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International Journal of Low Carbon Technologies 3/3

Split heat pipe heat recovery system

E. Azad

Solar Energy Lab., Iranian Research Organization for Science & Technology (IROST), 71 Forsat Ave. Ferdousi sq., Tehran-Iran

E-mail: azad_ezat@yahoo.com

Abstract This paper describes a theoretical analysis of a split heat pipe heat recovery system. The analysis is based on an Effectiveness-NTU approach to deduce its heat transfer characteristics. In this study the variation of overall effectiveness of heat recovery with the number of transfer units are presented.

Keywords effectiveness; fi ns; heat pipe; heat recovery; NTU

Nomenclature Symbol Description

A Total heat transfer area (m2 )

Afe Finned surface area (m2)

Aeo Total external surface area (m2)

C Flow-stream capacity rate (m.Cp) (W/K)

Cc Flow-stream capacity rate of cold-side fl uid (mc.Cp) (W/K)

Ce Flow-stream capacity rate of hot-side fl uid (me.Cp) (W/K)

CL Heat pipe working fl uid capacity (W/K)

Cmin Minimum of Ce or Cc

Cmax Maximum of Ce or Cc

Cp Specifi c heat at constant pressure (J/kg K)

Csf constant

Eo Overall exchanger effectiveness (dimensionless)

g Acceleration due to gravity (m/s2 )

gc Proportionality factor in Newton’s second law (kg m/Ns2)

G Exchanger fl ow-stream mass velocity (kg/m2 s)

h Heat transfer coeffi cient (W/m2 K)

J St Pr2/3

k Thermal conductivity(W/mK)

L Latent heat (KJ/kg)

m Fin effectiveness parameter (dimensionless)

mass fl ow rate, kg/s

M Molecular weight

n Number of tubes in direction of fl ow (dimensionless)

NTU Number of heat transfer units of an exchanger (dimensionless), AU Cmin

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International Journal of Low Carbon Technologies 3/3

Nu Nusselt number (dimensionless) h x

k

.

P Pressure (N/m2 )

Pr Prandtl number (dimensionless)

R Gas constant for vapour R = Ro/M

R Thermal resistances (K/W)

Ro Universal gas constant (8314 J/mol K)

Rv Heat pipe vapour thermal resistance (K/W) Re Reynolds number (dimensionless)

Sl Tube spacing in direction of fl ow (m)

St Stanton number (dimensionless)

T Temperature (K)

Ts Wall temperature (K)

t Thickness (m)

U Overall thermal conductance (W/m2 K)

h Effi ciency (dimensionless)

e Effectiveness (dimensionless)

s Surface tension of liquid-vapour interface (N/m)

e Volume fraction of solid phase

m Viscosity (N s/m2 ) s Surface tension (N/m) Subscripts C Condenser e Evaporator f Fin i Inside l Liquid

n For n row in direction of fl ow

o Outside p Pipe wall s Solid w Wall w Saturated wick 1. Introduction

It is in the fi eld of heat recovery from exhaust gas that the largest benefi t from investment in energy conservation equipment can be realized. There are a consider-able number of uses to which this waste heat from exhaust gas can be put, and these depend to a large extent on the temperature and condition of the exhaust gases or air, the heat recovery equipment used, and the economic assessment of the overall system performance [1].

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International Journal of Low Carbon Technologies 3/3 It is possible to categorize four main application areas for waste heat recovery equipment.

