International Journal of Heat and Mass Transfer 55 (2012) 7760–7771

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International Journal of Heat and Mass Transfer

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Performance analysis of metallic concentric tube recuperator in parallelflow arrangement

Harshdeep Sharma a,⇑, Anoop Kumar b, Varun b

a Department of Mechanical Engineering, School of Engineering & Technology, Galgotias University, Greater Noida, UP, Indiab Department of Mechanical Engineering, NIT-Hamirpur, HP, India

a r t i c l e i n f o

Article history:Received 1 December 2011Received in revised form 3 July 2012Accepted 31 July 2012Available online 23 August 2012

Keywords:Thermal radiationHeat transferRecuperatorConcentric shells

0017-9310/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.07

⇑ Corresponding author.E-mail address: tech_2000@indiatimes.com (H. Sh

a b s t r a c t

A performance model for parallel flow arrangement in metallic concentric tube recuperator that can beused to utilize the waste heat in the temperature range of 1100–1800 K is presented. The arrangementconsists of metallic concentric shells wherein flue gases pass through the inner shell and air to be pre-heated passes through annular gap in the same direction. The recuperator height is divided into small ele-ments and an energy balance is performed on each element. Necessary information about axial shell-surface, gas and air temperature distribution, and the influence of operating conditions on recuperatorperformance is obtained. The recuperative effectiveness is found to be increased with increasing inletgas temperature and with decreasing fuel flow rate. The present model provides a valuable tool for metal-lic concentric tube recuperator performance considerations in parallel flow arrangement.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

In most of the high temperature furnace based industries viz.,glass, aluminium, and steel, almost 30–70% of the available heatis wastefully discharged in the flue gases resulting in decreasedplant efficiency, economic losses and increased pollution due tounutilized heat that is discharged into the atmosphere [1]. A por-tion of this waste heat at high temperature is recovered by employ-ing a radiation recuperator. Within the recuperator, heat istransferred from the products of combustion to the air predomi-nantly by radiation. If recuperators are used with industrial fur-naces then fuel consumption will reduce and furnace efficiencywill increase by preheating the combustion air utilizing heat fromthe furnace exhausts. The selection of a recuperator depends on anumber of factors viz., type of furnace, type of operation, furnacecapacity burner make, type, size, no. of burners, fuel used, fluegas temperature, discharge volume and pressure of blower, fluegas exit duct diameter, chimney height etc. [2,3].

Fig. 1 shows the schematic diagram of metallic concentric tuberecuperator. The device consists of concentric tubes, with fluegases at temperatures up to 1800 K [4] flow through the inner tube,while the combustion air is preheated as it flows through the annu-lus. Heat transfer to the wall of the inner shell is dominated byradiative emission from the large volume of combustion gas withinthe tube, while heat transfer to the air is exclusively by convectionfrom the inner and outer surfaces of the annulus.

ll rights reserved..084

arma).

Radiation recuperators have undergone evolutionary changes intheir designs after they were introduced in the early twentiethcentury to accommodate improved heat transfer, better heat resis-tant materials, retaining strength at high temperatures and simpleconstruction for easier assembly and installation. The advanceshave generally been funded directly by the industry. Jacobs [5] pro-posed a design in which the heat transfer agents before inlet toannular passage, were made to pass through a channel consistingof vanes so as to impart twisting motion to increase the heat trans-fer rate. Earlier recuperators were less efficient when operated atless than their rated load. Schack [6] proposed a simple construc-tion to overcome the drawback without any danger of breakdownand without sacrificing the efficiency of operation. Radiation recu-perators due to their large passageways were difficult to manufac-ture as a single unit. Seehausen [7] proposed a new efficient modelhaving more strength at high temperatures and was easier toassemble. Recuperator surfaces suffer considerable deformationand degradation due to excessive operating temperatures. White[8], proposed an additional annular air passage to lower downthe excessive recuperator surface temperatures. Jacobs [9], pro-posed a new recuperator design with a series of ribs to avoid buck-ling and bulging of the inner tube material.

