1

1. Introduction

The process of improving the performance of a heat transfer system is

referred to as heat transfer augmentation, enhancement or intensification. In

general, this means an increase in heat transfer coefficient. A comprehensive

survey on hea t transfer augmentation is given by Bergles. [1] According to

him, heat transfer augmentation has been of interest since the earliest

documented studies of heat transfer. An example of this is Newton [2], who in

1701 suggested an effective way of increasing convective heat transfer “... not

in a calm air, but in a wind that blew uniformly upon it ...”. Even Joule [3]

reported in 1861 significant improvement in the overall heat transfer

coefficient for in- tube condensation of steam when a wire, spiralled aro und

the condenser tube, was inserted in the cooling water jacket.

According to Whitham [4], the efficiency of fire- tube boilers could be

increased by up to 18% when “retarders” or twisted- tape inserts were inserted

in the tube. It was suggested that the inserts should be used only when “the

boiler plant is pushed and the draught is strong”. In one of the first systematic

studies by Jakob and Fritz [5] on nucleate boiling, enhanced surfaces were

used. Patents dealing with enhanced heat exchangers date back to the 1920s

where fins were used on the shell side of a shell- in- tube heat exchanger. [6]

Furthermore, manufacturer’s literature [7] on heat transfer augmentation in

heat exchangers dates back to 1921, where an increase of the hot water

heating capacity of 50% was claimed as a result of enhancing both the tube-

side single- phase flow and the shell-side condensing of steam.

2

The techniques [8-9] of improving heat transfer can be classified as

passive methods which require no direct application of external power, and

active schemes which require external power. Passive techniques include

treated surfaces, rough surfaces, extended surfaces, displacement

enhancement devices, swirl f low devices, surface tension devices and fluid

additives. The active techniques include mechanical aids, surface vibration,

fluid vibration, electrostatic fields, injection, and suction. These techniques

can also be utilised simultaneously (compound augmentation). The

effectiveness of a given augmentation technique depends largely on the mode

of heat transfer or the type of heat exchanger to which it is applied as well as

the pressure drop over the given device that creates the enhancement.

Some types of heat exchangers used are found in residential and

commercial space heating and air-conditioning, residential and commercial

water heating and industrial petrochemical processing, which contributes to

more than a third of energy used [10] in the United States. Given that energy

is currently being used in the United States at a rate roughly equivalent to

39.8 million barrels of oil per day, [11] an efficiency improvement of 10% in

the cited applications by using heat transfer augmentation would save about

1.5 million barrels of oil per day, and reduce atmospheric CO2 emissions by

about 400 million metric tons per year. [12] Therefore, heat transfer

augmentation of evaporation and condensation for refrigeration,

air-conditioning and heat pump applications has received increasing attention

in recent years. This is due not only to an emphasis on energy efficiency, but

3

also a need for more compact and lighter heat exchangers packaging, possible

reductions in the charges of refrigeration gases, as well as the phasing out

programme since the end of 1995 of chlorofluorocarbon (CFC) refrigerants as

stipulated by the Montreal Protocol and later the Copenhagen and Vienna

amendments. [13]

According to Johannsen and Kaiser [14], 6% of South Africa’s primary

energy consumption could be saved if heat pumps were used to their full

technical potential. Although there is world-wide interest in the use of heat

pumps and considerable effort has been expended on heat-pump research, heat

pumps are not commonly used in South Africa.

In air source hot water heat pumps, two heat exchangers are used. One

is an air- heated fin-and- tube evaporator with the colder refrigerant flowing

inside the tubes and the warmer air moving over the tubes and fins in a

cross- flow configuration. The other heat exchanger is a water-cooled

condenser, either a tube- in- tube, shell- in- tube, coil- in- shell, plate heat

exchanger, and lately fluted- tube heat exchanger. Tube- in- tube heat

exchangers are inexpensive and easy to manufacture but not very effective. A

typical set- up for a hot water heat pump is shown in Fig. 1 with the

temperature entropy graph of the refrigerant cycle given in Fig. 2 .

