/s

m2 Pa, σp = 0.0015

m3/s

m2 Pa and

σp = 0.0030m3/s

m2 Pa.

For the uninsulated case, these leakage rates yield average volume flows of Va2p = 0 m3

h, Va2p = 8.64 m3

h and

Va2p = 15.98 m3

h. For the last value, the simulation results

and experimental data show good agreement. Most dis-crepancies between experimental data and simulation results are due to the fact that the simulation does not take into account thermal inertia, thus changes in tem-perature tend to be more rapid and bigger than in the experiment.

This effect is more pronounced in the insulated case, as displayed in Figs. 7 and 8 since the thermal mass of the

0 1 2 3 4 50

50

100

150

200

250

300

350

operation time [h]

T pipe

(at h

=3.9

m) [

°C]

Experimental dataVdota2p = 0 m3/h

Vdota2p = 8.6397 m3/h

Vdota2p = 15.9794 m3/h

Fig. 5 Flue gas temperature Tp(3.9m) for the unisolated single-wall case

0 1 2 3 4 5

0

5

10

15

20

25

30

35

40

operation time [h]

Del

ta p

p (at h

=0.4

5m) [

Pa]

Experimental dataVdotleak = 0 m3/h

Vdotleak = 8.6397 m3/h

Vdotleak = 15.9794 m3/h

Fig. 6 Pressure difference �pp(0.45m) for the unisolated single-wall case

which contains the diagonal elements

As in the single-wall case, this system is solved by matrix inversion and iteration.

4 Comparison to experimental data

The model for the single-wall setup described in Sect. 2 works reasonably well, if leak air is taken into account. As

(22)

C(2)11 = c(Tpu)mp,out +

(αA)wpi

2, C

(2)22 = (αA)wpi + (αA)wp,

C(2)33 = (αA)wp + (αA)wpo +�p2g,

C(2)44 = cp

(Tgl

)mg,out +

1

2cp(Tg)mg2p +

1

2(αA)wpo +

1

2(αA)wgi,

C(2)55 = (αA)wgi + (αA)wg +�p2g, C

(2)66 = (αA)wg + (αA)wgo +�g2a.

793Heat Mass Transfer (2015) 51:787–794

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chimney is larger in this setup. In this case, smaller leak-age rates are better suited to describe the experimental data. This is plausible since the additional layer of insulating material (rockwool) is expected to reduce leakage through the pipe wall.

Results are far more inconclusive for the double-wall model described in Sect. 3. While for some setups the agreement between simulation results and experimental data is reasonable, in other setups the discrepancy is unac-ceptably large.

In general, setups with insulated liner, as shown in Figs. 9 and 10, yield reasonable agreement with the experi-ment. For σp = σg = 0.0

m3/s

m2 Pa the simulation yields flue

gas temperatures which exceed the experimental values by

about 100 °C. Changing the porosity to σp = 0.00015m3/s

m2 Pa,

which results in a volume flow of Vg2p ≈ 5 m3

h, significantly

improves the agreement between simulation and experi-ment. Further parameter-tuning could be done to obtain an even better agreement; remaining deviations can, as in the single-wall case, be mostly attributed to thermal intertia which is not included in the simulation. The influence of σg on the flue gas temperature seems to be very small.

Results are far worse for setups with insulated case, as shown in Figs. 11 and 12. Reasonable leakage rates yield flue gas temperatures which are about 100 °C too high and air temperatures which are about 100 °C too low, which indicates severe problems with the proper description of heat transfer. For such setups, also numeri-cal problems, in particular instabilities, have been repeat-edly encountered.

0 0.5 1 1.5 2 2.5 3 3.5 4

0

50

100

150

200

250

300

350

400

450

operation time [h]

T pipe

(at h

=3.9

m) [

°C]

Experimental DataVdot

a2p = 0 m3/h

Vdota2p

= 7.0637 m3/h

Vdota2p

= 13.3999 m3/h

Fig. 7 Flue gas temperature Tp(3.9m) for the insulated single-wall case

0 0.5 1 1.5 2 2.5 3 3.5 40

5

10

15

20

25

30

35

40

operation time [h]

Del

ta p

p (at h

=0.4

5m) [

Pa]

Experimental DataVdot

a2p = 0 m3/h

Vdota2p

= 7.0637 m3/h

Vdota2p

= 13.3999 m3/h

Fig. 8 Pressure difference �pp(0.45m) for the insulated single-wall case

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

50

100

150

200

250

300

350

400

450

operation time [h]

T pipe

(at h

=3.9

m) [

°C]

Experimental DataVdot

g2p = 0 m3/h, Vdot

a2g = 0 m3/h

Vdotg2p

= 5.0779 m3/h, Vdota2g

= 0 m3/h

Vdotg2p

= 0 m3/h, Vdota2g

= 4.8687 m3/h

Vdotg2p

= 5.0378 m3/h, Vdota2g

= 4.5026 m3/h

Fig. 9 Flue gas temperature Tp(3.9m) for double-wall chimney with insulated liner