Though the radiation recuperators have been in use for a longwhile now yet there are only a few studies available that would re-veal the effect of operating and design conditions on recuperatorperformance. Loginov and coworkers [10] developed a computermodel using average values of heat transfer coefficients and with-out proper treatment of gaseous emission. Kim [11] developed amodel for parallel flow arrangement assuming adiabatic outer

Nomenclature

Af flow cross sectional area (m2)Cp specific heat (kJ kg�1 K�1)dx elemental height of recuperator (m)D tube diameter (m)E enthalpy (kJ/kg)hc convective heat transfer coefficient (W m�2 K�1)hr radiative heat transfer coefficient (W m�2 K�1)k thermal conductivity (W m�1 K�1)Lm geometric mean beam length (m)m mass flow rate (kg s�1)n number of isothermal elementsNu Nusselt numberp total pressure (Pa)pa partial pressure (Pa)pCO2 partial pressure of CO2

pH2O partial pressure of H2OPr Prandtl numberr tube radius (m)Re Reynolds numberRa Rayleigh numberT absolute temperature (K)

Subscriptsa Air

ai air inletao air outletc convectiong flue gasgi gas inletgo gas outleti element designationin insulationinr inner shellk conductionotr outer shellx axial directionr radial directionrad radiation

Greek lettersa absorptivitye emissivityb temperature coefficient of volume expansionl absolute viscosity (N s m�2)m kinematic viscosity (m2 s�1)r Stefan–Boltzmann constant (W m�2 K�4)n Effectiveness

H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771 7761

shell, but the results of the model could not be verified. The presentstudy shows a simplified yet comprehensive model of radiationrecuperator in parallel flow arrangement. This model is based onaxially dividing the exhaust gas, air, and annular walls into isother-mal zones and formulating energy balance equations to determinethe axial distribution of the zone temperatures [12,13].

2. Modeling and governing equations

Fig. 2 shows the model of a parallel flow radiation recuperator.The recuperator is divided axially into n isothermal elements. Theelements of the flue gas inside the inner tube are represented by

Fig. 1. Schematic diagram o

Tg,i and the elements of the air inside the annular space are repre-sented by Ta,i. The surface elements are represented by Tj,i, where jrepresents the surface and i represents the number of the zone orelement.

The governing equations for heat transfer problem of a single-pass, parallel-flow metallic concentric tube recuperator are devel-oped. The outlet temperatures of both the fluids as well as the heattransfer capabilities on each side of the exchanger can then bedetermined with the help of these equations. Two distinct con-trol-volumes (Fig. 1) are considered for heat transfer analysis be-tween the high temperature flue gas and the preheated air. Thegoverning equations for control-volumes and control-surfaces aregiven as follows:

f radiation recuperator.

Fig. 2. Radiation recuperator (half section) shows various heat transfer coefficients and their direction and temperature locations.

7762 H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771

Continuity equation for control volume:

@q@tþ 1

r@ðqrbV rÞ@r

þ @ðqbV xÞ

@x¼ 0 ð1Þ

Momentum equation for control volume in axial direction:

q@ bV x

@tþ bV r

@ bV x

@rþ bV x

@ bV x

@x

!¼�@P

@xþl @2 bV x

@r2 þ1r@ bV x

@rþ@

2 bV x

@x2

!þ Fx

ð2Þ

Momentum equation for control volume in radial direction:

q@ bV r

@tþ bV r

@ bV r

@rþ bV x

@ bV r

@x

!¼�@P

@rþl @2 bV r

@r2 þ1r@ bV r

@r�bV r

r2 þ@2 bV r

@x2

!þ Fr

ð3Þ

Energy equation for control volume:

qCp bV r@T@rþ bV x

@T@x

� �¼ k

@2T@r2 þ

1r@T@rþ @

2T@x2

!ð4Þ

Energy equation for control surface:

1r@

@rr@T@r

� �þ @

@x@T@x

� �þ _q ¼ qc

k@T@t

ð5Þ

The geometrical configuration and operating parameters in thepresent model are known. Some assumptions have been taken forsimplifying these equations. The recuperator operates under stea-dy-state conditions. In each isothermal zone the velocity and tem-perature of each fluid is uniform. The fluid flow rate is uniformlydistributed over the cross-section on each fluid side. The longitudi-nal heat conduction and radial temperature gradients in recupera-tor walls as well as in the fluids is negligible. The flue gas is a graygas and the gaseous radiation is dominated by emission andabsorption due to CO2 and H2O vapor [14,15]. Radiation from theupstream and downstream surroundings is not considered.