4

W a t e r p u m p

H o tw a t e r

r e s e r v o i rE x p a n s i o n v a l v e C o m p r e s s o r

C o n d e n s e r

E v a p o r a t o r

Refr igerantCycle

Hea ted Water Cyc le

14

3 2

Fan

P r o p o s e dc o m b i n a t i o n o fw a t e r p u m p a n d

c o n d e n s e r

F i g . 1 . Schemat ic represen ta t ion o f an a i r source ho t wa te r hea t pump

Entropy

Temperature

Condensat ion temperature

Evaporat ion t emperature

Expansionvalve

Condenser

Evaporator

Compressor

2

1

3

4

F i g . 2 . Tempera tu re en t ropy g raph o f the r e f r ige ra t io n cyc le in an a i r source ho t wa te r

heat pump

5

By improving the heat transfer in the condenser and evaporator, the

condenser and evaporator can be made smaller and therefore cheaper since

less material is used. Another way of making the heat pump cheaper and

smaller is to combine different components of the heat pump. Such a proposed

combination could be the condenser and the water pump (condenser pump) or

the fan and the evaporator (evaporator fan). This can be done by placing the

refrigerant channels inside the rotor of a pump, or blades of a fan. Fig. 3

shows an example of a mono positive displacement pump with the refrigerant

flowing in a counterflow configuration in the rotor as well as in the spiralled

casing of the pump. The original idea came from this configuration since this

pump has the resemblance of a tube- in- tube heat exchanger.

Water inside pump cavityflowing from left to right

Refrigerantflowing in rotorfrom right to left

Refrigerant flowingin casing from pump

from right to left

F i g . 3 . Ref r igeran t f low in a mono pos i t ive d i sp lacement pump

The same configuration can be used with a centrifugal pump or any

other pump but the manufacturing process will be much more complicated

because of the physical size of the centrifugal impeller blades. In the

condense r pump the refrigerant will be condensed while the pump will pump

and heat up the water at the same time. Cheaper heat pumps will make them

much more viable and competitive than normal resistance element geysers.

6

This method of combination can be seen as an active method of heat transfer

augmentation, but the difference is that the external power source is not in

addit ion to the existing system.

In order to investigate such a condenser pump the first step is to obtain

a specific application in which the condenser pump can be used. This is

important since pumps are used for specific applications with different flow

rates relative to a specific pressure rise. Conceptual ideas (Appendix A) were

considered in terms of viability of manufacturing and cost. After careful

consideration and refinement , it was decided to use a rotary lobe pump as the

first prototype (Appendix B) to investigate the viability of a condenser pump.

The rotary lobe pump consists of two contra-rotating rotors. The product is

moved gently through the pump with a non-pulsating low-shear action. All

wetted parts are made from 316 stainless steel and are basically the pump

casing, two lobes and a front cover for easy access to the pumping chamber.

The front cover and pump casing are two separate units which make it

possible to place refrigerant channels in each part separately. This is different

from, for example , a centrifugal pump which has one cast casing unit.

In order to simplify the manufacturing process it was decided to place

heating channels only in the front cover at first. If insufficient heat transfer

was obtained, heating channels would be placed in the pump casing and, as a

last resort, in the lobe, which would result in high-cost mechanical seals. Fig.

4 shows the rotary lobe pump with heating channels in the front cover.

7

F i g . 4 . Ro ta ry lobe pump wi th hea t ing channe l s in f ron t cover p la te

In order to obtain a counterflow configuration the flow in the heating

channels is arranged as in Fig. 4, while the top lobe is rotating clockwise and

therefore the bottom lobe anticlockwise. In the analys is of the heat transfer

the simplified model can be represented in Fig. 5. I t is a half round heating

channel with heat transfer only from the flat surface side. On the other side of

the separating plate the product is being rotated (by the rotating lobes).