(i) Gas-to-gas (ii) Gas-to-liquid (iii) Liquid-to-gas (iv) Liquid-to-liquid

The application of heat pipe for heat recovery is not new. D.A.Reay [1] has reported a review of gas-to-gas heat recovery systems. Azad and Geoola [2] inves-tigated the variation of overall effectiveness with Ce/Cc for different values of tube spacing normal to the direction of fl ow; number of fi ns per metre; fi n thickness and evaporator lengths. Peretz and Horbaniuc [3] applied the effectiveness-NTU method to study the infl uence of geometry on heat pipe heat recovery (HPHR) operation. Shao et al. [4] have presented a study of pressure loss and heat recovery effi ciency of heat pipe units for natural ventilation, using both experimental and computational approaches. It is found in their research that heat recovery effi ciency decreased with increasing air velocity. The effectiveness-NTU model for gravity-assisted air-to-air HPHR was applied by Azad and Geoola [2]. As in the log mean temperature difference method, this requires the total thermal resistance of the HPHR. For internal resistances, the Rohsenow correlation inside the evaporator was used. For the interior condenser resistance, Azad and Geoola [2] developed a new correlation for condensing water vapour on vertical carbon-steel. Azad et al. [5] extended the methodology of Azad and Geoola [2] to model water-to-air heat pipe heat exchangers. Azad et al. [6] and Azad and Gibbs [7] further extended this method to model co-axial air-to-water heat pipe heat exchanger and water-to-air heat exchanger.

Recently, Lamfon et.al [8] applied two-phase thermosyphon for extracting waste heat from the gas turbine chimney and delivering this energy to the generator of an aqua-ammonia absorption chiller. Riffat et al. [9] have applied heat pipe for ther-moelectric refrigeration. Furthermore, substitute of the conventional heat sink system with an encapsulated phase change material was found to improve the performance of the thermoelectric refrigeration system. So¨ylemez [10] studied thermoeconomic feasibility analysis yielding a simple algebraic optimization formula for estimating the optimum length of a fi nned pipe used for waste heat recovery. Li et al. [11] pre-sented the performance analysis of a multifunction heat pipe type adsorption ice maker with activated carbon–CaCl2 as compound adsorbent and ammonia as refrig-erant. Filippeschi [12] proposed particular passive wickless two-phase loop devices that are able to operate with or against gravity. Therefore, due to their considerable advantages, since the 1970s, heat pipe heat exchangers have been extensively applied in many industries such as energy engineering, chemical engineering and metallurgical engineering as waste heat recovery systems. Ong and Haider-E-Alalhi [13] described work on the hysteresis effect during start-up and cooling down of thermosyphon elements in an HPHE, using R-22, R-134a and water as working fl uids.

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International Journal of Low Carbon Technologies 3/3

The heat transfer in the system is based on the continuous cycle of the vaporiza-tion and condensavaporiza-tion process. The heat pipe can transfer a large quantity of heat with a relatively small temperature drop by the evaporation of a part of the fl uid. The vapour fl ows to the condenser, where the fl uid condenses while giving off its latent heat, caused by cooling from the outside. After condensation at the condenser section the working fl uid returns to the heated section along the wall by gravitation or capillarity, which closes the cycle. The heat pipe can be used to promote heat transfer between two gas streams. The heat pipe advantages are high heat recovery effectiveness, compactness, no moving parts, light weight, relative economy, no external power requirements, pressure tightness, no cross-contamination between streams and reliability. In selection of the working fl uid, the latent heat of the fl uid is an important parameter. The higher the latent heat of a fl uid, the higher the transfer of heat is at a lower pressure. The heat pipe is represented schematically in Fig.1.

2. Split Heat Pipe Heat Recovery (SHPHR) system description

The basic confi guration of the Split Heat Pipe Heat Recovery (SHPHR) is shown in Fig.2. The SHPHR and conventional heat pipe have the same principal function of transferring heat energy from one location to another location where heat can be rejected. It essentially comprises four components; evaporator, vapour transport line, liquid return line, and condenser.

In the SHPHR the evaporator is connected to the condenser through a piping system. The condenser section is located above the evaporator so that the condensate is returned by gravity. The vapour fl ows through a tube (vapour line) to the con-denser and condensate returns to the evaporator through a tube (liquid line) by gravity. The vapour line is connecting the top of the evaporator to the top of the condenser, and the liquid line is connecting the lower part of the condenser to the lower part of the evaporator.

The evaporator section of the heat pipe consists of one bank of externally fi nned heat pipes, the evaporator section is lined with capillary wick structure

Figure 1. Heat pipe.

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International Journal of Low Carbon Technologies 3/3 to protect the liquid against the shear stress and to keep the surface of the evaporator wet.