After applying the assumptions, the continuity equation (Eq.(1)) for steady flow in longitudinal direction and for the ith ele-ment takes the following form:

_mi ¼ qi � Af � v i or ð6Þ

va;i ¼ _ma=ðqa;i � AfaÞ for air and

vg;i ¼ _mg=ðqg;i � AfgÞ for fluegas

Due to the temperature variation, the density of flue gases andcombustion air varies along the height of the recuperator. For thepresent recuperator conditions the following relations of flue gasdensity (qg = f(Tg)) and combustion air density (qa = f(Ta)) [16] havebeen used.

qg ¼ 13:9237� 6:62658� 10�2 � Tg þ 1:38589� 10�4 � T2g

� 1:58462� 10�7 � T3g þ 1:05672� 10�10 � T4

g

� 4:0731� 10�14 � T5g þ 8:3068� 10�18 � T6

g � 6:7821

� 10�22 � T7g ð7Þ

qa ¼ 1:9484� 10�19 � T6a � 1:8437� 10�15 � T5

a þ 7:0661

� 10�12 � T4a � 1:4089� 10�8 � T3

a þ 1:5624� 10�5

� T2a � 0:0095� Ta þ 2:93076 ð8Þ

Similarly other physical properties viz., viscosity, specific heatand thermal conductivites can be expressed in terms of tempera-ture [16]. For the known values of mass flow rates and cross sec-tional area of air and fluegas passages, the respective velocity canbe determined using Eqs. (7) and (8).

The boundary conditions for fluegas control volume is pre-scribed by

Eg;i ¼ Eg;iþ1 þ Q rad;g!1 þ Qc;g!1 ð9Þ

H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771 7763

The boundary conditions for air control volume is prescribed by

Ea;i þ Qc;2!a ¼ Ea;iþ1 þ Qc;a!3 ð10Þ

The boundary conditions for control surface are prescribed bythe heat fluxes at the boundary.

at r ¼ r1; Qrad;g!1 þ Q c;g!1 ¼ Q k;1!2 ð11Þ

at r ¼ r2; Qk;1!2 ¼ Q rad;2!3 þ Q c;2!a ð12Þ

at r ¼ r3; Qrad;2!3 ¼ Q c;a!3 þ Q k;3!5 ð13Þ

at r ¼ r5; Qk;3!5 ¼ Q c;5!1 þ Qrad;5!1 ð14Þ

After applying assumptions and boundary conditions to Eqs.(1)–(5), the equations are written for ith element of recuperator.

The equation for ith element of gas control volume and air con-trol volume can be written as;

mgCpg;idTg

dx¼ �pD1ðhr1;i þ hc1;iÞ ðTg;i � T1;iÞ ð15Þ

maCpa;idTa

dx¼ pðhc2;iD2T2;i þ hc3;iD3T3;i � ðhc2;iD2

þ hc3;iD3ÞTa;iÞ ð16Þ

The Eqs. (15) and (16) are the differential equations. By usingTaylor Series, the two differential equations can be expressed inthe algebraic form as follows:

Tg;iþ1 ¼ Tg;i �pD1dxmgCpg;i

ðhc1;i þ hr1;iÞðTg;i � T1;iÞ ð17Þ

Ta;iþ1 ¼ Ta;i

þ pdxmaCpa;i

hc2;iD2 T2;i � Ta;i� �� �

� hc3;iD3 Ta;i � T3;i� �� �� �

ð18Þ

There are four heat exchanging surfaces in the present analysis andafter applying energy balance to the each elemental surface, fourEqs. (19)–(22) involving the surface temperatures T1,i, T2,i, T3,i, T5,i

are obtained as under.