Inlet

Outlet

8

R o t a t i n g p r o d u c t b e i n g p u m p e d

R e f r i g e r a n t f l o w i n g i nh e a t i n g c h a n n e l

S e c t i o n a l v i e w o fh e a t i n g c h a n n e l

T h i c k n e s s o f p l a t e c o v e r i n g h e a t i n g c h a n n e l s

H e a t t r a n s f e r t or o t a t i n g p r o d u c t

W i d t h o f p l a t e

F i g . 5 . Sec t iona l d rawing o f hea t t r ans fe r geomet ry

After an extensive literature survey on flow in non-circular tubes it was

found that heat transferred from the semicircular duct has been explored.

However, but the case where the circular section is adiabatic with only heat

transfer from the flat side could not be found in literature. A comprehensive

and excellent summary of different geometr ies was found in the Handbook of

Single -Phase Convective Heat Transfer [15]. Another important fact that

makes this geome try unique is that the heating channel is vertical and curved

(S-shaped). Correspondence [16-17] was made with leading researchers in

heat transfer and to their knowledge there is no literature on a semicircular

tube where fluid is rotated on the opposite side. Very little research has also

been done on semicircular heat exchangers with turbulent flow.

9

In the light of the previous discussion the purpose of this study is to

determine expressions for characteristics such as heat transfer coefficients

and pressure drop for this principal, semicircular geometry. The research

focuses on semicircular heat exchangers with turbulent flow in order to make

the design of such a rotary lobe condenser pump possible.

10

2. Experimental set-up

The experimental work was done with the use of water- to-water heat

transfer. The semicircular heat exchanger was manufactured (Appendix B)

from a standard 28.58 mm hard drawn copper tube, cut through the middle,

with a 1.6 0 mm copper plate in between (Fig. 6) to obtain a semicircular heat

exchanger. Turbulent flow was investigated with the flat side of the

semicircular heat exchanger being horizontal or vertical and a spiralled

semicircular heat exchanger. A S-shap ed semicircular heat exchanger was also

tested.

F i g . 6 . D imens ions o f t he coppe r p l a t e and tube o f t h e s e m i c i r c u l a r h e a t e x c h a n g e r

The experimental set- up is shown in Fig. 7. In the experimental set- up

there were two closed loops - one with cold fluid and the other with hot fluid

- linked by the semicircular heat exchanger.

Diameter 28.58 mm Wall thickness 1.02 mm Plate thickness 1.60 mm

1.60 mm

11

Resistanceelement

Hot waterreservoir

Centrifugalpump

Semicircularheat

exchanger

Chiller

Cold waterreservoir

Oscillating-pistonflow meter

Tco

Pco

Tci

Pci

Tho

Pho

Thi

Phi

Centrifugalpump

19765.6543

19765.6543

Oscillating-pistonflow meter

F i g . 7 . Exper imenta l se t -up

The design of the experimental set- up is given in Appendix C .

Calibration of the measuring instruments is given in Appendix D. All the

temperature readings were measured with K-type thermocouples (accuracy

± 01. o C ), connected to a data logger, on the outside of the tube since the

temperature gradient over the copper tube is negligible. The volume flow of

the water in the hot and cold water cycle s was measured with oscillating-

piston flow meters (accuracy ± 1% ). The temperature readings , together with

the volumetric flow rate of the hot and cold water, were used to determine the

12

heat transfer between the hot and cold fluid. This was used to determine the

energy balance over the heat exchanger. The experimental results were

analysed using the Wilson plot method to determine the heat transfer

coefficients of the semicircular geometry.

In order to calculate the energy balance , the equations to determine the

properties of water were obtained from literature [18] (Appendix E). In order

to compare the semicircular heat exchanger with existing heat exchangers a

theoretical analys is (Appendix F) was done on a normal round tube- in- tube

heat exchanger with equal hydraulic diameter to that of the semicircular heat

exchanger.

The straight semicircular heat exchanger test section is shown in Fig. 8,

the spiralled heat exchanger in F i g . 9 and the S-shaped heat exchanger in

Fig. 10.