The SHPHR possesses all the main advantages of a conventional HPHR. The only difference between the SHPHR and conventional heat pipe heat recovery lies mainly in the separation of the evaporator and condenser. In a SHPHR the evaporator and condenser can be located in different locations.

3. Theoretical analysis

In the following analysis the water heat pipes are considered to be in a staggered arrangement with continuous aluminium fi nned circular tubing and only the

Condenser

Fins

Liquid line Vapor line

Heat pipe

Evaporator

Figure 2. Split heat pipe heat recovery system.

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International Journal of Low Carbon Technologies 3/3

inner wall of the evaporator section of the heat pipe is lined with the capillary structure. Assuming the axial heat conduction through the heat pipe walls is negligible, the following equations for steady-state operation of the heat recovery can be written.

3.1 Heat pipe evaporator external surface resistance Reo

The calculation of thermal resistances is based on analysis presented by Riffat [14]. The thermal resistance Reo exists between the air and heat pipe evaporator external surface. The total thermal resistance Reo is given by:

R h eo eo eo = 1 η (1)

3.2 Heat pipe evaporator tube wall resistance Rep

The thermal resistance across the tube wall thickness in the evaporator is as follows: R t A k A ep p eo p ei = (2)

3.3 Heat pipe evaporator wick resistance Rew

The thermal conductivity of saturated wick in kw is given by Dunn and Reay [15] as follows: kw= − kl +    β ε β ε (3) where β =

(

+

)

(

)

1 1 k k k k m l m l The resistance is then:

R t A k A ew w eo w ei = (4)

3.4 Heat pipe evaporator thermal resistance Rei

The thermal resistance due to evaporation can be given by:

R A h A ei eo ei ei = (5)

where resistances are based on outside total area of evaporator sections.

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International Journal of Low Carbon Technologies 3/3 3.5 Heat pipe vapour thermal resistance Rv

There is a pressure drop to maintain the vapour fl ow from the heat pipe evaporator to its condenser. A temperature difference therefore exists and gives rise to a thermal resistance: R RT P Q L P v v v l l v = 2∆ (5)

Rv can be normally neglected but may be important in the starting up of gas-loaded heat pipes [15].

3.6 Thermal resistance due to condensation within the heat pipe Rci

The thermal resistance at the condenser is similar to the evaporator:

R A h A ci co ci ci = (6)

3.7 Heat pipe condenser wall resistance Rcp

R t A k A cp p co p ci = (7)

3.8 Heat pipe condenser external surface resistance Rco

R h co co co = 1 η (8)

where resistance is based on outside total area of condenser sections. The overall heat transfer coeffi cients of the evaporator and condenser are:

U h t A k A t A k A A h A e eo eo p eo p ei w eo w ei eo ei ei = 1 + + + η (9) U h t A k A A h A c co co p co p ci co ci ci = 1 + + η (10)

heo and hco in Equations 1 and 8 are estimated from correlations developed by Rich [16] for continuous fi n with circular tubing. The correlations are:

ReL GS l = µ (11) Where J = St.Pr2/3 J=0 195 −L 0 35 . Re . (12)

The total surface temperature effectiveness ho estimated as follows (for evaporator sections): ηeo η fe eo fe A A = −1

(

1−

)

(13)

hfe can be calculated from equation 14:

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International Journal of Low Carbon Technologies 3/3 Evaporator section ηfe f f ml ml = tanh

( )

(14) m h k t eo f f 2= 2 (15) The same equations can be written for the condenser sections (i.e. hco).

The heat transfer coeffi cient hei can be determined from relation given by Rohse-now [17] as follows: C T T L C h T T L g g pl w s sf ei w s l c l v

(

)

=

(

)

(

)

           µ σ ρ ρ 0 5. 0.333 1 7 Pr. (16)

In equation 16, all properties are evaluated at the saturation temperature Ts, and the value of coeffi cient Csf for a variety of fl uid-surface combinations can be obtained from Rohsenow [17] and Tong [18].