T1;i ¼ ððhr1;i þ hc1;iÞD1 Tg;i þ 2jinrT2;iÞ=ððhr1;i þ hc1;iÞD1

þ 2jinrÞ ð19Þ

T2;i ¼ hc2;i D2 Ta;i þ hr2;i D2 T3;i þ 2jinrT1;i� �

= hc2;i D2 þ hr2;i D2 � 2jinr� �

ð20Þ

T3;i ¼ hr2;i D2 T2;i þ hc3;i D3 Ta;i þ 2jotrT5;i� �

= 2jotr þ hr2;i D2 þ hc3;i D3� �

ð21Þ

T5;i ¼ 2jotrT3;i þ D5 T1ðhr5;i þ hc5;iÞ� �

= 2jotr þ D5ðhr5;i þ hc5;iÞ� �

ð22Þ

where jinr = kinr/ln(D2/D1), and jotr = ((ln (D4/D3)/kotr) + ln(D5/D4)/kin))�1The governing Eqs viz. (17)–(22) contain geometrical param-eters, thermal conductivities of the recuperator surfaces, and con-vective and radiative heat transfer coefficients in addition to thetemperatures. Since the heat transfer coefficients are not the prop-erties and are the functions of temperatures [17,18], and vary alongthe recuperator height, these are to be determined separately foreach element of the recuperator.

2.1. Radiation heat transfer coefficients

In high-temperature applications, the products of combustionare not transparent to radiation but may absorb, emit, and scatter

radiation. At the wavelengths that correspond to thermal radiationat typical temperatures, transitions in the vibrational and rotationmodes of molecules have the greatest influence on radiativeabsorptance. Such transitions can be driven by photons only whenthe molecule has some asymmetry i.e. the dipole moment. Thus,monatomic and symmetrical diatomic molecules are transparentto thermal radiation. The major components of air–N2 and O2 –are therefore nonabsorbing; so, too, are H2 and such monatomicgases as argon. Asymmetrical molecules like CO2 and H2O, the ma-jor constituents of products of combustion, on the other hand, eachabsorb emit radiation in limited spectral ranges, called bands[14,15]. To obtain effective values of the emittance or absorptance,a summation over all of the radiation bands is necessary. For engi-neering calculations an approximate method developed by Hotteland Sarofim [12], yields results of satisfactory accuracy. The totalemissivity, eg, of the flue gas layer having isothermal temperatureTg, and thickness Lm is given by the correlation [12]

egðpaLm; p; TgÞ ¼ f1ðpaLm; TgÞ � f2ðp;pa;paLmÞ ð23Þ

The total absorptance ag, of the flue gas is estimated from thecorrelation [12] and radiation heat transfer coefficient is thus cal-culated by

ag ¼ Tg=T1� �1=2 � eg paLmT1=Tg ; p; T1

� �ð24Þ

hr1;i ¼ r� ð0:5Þ � ð1þ e1Þ � eg T4g;i � ag T4

1;i

� �= Tg;i � T1;i� �

ð25Þ

The radiation heat transfer coefficient between the two graysurfaces-2 and 3 becomes as:

hr2;i ¼ r� T32;i þ T3

3;i þ T2;iT23;i þ T2

2;iT3;i

� �=fe;s ð26Þ

where

fe;s ¼ ðe2Þ�1 þ ðf2�3Þ�1 � 1� �

þ ðA2=A3Þ � ððe3Þ�1 � 1Þ� �

The shape factor f2�3 [15] of the adjoining annular elements (2–3) for an elemental height L/n is given by

f2�3 ¼0:5ðS1S2 � 1ÞpðS1 � S2Þ

cos�1 S1 � S2

S1 þ S2

� �� �þ 1� 0:5pS1S2

pðS1 � S2Þ

� �� 2

ptan�1ðS1S2Þ0:5

� �

þð1þ S2

1Þð1þ S22Þ

� �0:5

pðS1 � S2Þtan�1 ð1þ S2

1ÞS2

ð1þ S22ÞS1

!0:50B@

1CA ð27Þ

where

S1 ¼ nðr þ 3þ r2Þ=L and S2 ¼ nðr3 � r2Þ=L

The radiation heat transfer coefficient for the elemental area ofthe external surface to the surroundings at the ambient tempera-ture T1 may be obtained by:

hr5;i ¼ r� e5 � T35;i þ T5;i T2

1 þ T1 T25;i þ T3

1

� �ð28Þ

2.2. Convective heat transfer coefficients

Convective heat transfer coefficient depends on a number offactors and variables. In general, it is a function of the size, shapeand temperature of the surface, fluid dynamics, fluid regime, tem-perature and the physical properties of the fluid etc. [17]. In engi-neering practice the Nusselt number for flow in conduits is usuallyevaluated from empirical equations based on experimental results.For fully developed turbulent flow in circular tubes for high tem-peratures, Nusselt number is of the form Nu = f(k, Re, Pr) where k

Fig. 3. Flow diagram of solution procedure.