Fi g . 8 . S t r a i g h t s e m i c i r c u l a r h e a t e x c h a n g e r

W a t e r f l o w c o n n e c t i o n

p o i n t s

P r e s s u r e d i f f e r e n c e c o n n e c t i o n p o i n t s

13

F i g . 9 . S p i r a ll ed s emic i r cu l a r hea t exchange r

F i g . 1 0 . S -s h ape semic i r cu la r hea t exchanger

950 mm

14

3. Results

3.1 Heat transfer

Results of experiments done on a semicircular heat exchanger are given

in Appendix G. Experiments wer e done with the separating plate between the

two semicircles in a vertical as well as horizontal orientation for the straight

heat exchanger. Experiments were conducted in each case with hot water a t

the bottom or top and inside or outside spiral in order to determine all

possible variations. The experimental results wer e analysed using the

modified Wilson plot technique [19] and are given in Appendix H.

The results for the modified Wilson plot Eq. 1 and 2 (Sieder- Tate) [20]

are given in Table 1.

Nuh D

kCh

h h

hh h

Ph

w h

= =

Re Pr1 3

0.14µµ

(1)

Nuh D

kCc

c c

cc c

Pc

w c

= =

Re Pr

.

1 3

0 14µ

µ (2)

15

T a b l e 1 . Summary o f resu l t s f rom modi f i ed Wi l son p lo t ana lys i s

P Ch Cc U Average % Error

Plate vertical 0.6585 0.1564 0.1359 0.692

Plate horizontal hot water bottom 0.6706 0.1344 0.1359 0.583

Plate horizontal hot water top 0.6303 0.2035 0.1933 0.594

Spiral hot water outside 0.7245 0.0848 0.0971 0.714

Spiral hot water inside 0.7363 0.0829 0.0673 0.313

S-shape 0.7220 0.0902 0.0904 0.607

The median and standard deviation given in Table 1 are for the

percentage difference between the overall heat transfer coefficient calculated

with the logarithmic mean temperature difference and with the results from

the modified Wilson plot technique. As expected, the hot and cold water

coefficients are very similar since the cross- flow areas are equal.

Graph s 1 and 2 show the results of the Nusselt number relative to the

Reynolds number for different configurations of the semicircular heat

exchanger. These graphs are constructed with the Wilson plot correlations

obtained. Both graphs are calculated at a Prandtl number of 6 (average

temperature 25.65 o C ) in order to compare the difference between the hot and

cold water in each of the semicircular sections.

16

Water Heating COLD WATER

50

150

250

350

450

550

10000 20000 30000 40000 50000 60000 70000

Reynolds number [ ]

Nus

selt

num

ber

[ ]Spiral cold water insideS-shape cold waterSpiral cold water outsidePlate horizontal cold water topPlate horizontal cold water bottomPlate vertical cold water Inner tube-in-tube Sieder and Tate

G r a p h 1 . Nusse l t number ve r sus Reyno lds number fo r wa te r be ing hea ted wi th d i f f e ren t

con f igu ra t ions o f s emic i r cu la r hea t exchange r s a t a P rand t l number o f 6

Water Cooling HOT WATER

50

100

150

200

250

300

350

400

450

500

550

10000 20000 30000 40000 50000 60000 70000

Reynolds number [ ]

Nus

selt

num

ber

[ ]

Spiral hot water insideS-shape hot waterSpiral hot water outsidePlate vertical hot waterPlate horizontal hot water bottomPlate horizontal hot water topInner tube-in-tube Sieder and Tate

G r a p h 2 . Nusse l t number ve r s us Reyno lds number fo r wa te r be ing coo led wi th d i f f e ren t

con f igu ra t ions o f s emic i r cu la r hea t exchange r s a t a P rand t l number o f 6

