Design of air-to-water co-axial heat pipe heat exchanger

Heat Recovery Systems Vol. 5, No. 3, pp. 217-224, 1985

0198-7593/85 $3.00 + 0.0 Pergamon Press Ltd

Printed in Great Britain

DESIGN OF AIR-TO-WATER CO-AXIAL HEAT PIPE HEAT E X C H A N G E R E. A Z A D and F. MOZTARZADEH Materials and Energy Research Center, P.O. Box 14155-4777, Tehran, lran Abstract--This paper describes a theoretical analysis of co-axial heat pipe heat exchanger (CAHPHE). The analysis is based on NTU-effectiveness approach to deduce its heat transfer characteristics. In this study the variation of overall effectiveness of C A H P H E with C J C c is presented and the effects of the number of rows of co-axial heat pipes on the thermal performance of the exchanger were determined.

NOMENCLATURE A Cc C, CI Cp C

g h hf~ k k,~ L Lr Nr

N, n NTU Nu P Pr Q Re S/ SI S,

t T Ts T~a, U A e,. e,

eo ~o r/r # p

heat transfer area [m 2] flow-stream capacity rate of cold-side fluid [WK-~] flow-stream capacity rate of hot-side fluid [WK-~] heat pipe working fluid capacity rate [WK -~ ] specific heat at constant pressure [J K g - t K - i ] exchanger flow-stream mass velocity [kg m - 2 s - t ] acceleration due to gravity [ms -2] heat transfer coefficient [ W m - 2 k =t] latent heat of vaporisation [J kg- I] thermal conductivity [W i n K - ~] effective thermal conductivity of saturated wick [W m - ~K - ~]. co-axial heat pipe length [In] fin length [m] number of fins per meter [dimensionless] total number of co-axial heat pipes [dimensionless] number of rows in direction of flow [dimensionless] number of heat transfer units of an exchanger [dimensionless] Nusselt number [dimensionless] pressure [N m -2] Prandtl number [dimensionless] heat in [W] Reynolds number [dimensionless] fin spacing [m] tube spacing in direction of flow [m] tube spacing normal to direction of flow [m] thickness [m] temperature [K] surface temperature [K] saturation temperature [K] overall heat transfer coetficient [W m - 2 M - i ] denotes difference single row effectiveness in the exaporator sections [dimensionless] single row effectiveness in the condenser sections [dimensionless] single row overall effectiveness [dimensionless] n-row overall effectiveness [dimensionless] total surface temperature effectiveness [dimensionless] fin temperature effectiveness [dimensionless[ a fin effectiveness parameter (equation 6) viscosity coe~cient [Ns m -z] density [k m - 3]

subscripts

c e f i l m o t w

condenser evaporator fin inside liquid wick outside total water 217

218

E. AZAD and F. MOZTARZADEH

1. INTRODUCTION Gas-to-gas heat pipe heat exchangers have been studied extensively in recent years owing to their application to heat recovery systems. In most of these investigations the axial heat pipes were used as heat transfer elements [1-10]. Liquid-to-liquid, liquid-to-gas and gas-to-liquid heat pipe heat exchangers have received only limited attention [11-15]. This work is concerned with the design of an air-to-water heat exchanger using finned co-axial heat pipes as the heat transfer element (Fig. 1). This type of heat exchanger offers two significant advantages over the other types of heat exchanger: 1. 2.

Redundancy: A leak in one pipe, for instance, does not affect the operation of the rest of the heat pipes. Thermal flux transformer: Because of the large evaporator heat transfer surface area the system becomes more compact.

This paper presents an analytical study of the performance of CAHPHE. The analysis is based on effectiveness-NTU approach to deduce its heat transfer characteristics. In this study the variation of the overall effectiveness of CAHPHE with the ratio of the hot to cold flow-stream capacity rate are presented and the effects of the number of rows on the thermal performance of the heat exchanger were determined. fin

co-axial heat Dioe

der lenser

Fig. 1. Co-axial heat pipe heat exchanger.