7764 H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771

is the friction factor that can be determined from Eqs. (2) and (3). Anumber of such correlations are well documented in the availableliterature [18].

For the present recuperator condition of fully developed turbu-lent flow in the inner tube, Gnielinski [19] correlation for the con-dition of forced turbulent convection from gas side to wall havebeen used;

Table 1Predicted and observed values of air outlet temperature.

Mass flow rate Geometrical parameters

ma mg D1 gap L

kg/s kg/s M m m

0.87 0.92 0.7 0.04 81.70 1.81 1.00 0.05 162.31 2.45 1.50 0.05 143.25 3.44 1.75 0.05 17

Nu ¼ k ðRe� 1000ÞPrð Þ=8� 1þ 12:7ðk=8Þ0:5 Pr0:67 � 1� �� �

ð29Þ

where, k = 1/(1.82(ln (Re) - 1.64))2 and Re = q � m � D/l and q and mare calculated using Eqs. (1) and (7).

For the flow of air through the annulus, the forced convectionheat transfer coefficient has been calculated by using empiricalrelationship [20] given by

Fluegas inlet temperature Air outlet temperature

Tgi Tao

K Predicted K Observed K

1648 807 8151648 969 9851648 982 10101648 827 873

Table 3Values of constant parameters used in recuperator.

S. No. Parameter Value Units

1. Height of the recuperator 12 m2. Inner radius of inner shell 0.5 m3. Outer radius of inner shell 0.503 m4. Inner radius of outer shell 0.553 m5. Outer radius of outer shell 0.556 m6. Thickness of insulation 0.15 m7. Mass flow rate of air 1.25 kg s�1

8. Mass flow rate of flue gas 1.33 kg s�1

9. Thermal conductivity of inner and outershell

35 W m�1 K�1

10. Thermal conductivity of insulating material 0.036 W m�1 K�1

11. Ambient temperature 303 K12. Inlet air temperature 303 K

Table 2Percentage deviation between the observed and predicted values.

Air outlet temperature Percentage error (%) Mean percentage error (%)Tao (K)

Predicted Observed

807 815 1.00 2.77969 985 1.65982 1010 2.85827 873 5.56

H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771 7765

Nu ¼ 0:023ðReÞ0:8ðPrÞ0:4ðD3=D2Þ0:45 ð30Þ

where Re = q � v � Dh/l and q and m are calculated using Eqs. (1)and (8).

The heat lost by convection from the external surface to, sur-roundings is by the natural convection and the respective heattransfer coefficient, hc5, can be obtained by using the following cor-relation [21];

Nu ¼ 0:68þ 0:67Ra1=4 1þ ð0:492=PrÞ9=16� ��4=9

ð31Þ

2.3. Effectiveness of the recuperator

After the determination of outlet temperatures of flue gas andcombustion air, the effectiveness [22] of the recuperator is calcu-lated by the expression for effectiveness

Fig. 4. Temperature distribution of flue gas and air for differen

n ¼ ðTao � TaiÞ=ðTgi � TaiÞ ð32Þ

3. Procedure

It is clear that, the first element has four unknown temperatureswhereas all the other elements have six unknown each. For n num-ber of elements, the number of equations will be 6n � 2 with 6n � 2variables to be solved. The above equations are solved by iterativemethod. For the initial element, the surface temperatures viz., T1,T2, T3, and T5 are assumed based on the flue gas and air inlet temper-atures. The physical properties and various heat transfer coeffi-cients are then determined using Eqs. (23)–(31). Eqs. (19)–(22)are then used to get new values of surface temperatures. The stepsare repeated until the convergence criteria of difference of two suc-cessive values of T1 6 0.01 K is achieved. The flue gas and air tem-peratures for the next element are then obtained from Eqs. (17)and (18) respectively. The sequence of calculations for predictingthe performance of recuperator is summarized as shown in Fig. 3.