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

20

40

60

80

100

120

140

operation time [h]

T gap (a

t h=0

.45m

) [°C

]

Experimental dataVdot

g2p = 0 m3/h, Vdot

a2g = 0 m3/h

Vdotg2p

= 5.0779 m3/h, Vdota2g

= 0 m3/h

Vdotg2p

= 0 m3/h, Vdota2g

= 4.8687 m3/h

Vdotg2p

= 5.0378 m3/h, Vdota2g

= 4.5026 m3/h

Fig. 10 Air temperature Tg(0.45m) for double-wall chimney with insulated liner

794 Heat Mass Transfer (2015) 51:787–794

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5 Conclusions and outlook

Even components which are tight according to engineer-ing standards still admit a considerable amount of leak air. This fact has to be taken into account for calculations and simulations of chimney systems, even for systems which, according to standard specifications, qualify as room inde-pendent (and indeed have a significantly lower demand of room air).

The one-dimensional model presented in this arti-cle seems to grasp certain features of the system in a

satisfactory manner, but in some setups the discrepancy between model predictions and experimental data is large. Some deviations can be explained by the absence of ther-mal masses in the quasi-stationary calculation. This par-ticular problem could be eliminated by setting up a fully dynamical simulation which includes heat storage as well.

A more serious issue is the yet unsolved problem of heat transfer coefficients for the asymmetrically heated annular gap. Here some progress on theoretical grounds is required in order to improve the model or at least obtain a reliable estimate for systematic errors. Maybe a two- or three-dimensional model (possibly employing CFD meth-ods) might be required to obtain accurate results.

A further problem is the fact that the current model relies on experimental data for setting some boundary conditions. In particular the fluctuations in the velocity data are large, which might be an additional source of problems. Here it seems desirable to develop an advanced combustion model which can be coupled to the chimney system. This would allow to study the influence of chimney height, thickness of the insulating layers and possibly other parameters on the functionality of the system.

Acknowledgments The authors are grateful to Schiedel AG, in par-ticular to Gerald Steinecker, for the excellent cooperation during the research project.The model has been developed in the project FLOWS within the framework of the competence center Bioenergy 2020+. The competence center Bioenergy 2020+ is supported in the frame-work of COMET—Competence Centers for Excellent Technologies by BMVIT, BMWFJ and the provinces of Burgenland, Niederöster-reich and Steiermark. The program is operated by the FFG.

References

1. Brussels European Council 2007 March 8/9 Presidency Con-clusions, see http://ec.europa.eu/clima/policies/package/index_en.htm for details and supplementary documentation

2. Pointner C, Lichtenegger K, Hebenstreit B (2012) Flows—future log wood stove: untersuchung eines doppelwandigen Edelstahl–Schornsteinsystems für den raumluftunabhängigen Ofenbetrieb final report for project C-I-1-5-3 (Graz Wieselburg: Bioenergy 2020+)

3. Lichtenegger K, Hebenstreit B, Pointner C (2013) Leak air in a double-wall chimney system. In: Journal of physics: conference series, vol 410, p 012059

4. Verein Deutscher Ingenieure VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen (eds) (2002) VDI-Wärmeatlas, 9th edn. Springer, Berlin

5. Mitrovic J (2005) Wärmeübergang im konzentrischen Ring-spalt bei unterschiedlichen Wandtemperaturen. Chem Ing Tech 77:1618–1620

0 1 2 3 4 5 6 7 8

50

100

150

200

250

300

operation time [h]

T pipe

(at h

=3.9

m) [

°C]

Experimental dataVdot

g2p = 0 m3/h, Vdot

a2g = 0 m3/h

Vdotg2p

= 5.6409 m3/h, Vdota2g

= 0 m3/h

Vdotg2p

= 0 m3/h, Vdota2g

= 2.9925 m3/h

Vdotg2p

= 5.7269 m3/h, Vdota2g

= 3.0809 m3/h

Fig. 11 Flue gas temperature Tp(3.9m) for double-wall chimney with insulated case

0 1 2 3 4 5 6 7 80

50

100

150

200

250

operation time [h]

T gap (a

t h=0

.45m

) [°C

]

Experimental dataVdot

g2p = 0 m3/h, Vdot

a2g = 0 m3/h

Vdotg2p

= 5.6409 m3/h, Vdota2g

= 0 m3/h

Vdotg2p

= 0 m3/h, Vdota2g

= 2.9925 m3/h

Vdotg2p

= 5.7269 m3/h, Vdota2g

= 3.0809 m3/h

Fig. 12 Air temperature Tg(0.45m) for double-wall chimney with insulated case