2. CO-AXIAL HEAT PIPE DESCRIPTION Figure 2 presents a schematic of a co-axial heat pipe. It consists of two pipes of different diameter and they are mounted one with in the other so as to form a concentric annulus. The inner surface of the outer pipe is covered with wick material and filled with water and permanently sealed. The operation of the heat pipe is based on the evaporation of a liquid in the evaporator section and subsequent flow in the core toward a region of low pressure. The vapour condenses on the outer surface of the inner pipe (condenser). After the latent heat of condensation has been released at the condenser the liquid drops to the lower section of evaporator and through wick by capillary pumping the liquid returns to the heat source, where it is re-evaporated. wick

evaporator \ fi~

Illllll IIll Illllll Illlllllll lltltltllll lLllllllllliLlllllllll

Ill!!!!,, Illllllllllllllllllllllllllllllllllllllllllll[llllllllllllll Fig. 2. Co-axial heat pipe schematic.

Design of air-to-water co-axial heat pipe heat exchanger

219

3. ANALYSIS In the following analysis co-axial heat pipes with water as a working fluid are considered to be The evaporator overall heat transfer coefficient based on air side area, A,,,, is given by

U=[

1___~ A,
(1)

Convection heat transfer coefficient for air normal to staggered circular finned tube bank (Fig. 3) is given by (16). Nu.o

O.134Re°68'pr°38(Sf'~°2 (Sf'~T M

=

\ L:)

\ ts/

(2)

•

Where S: is the distance between adjacent fins and L/is the fin height. Equation (2) can be used to predict t~eofor a bank of tubes six-rows deep. Figure 11 of ref. (17) is used to correct for banks of other than six-rows. The total surface temperature effectiveness rho is influenced by the fin thickness, thermal conductivity and fin length which can be estimated from equation (4) as follows: r/~o = 1 - A~, (1 - T//)

(4)

r/y can be estimated from equation (5): r//=

tanh (~Ly) ($L/)

(5)

where

p.oy.,

ck = \ k:t:/ " In equation (14), the finned area, follows:

(6)

,,If, and the total heat transfer area, A,<, are computed as

A:= N, L [N:~ (D~- O,.,,) ~D:t:N:] n_ A,, = t . N , [ ; N : 4 ( D ~ -

(7)

D,o) 2 + nDrtrN:+ nD,oS:(N:- 1)]

In equation (1) k, and h,t can be calculated from ref. (18).

: air flow IlL

Dco

Fig. 3. Arrangementsof co-axial heat pipes in heat exchanger.

(8)

220

E. AZADand F. MOZTARZADEH

The condenser overall heat transfer coefficient based on air side area is calculated as follows:

At e

Ate 1 -|

(9)

U, = LAcoh,,o+ A,h,,J Inside tube heat transfer coefficient is calculated as follows (19): For laminar flow (Re,. < 2300)

(. ~0,4 Nuci = 1.86 ( R e , P r , -~-2) \~--~,/

.

(10)

For transition regions (2100 < Re..< 10,000) Nusselt, number is calculated from Hausen's relation.

=

__

[

NUci 0.116(Re °:67 125)Pr°:33 1 +

(_~)0.67J (\/~,,/ ~..~0.14•

(ll)

For turbulent flow (Re,, > 10,000) water side heat transfer coefficient, hci, has been calculated from the following relation. Nuci = 0.027 Re,°:8 Pl~: _033.

(12)

This formula is the Sieder and Tate version of the Dittus-Boelter equation for viscous liquids, but neglecting the final term (p/p,)0.~4 which is close to unity for water. In equation (9) the condensation film coefficient, hco, on the surface of a horizontal tube Nusselt [21] recommended the following equation.

(k~p~gh;g ~o.2, h,,,=0.72\~ ]

(13)

where

'=h

+-g3 cpav

AT=Tso,-L. For condensation of steam on surface of a horizontal tube Brown [22] has developed an empirical equation for condensation film coefficient as follows. h,,, = 133857/(Q/A,o) °'88.

(14)

4. E X C H A N G E R HEAT T R A N S F E R E F F E C T I V E N E S S In the evaporator sections of a single row co-axial heat pipe, the hot fluid is in parallel flow with vapour flow inside the heat pipe. In evaporator sections energy transfer results in a change of phase rather than of temperature, its capacity rate, CL, becomes, by definition, equal to infinity and as a result Ce/Q = 0. Therefore, the effectiveness-NTU equation for a single row co-axial heat pipe heat exchanger are as follows [23]. /;,, = 1--e -NT~'.

(15)

In condenser sections vapour and cold fluid are in cross flow and Cc/CL = 0 e, = i - - e -NvU, .