4. Results and discussion

To visualize the effect of the number of elements on the results,calculations were done using operating and design conditions asgiven in Table 3. The values of Tao, n were found to increase andthe values of Tgo were found to decrease with increasing n, andthe changes were less than 2% for n P 10.

4.1. Validation of the model

Industrial data for the double shell radiation recuperators em-ployed in the fibre glass industry has been reported by Seehausen[23]. The same has been used to validate the present model.

The developed computer code was run for a set of input data gi-ven in Table 1. The predicted and observed values of air outlet tem-perature from the recuperator are also shown in the Table 1. Thepercentage error of air outlet temperature between the observedand the predicted values to that of the observed value is given inTable 2.

It is observed that the percentage deviation lies from 1.00 to5.56. The mean percentage deviation is 2.77. Thus the developedmodel can be used to predict the performance of parallel flow radi-ation recuperator.

t inlet flue gas temperatures along the recuperator height.

7766 H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771

After the mathematical analysis and software development, theeffect of main operating variables viz., inlet temperature and massflow rate of the flue gas on recuperator performance has been stud-ied. Glass wool has been selected as the insulating material in thepresent work. Fuel oil no. 2 having the flash point at 311 K is usedand the air–fuel ratio for fuel has been taken as 16:1. The values ofthe parameters which were not varied while executing the pro-gram for calculating heat transfer coefficients are given in Table 3.

Fig. 4 shows the effect of Tgi on gas and air temperature distri-butions. For Tgi = 1173 K, the air outlet temperature is 669.4 K, forTgi = 1473 K the air outlet temperature is 848.8 K and for Tgi

= 1773 K the air outlet temperature is 1031.4 K. The correspondingvalues of outlet temperatures of the flue gas are 910 K, 1084.4 Kand 1256.6 K, respectively. As expected that for higher inlet fluegas temperature the air outlet temperature also remains higheralong the height of the recuperator. Also for Tgi = 1773 K, about

Fig. 5. Effect of different inlet flue gas tem

Fig. 6. Effect of inlet flue gas temperature o

88% of the total drop has been observed in a height of first 9 mwhile the balance of the temperature drop is found in the remain-ing 3 m height. This may be attributed to higher temperatures pre-vailing in the initial part of recuperator.

A higher inlet temperature of flue gas results into more heattransfer to surface-1 (Fig. 5). Along the height of the recuperatorwith continuous drop in temperature of flue gas, the temperatureof surface-1 also decreases. Contrary to the decreasing trend oftemperature of inner tube surface-1, the temperature of inner sur-face of outer shell (T3) increases along the recuperator height. Thiscan be attributed to increase in the heat transfer coefficients hc2

and hr2 in the annular space. Figs. 6 and 7 shows the variation ofconvective and radiative heat transfer coefficients along the recu-perator height for different inlet flue gas temperatures. Due tomore heat transferred to surface-1, hr1 and hc1 also increases.However there is marked increase in the values of hr1 compared

peratures on surface temperatures.

n convective heat transfer coefficients.

H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771 7767

to hc1. The irregular variation of hr1 along the recuperator heightcan be explained from temperature dependent gaseous emission.The higher the temperature the higher will be the emission. More-over gaseous emissivity and absorptivity are a function of gas aswell as surface-1 temperature (Eqs. (23) and (24)). Also the tem-perature T1 remains higher at the entry zone for less heat is trans-ferred to adjacent air zone. Moreover the thermal conductivity ofthe recuperator material is a nonlinear function of temperature[23]. Due to these reasons the slope of hr1 changes abruptly. Thisvariation is more pronounced at higher fluegas inlet temperature(Figs. 7 and 12) and is a typical nature of parallel flow configuration[16]. The value of hr2 increases with increase in flue gas inlet tem-perature due to an increase in the surface temperatures of theannular space since hr2 is function of third power of annular sur-face temperatures (Eq. (26)). The lower values of hc1 indicate that

Fig. 7. Effect of inlet flue gas temperature

Fig. 8. Effect of increasing inlet flue gas temperature on o

major portion of heat transferred from flue gas to surface-1 is byradiation. Also with increase in Tgi, the film temperature in theannular space rises which result in change in the physical proper-ties of combustion air and due to which hc2 increases (Fig. 6). Theheat transfer to air is due to convection from both surfaces of annu-lar gap. The result indicates a continuous rise in air temperaturealong the recuperator height (Fig. 4). It is also evident that rateof change of air temperature is large compared to that of flue gasesalong the height. This is due to the fact that mass flow rate and spe-cific heat of air are less compared to those of flue gas. Consequentlythe gradients of air temperature profile are more to those of fluegases.