The value of internal heat transfer coeffi cient in the condenser section, hci, for water vapour is calculated from Chapman [19].

For Rev≤ 50,000 Nuci=5 03

(

v

)

1 3 1 3 . Re Pr (17) For Rev≥ 50,000 Nuci=0 0265

(

v

)

0 8 1 3 . Re . Pr (18)

4. Heat transfer effectiveness

In the evaporator sections of a single row heat pipe heat recovery, the hot fl uid is in crossfl ow with the vapour fl ow inside the heat pipes. However, since the vapour inside a heat pipe is almost at constant temperature, its specifi c heat, Cp, and capacity rate, CL, become by defi nition, equal to infi nity and as a result Ce/CL= Cc/CL= 0. Therefore, the effectiveness-NTU equations for single row heat pipe heat recovery are as follows [20].

For evaporator sections:

εe1= −1 exp

(

NTUe1

)

(19)

For condenser sections:

εc1= −1 exp

(

NTUc1

)

(20)

Now for a heat pipe heat recovery with n rows of heat pipes in the direction of fl ow, the effectiveness-NTU equations are as follows [2].

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International Journal of Low Carbon Technologies 3/3 For evaporator sections:

Εen e L e e n e L e e n C C C C C = − −           − − −           − 1 1 1 1 1 1 1 1 1 ε ε ε ε ee L C (21)

For condenser sections:

Εcn c L c c n c L c c n C C C C C = − −           − − −           − 1 1 1 1 1 1 1 1 1 ε ε ε ε cc L C (22)

For Ce/CL= 0 and Cc/CL= 0 equations 21 and 22 reduce to:

Εen e n = − −1

(

1 ε1

)

(23) And Εcn c n = − −1

(

1 ε1

)

(24)

The overall effectiveness of the heat pipe heat recovery, Eo, may be obtained from Azad and Geoola [2] as follows:

For Ce>Cc Ε Ε Ε o cn c e en C C = + 1 1 (25) For Cc>Ce Ε Ε Ε o en e c cn C C = + 1 1 (26) ijlct_05.indd 199 ijlct_05.indd 199 2/13/2009 11:56:48 AM2/13/2009 11:56:48 AM

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International Journal of Low Carbon Technologies 3/3 5. Results and discussion

The theoretical analysis presented in this study can be used to predict the SHPHR performance. In general, heat exchange data may be presented by heat exchanger effectiveness which depends upon fl ow confi guration, capacity rate (m˙ Cp) of the two streams fl uids and the NTU. The following variations of parameters were chosen: number of rows in direction of fl ow 1 to 4; Ce/Cc from 1 to 3; and number of heat transfer units from 1 to 5.

Fig. 3 shows the overall heat transfer effectiveness as a function of number of transfer units and number of rows; Ce/Cc = 1. From this fi gure it can be observed that an increase in value of number of rows from 1 to 4, at Ce/Cc = 1, the overall effectiveness increases from 32% to 48.25% (increased by 50.8%) for NTU = 1. For n = 1 the overall effectiveness varies sharply up to NTU = 2 and then increases gradually. This rise is less in n = 2–3 and in n = 4 almost remain constant. However, it is important to note that the infl uence of n > 4 at Ce/Cc = 1 on overall effectiveness is not obvious from Fig. 3.

The overall effectiveness as a function of NTU for Ce/Cc = 2 is shown in Fig. 4. The effectiveness for n > 2 and NTU≥ 3 reaches to 67% and in Fig. 5 at Ce/Cc = 3 for n > 2 and NTU≥ 2 maximum effectiveness is 74%.

6. Conclusions

This paper describes how heat pipes can be used in a split heat pipe heat recovery system.

1-The theoretical model based on e-NTU (effectiveness-Number of Transfer Units) method has been developed to predict the performance of the split heat pipe heat recovery system.

Figure 3. Overall effectiveness as a function of NTU for Ce/Cc= 1.

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International Journal of Low Carbon Technologies 3/3

Figure 4. Overall effectiveness as a function of NTU for Ce/Cc= 2.