(16)

The co-axial heat pipe heat exchanger can be considered similar to a liquid-coupled, indirecttransfer-type exchanger system. This system (Fig. 4) consists of two direct-transfer type exchangers coupled together by the circulation of a suitable fluid. For the co-axial heat pipe considered in the present study, the hot-side exchanger and cold-side exchanger represent the evaporator and condenser sections, respectively. The coupling fluid is the heat pipe working fluid with capillary force as the pump.

221

Design of air-to-water co-axial heat pipe heat exchanger

hot-sideexchanger =[ ! _,~ A E'' ........................... ]D-"

hot-side e x c ~ o

I

cL

A

=

----------~ B

=[ . . . . . . . . . . . . . . . . . . . . - ~ .

.

.

.

-~G

coldfluid Cc

cold-side exchanger Fig. 4. Liquid-coupled indirect-transfer-type heat exchanger used as a model for the analysis of CAHPHE.

With respect to the above remarks, the effectiveness may be obtained from that of a liquid-coupled, indirect-transfer-type exchanger as follows [23]. For Ce > Cc 1 e = 1 CdC, (17) ) e~

ee

for C~ > C, 1 = 1

(18)

C/c/

) 8e

8c

For a co-axial heat pipe heat exchanger with n-rows in the direction of flow and with n-passes which can be assumed to be in overall counter flow the heat exchanger, overall effectiveness, co, is obtained from [23]

.... )"-c.:,.. where Cm= and C~x are, respectively, the smaller and the larger of the two magnitudes C, and Cc. The basic equations that will be used for the calculation of the pressure loss for airside is as follows [16]. AP

i/ S \ - 0 9 2 7 / 5 = 1 8 . 9 3 R e - ° m 6 | ~t |

\D,.,,)

XtO'515

G2n

l---t|

--

kS,)

p

•

(20)

5. RESULTS

The results reported in this paper have been obtained on a finned co-axial heat pipe heat exchanger having the characteristics given in Table I. The finned tubes have circular fins. The heat Table I. Characteristics of circular finned tube Evaporator outside diameter

Fin outside diameter Fin thickness Fin spacing Fin density Condenser outside diameter Heat pipe length Transverse tube spacing Longitudinal tube spacing Tubes materials Fin materials

0.026 m 0.044 m

0.00036 m 0.00289 m 346.46 fins m0.0127 m 0.94 m 0.0782 m 0.0524 m copper aluminium

222

E. AZAD and F. MOZTARZADErt

Cc =1/,1 70

65 60 E:%

50 ~5

/*0

~

1.2

.

.

.

I

.

1.5

,

,

,

I

,

2.0

2.5

ce/c¢

Fig. 5. Variation of overall effectiveness with

CJC~.

70

Cc =1650

60

C'/,

50

/.0

.

1.0

.

.

.

1

t5

.

.

.

.

•

.

.

2.0

Fig. 6. Variation of overall effectiveness with

C,./C,..

exchanger configurations used were n-rows, n-passes, with n can go from 4 to 8 with twelve tubes per row and with tubes set on a staggered arrangement. Figures 5 to 8 show the variations of overally effectiveness, eo, with C,,/C,. for different values of number of rows. As is expected, the effectiveness increases with increasing number of rows. For

Design of air-to-water co-axial heat pipe heat exchanger

223

70

Cc=1900 65

60

Co/. 55

50

45

z,O

35

|

1.1

1.3 '

112

1.5 '

I'.Z,

1.6 '

1.8

1.7 '

1.9

cj£ Fig. 7. Variation of overall effectiveness with C,/C~.

65 Cc=2150 60

55

e/g 0 /.5 40

1.0

I.I

1.2

1.3

1.4

1.5

1.6

1.7

%Cc Fig. 8. Variation of overall effectiveness with C,/C~.

example an increase in n from 4 to 8 at CdC,. = 1.5 and C,. = 1410, causes an increase in effectiveness from 45.2 to 65.2%. Figure 9 represents the variation o f pressure drop vs number of rows. This figure shows that pressure increases with increasing number of rows.

Acknowledgements--The financial support provided by the Ministry of Culture and Higher Education of the Islamic Republic of Iran is gratefully acknowledged.

224

E. AZAD and F. MOZTARZADEH

150

100 A P(N/m 2 )

50

10 /-

5

6

7

8

n -No. of rows

Fig. 9. Variation of pressure vs number of rows.

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