For Tgi = 1373 K, air outlet temperature is 793.1 K and it be-comes 1031.4 K against the flue gas entry temperature of 1773 K.Accordingly, the recuperator effectiveness is found to increase

on radiative heat transfer coefficients.

utlet air and flue gas temperatures and effectiveness.

7768 H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771

from 0.52 to 0.59 (Fig. 8).The difference in the outlet temperaturesof flue gas and air for all the Tgi values has been found to be 232 Kapproximately.

The results clearly emphasize that for a higher inlet tempera-ture of flue gas, the temperatures of all the surfaces remain rela-tively high. Undoubtedly, this would require better and costlierheat resistant materials for the recuperator surfaces. But to havea better heat recovery from waste flue gases, the gas inlet temper-ature should be as near the melting temperatures prevailing in thefurnaces, as possible. For this the recuperators should be installednear the furnace exit.

Due to the constant air–fuel ratio, the mass flow rate of flue gasis proportional to the mass flow rate of air burned. The effect ofmass flow rate of air and flue gas has been studied to see theirinfluence on the recuperator effectiveness as well as to predictthe temperature distributions for the flue gas, air, and the surfaces.The data for the present analysis is same, only difference being thathere inlet fluegas temperature is kept constant at 1648 K and massflow rates are varying. Calculations are done for the following val-ues of mass flow rates.

Fig. 9. Temperature distribution of flue gas and air for differ

Fig. 10. Effect of different mass flow ra

Mass flow rate of air, ma = 1.0, 2.0, and 3.0 kg/sMass flow rate of flue gas, mg = 1.06, 2.13, and 3.19 kg/sThe temperature distribution of the flue gas, and air at an inter-

val of 1.5 m height for mass flow rates of 1.0, 2.0, 3.0 kg/s areshown in Fig. 9.

As is evident, with the increase in the air flow rate there is a cor-responding increase in the flow rate of the flue gas. With the in-crease in the flow rate, the velocity of the flue gas and airincreases, but their residence time in the recuperator decreases.This in turn causes an increase in the Reynolds numbers, therebyincreasing the values of hc1, and hc2 as shown in the Fig. 11. An in-crease in the flow rate undoubtedly results in more heat transferfrom gas to the surface-1. However, due to the large cross-sectionalarea of the inner-shell, the effect of mass flow rate on the gas sideis very little. This is exhibited by the relatively small changes in thevalue of hc1 and hr1 (Fig. 12). On air side i.e., in the narrow annularduct the air velocities are relatively higher. Due to this, the increasein the value of convection coefficient, hc2, is more pronounced. Byincreasing the air flow rate from 1.0 to 3.0 kg/s, the increase in hc2

is almost 2.3 times. In spite of the increase in the convection coef-

ent mass flow rates of air along the recuperator height.

tes of air on surface temperatures.

Fig. 11. Effect of mass flow rate of air on convective heat transfer coefficients.

H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771 7769

ficients (hc1, and hc2), the temperatures of the surfaces 1, and 3, de-crease (Fig. 10). The reason for the reduction in the surface temper-ature is the decrease in the fluids residence time. The drop in thesurface temperature T3 is far more to that of temperature T1. In factthe temperature T1 slightly increases in the exit region of the recu-perator at higher flow rates. This may be attributed to the fact thatin the exit region fluegas velocity decreases due to an increase inthe density resulting in increased residence time of flue gases. Thusthe temperature of the adjoining surface-1 increases slightly. Thisis a typical nature of parallel flow configuration for larger recuper-ator heights as no such behavior is observed in counterflow config-uration [16]. It has been noted that due to the increase in the airflow rate, the convective heat transfer from the surface-2 increases.This is clear from the proportion of increase in the value of hc2.Along with the convection coefficients the heat lost by the fluegas,the heat gained by the air, and the temperatures difference, (Tg�Ta)