2- Increasing the ratio of Ce/Cc and number of rows of heat pipes within the normal design ranges can improve the performance of the split heat pipe heat recovery system.

References

[1] D. A. Reay, ‘A review of gas-gas heat recovery systems’, Heat Recovery Systems, 1 (1980), 3–41.

[2] E. Azad and F. Geoola, ‘A design procedure for gravity-assisted heat pipe heat exchanger’, Heat

Recovery Systems, 4 (1984), 101–111.

[3] R. Peretz and B. Horbaniuc ‘Optimal heat pipe heat exchanger design’, Heat Recovery Systems, 4 (1984), 9–24.

Figure 5. Overall effectiveness as a function of NTU for Ce/Cc= 3.

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International Journal of Low Carbon Technologies 3/3

[4] L. Shao, S. B. Riffat and G. Gan, ‘Heat recovery with low pressure loss for natural ventilation’,

Energy and Buildings, 28(2) (1998), 179–184.

[5] E. Azad, F. Bahar and F. Moztarzadeh, ‘Design of water-to-air gravity-assisted heat pipe heat exchanger’ Journal of Heat Recovery Systems, 5 (1985), 89–99.

[6] E. Azad and F. Moztarzadeh, ‘Design of air-to-water co-axial heat pipe heat exchanger’ Journal of

Heat Recovery Systems, 5 (1985), 217–224.

[7] E. Azad, B. M. Gibbs, ‘Analysis of air-to-water heat pipe heat exchanger’, Journal of Heat Recovery

Systems and CHP, 7 (1987), 351–358.

[8] N. J. Lamfon, Y. S. H. Najjar and M. Akyurt, ‘Modelling and simulation of combined gas turbine engine and heat pipe system for waste heat recovery and utilization’, Energy Conversion and

Man-agement, 39 (1998), 81–86.

[9] S. B. Riffat, S. A. Omer and X. L. Ma, ‘A novel thermoelectric refrigeration system employing heat pipes and a phase change material: an experimental investigation’, Renewable Energy, 23 (2001), 313–323.

[10] M. S. So¨ylemez, ‘Optimum length of fi nned pipe for waste heat recovery’, Energy Conversion and

Management, 49 (2008), 96–100.

[11] T. X. Li, R. Z. Wang , L. W. Wang, Z. S. Lu and C. J. Chen, ‘Performance study of a high effi cient multifunction heat pipe type adsorption ice making system with novel mass and heat recovery pro-cesses’, International Journal of Thermal Sciences.

[12] S. Filippeschi, ‘On periodic two-phase thermosyphon operating against gravity’ International

Journal of Thermal Sciences, 45 (2006), 124–137.

[13] K. S. Ong, Md. Haider-E-Alalhi, ‘Experimental investigation on the hysteresis effect in vertical two-phase closed thermosyphons’ Applied Thermal Engineering, 19 (1999), 399–408.

[14] S. B. Riffat and J. Zhu ‘Mathematical model of indirect evaporative cooler using porous ceramic and heat pipe’ Applied Thermal Engineering, 24 (2004), 457–470.

[15] P. D. Dunn and D. A. Reay, ‘Heat pipes’, third ed., Pergamon Press, Oxford, 1982.

[16] D. G. Rich, ‘The effects of fi n spacing on the heat transfer and friction performance of multi-row smooth plate fi n-and-tube heat exchanger’ ASHRAE Trans.79 (1973), 137–145.

[17] M. W. Rohsenow and H. Y. Choi, ‘Heat, mass and momentum transfer’ John Wiley, New York (1965).

[18] L. S. Tong, ‘Boiling heat transfer and two phase fl ow’ New York (1965). [19] A. J. Chapman, ‘Heat transfer’ 3rd edition, Macmillan, New York (1974).

[20] M. W. Kays, A. L. London ‘Compact heat exchanger’ Mc Graw-Hill Book Co. (1964).

[21] Y. Lee, A. Bedrossian ‘ The characteristics of heat exchangers using heat pipes or thermosyphons’

Int. J. Heat and Mass transfer, 21 (1978), 221–229.

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References

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