Fig. 12. Effect of mass flow rate of air on

also increase with the increasing flow rates. But due to increase inthe fluids velocities, there is an increase in the gas temperaturesand fall in the air temperatures throughout the recuperator(Fig. 13). In the present analysis as the gas flow rate is increasedfrom 1.06 to 3.45 kg/s, an increase of 143 K in the fluegas outlettemperature and a reduction of 197.6 K in the air outlet tempera-ture has been observed. Correspondingly, there is a decrease inthe recuperator effectiveness from 0.592 to 0.404 as shown inthe Fig. 13.

It should be noted that, although mass flow rates strongly influ-ences recuperator performance, its value will be determined by thefurnace, not the recuperator operating requirements. In practice,an increased air flow rate through the annulus is one of the meth-ods, commonly employed to protect the recuperator from over-heating. For inlet fluegas temperature Tgi = 1648 K and for massflow rate of 1 kg/s, the result of air outlet temperature, Tao is

radiative heat transfer coefficients.

Fig. 13. Effect of increasing mass flow rate of air on outlet air and flue gas temperatures and effectiveness.

7770 H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771

980.3 K. Thus the net gain in air temperature, DTa is 677.3 K. Thistemperature gain will be utilized in the combustion of fuel oil.Thus the recuperator is found to be useful in other ways than justimproving the overall efficiency of the unit. It will reduce the timerequired for fuel ignition, thereby improving fuel combustion. Also,the lower grade viscous oil can be used for such a gain in air tem-perature which will further result in fuel savings.

4.2. Effect of design variables

The design parameters which affect the recuperator perfor-mance are inner tube diameter (D1), annular gap (gap) and heightof the recuperator (L). As can be seen from Fig. 14, the recuperatoreffectiveness increases with increase in diameter and recuperatorheight. It is also observed that there exists a value of annular gapfor which recuperator effectiveness is maximum. With an increasein inner tube diameter and recuperator height, the surface area of

Fig. 14. Effect of design parameter

the primary heat exchanging surface-1 increases due to whichthere is reduction in flue gas exit temperature and increase in airexit temperature and consequently effectiveness increases. An in-crease in annular gap results in decrease in air velocity therebyreducing heat transfer coefficients in annular space and due towhich air exit temperature decreases. For lower values of annulargap, however, decrease in flues gas exit temperature is more due towhich effectiveness increases slightly.

4.3. Effect of radiation on recuperator performance

At higher temperatures, the contribution of radiation heattransfer from flue gases to the total heat transfer is far more whencompared to convection heat transfer. In the present model, for aninlet flue gas temperature of 1773 K and with radiation from fluegases, the recuperator effectiveness is 0.589 and without radiationthe recuperator effectiveness drops to 0.14.

s on recuperator effectiveness.

H. Sharma et al. / International Journal of Heat and Mass Transfer 55 (2012) 7760–7771 7771

5. Conclusions

A performance model has been developed for predicting theperformance of an annular radiation recuperator with parallel flowarrangement. Heat transfer is dominated by radiation emission andabsorption in the combustion gases flowing through the tubularsection of the recuperator and by convection to air flowing throughannular section. The non linear energy balance equations weresolved for axial distributions of the gas, air and surface tempera-tures, as well as recuperative effectiveness. The results are ob-tained for a height of 12 m, annular width of 0.05 m and innerradius of 0.5 m.

1. The air outlet temperature, and hence the recuperativeeffectiveness, found to increase with increasing inlet gastemperature. It decreased with increasing fuel flow rate.

2. The recuperator effectiveness for the different inlet fluegastemperatures in the range of 0.52–0.589 is obtained whichis significant enough for its use in commercial applications.

The model of this study provides a valuable tool for perfor-mance considerations. Also this would certainly help in the selec-tion of a heat recovery device viz., recuperator or regenerator fora particular application with known set of operating conditions.Although important trends may be inferred from its use, morecomparisons with different set of industrial data will establish acomplete confidence in the model.

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