17

Both these graphs show similar trends to corresponding graphs for

normal round tube- in- tube heat exchangers (Appendix F). In G raphs 1 and 2

the average increase in the Nusselt number for semicircular heat exchangers

over the inner tube of a normal tube- in- tube heat exchanger remains almost

constant with a change in Reynolds number. At low Reynolds numbers the

Nusselt numbers of the semicircular heat exchangers are almost equal, but as

the Reynolds numbers increase, the difference between the Nusselt numbers

of the different configurations of semicircular heat exchangers increase s. The

highest Nusselt number is obtained for the flo w in the inside spiral, followed

by the S-shaped heat exchanger and then the flow in the outside spiral. The

three different straight semicircular heat exchangers have similar results for

Nusselt numbers. For the separating plate in the horizontal position the

highest Nusselt number is obtained for the hot water in the bottom and cold

water in the top semicircular section. Theoretically this can be explained as

follows: With the hot water in the bottom section the water is cooled down

and then moves to the bottom of the bottom semicircular section and therefore

creates a natural convection pattern. The explanation for the cold water in the

top section is similar. In order to compare the semicircular heat exchanger

quantitatively to a normal round tube- in- tub e heat exchanger the percentage

increase in the Nusselt number is calculated at a Reynolds number of 40 000

and presented in Table 2 and in Graph 3 and Graph 4 for water being heated

and cooled, respectively.

18

T a b l e 2 . Percentage increase in Nussel t numb er fo r Reyno lds number o f 40 000 and

Prand t l number o f 6

Water

heating

Water

cooling

Nu % increase Nu % increase

Inner tube Sieder and Tate 240.4 230.6

Plate vertical 273.5 13.8 294.8 27.9

Plate horizontal hot water bottom 309.7 28.9 287.7 24.8

Plate horizontal hot water top 287.9 19.8 283.8 23.1

Spiral hot water outside 389.7 62.2 322.3 39.8

Spiral hot water inside 307.6 28.0 358.2 55.3

S-shape 354.0 47.3 334.5 45.1

Average increase 33.3 36.0

Water Heating Pr = 6

0

10

20

30

40

50

60

70

Percentage increase at Reynolds number of 40 000 for heatingwater

Per

cent

age

[%]

Plate vertical

Plate horizontal hotwater topSpiral hot waterinsidePlate horizontal hotwater bottomS-shape

Spiral hot wateroutsideAverage increase

G r a p h 3 . Pe rcen tage inc rease o f Nusse l t number a t Reyno lds number o f 40 000 for water

be ing hea ted

19

Water Cooling Pr = 6

0

10

20

30

40

50

60

Percentage increase at Reynolds number of 40 000 for coolingwater

Per

cent

age

[%]

Plate horizontal hotwater topPlate horizontal hotwater bottomPlate vertical

Spiral hot wateroutsideS-shape

Spiral hot waterinsideAverage increase

G r a p h 4 . Pe rcen tage inc rease o f Nusse l t number a t Reyno lds number o f 40 000 for water

be ing coo led

In Graph s 3 and 4 the quantitative percentage increase in the Nusselt

number at a Reynolds number of 40 000 reveals the similarity between the

different configurations of the straight semicircular heat exchanger. It also

clearly shows that the results of the S-shaped semicircular heat exchangers lie

between those of the two different spiralled semicircular heat exchangers,

which should clearly be the case since the S-shaped heat exchanger consists

of a section of each of the spiralled heat exchangers. The average increase in

Nusselt number is 33% for water being heated and 36% for water being cooled

at a Reynolds number of 40 000 and Prandtl number of 6.

3.2 Pressure loss

The pressure loss exp eriments (Appendix I) were done separately from

the heat transfer experiments in order to obtain more accurate results since

the water temperature re mains constant. In the pressure loss experiments it

20

was found that care must be taken to ensure that no air is trapped in the

pressure connection pipes, since this influence s the results. Graph 5 shows

the pressure loss coefficient relative to the Reynolds number for the

separating plate in the horizontal orientation section 2. The corresponding

trendline and equation are also given on the graph. A clear set of data can be

seen on each side of the graph. This is data obtained with hot water (high

Reynolds numbers) and cold water (low Reynolds numbers).

Horizontal II

y = 52.671x-0.1543

R2 = 0.9698

9.5

10

10.5

11

11.5

12

12.5

10000 20000 30000 40000 50000 60000 70000

Reynolds number [ ]

Pre

ssu

re lo

ss c

oeff

icie

nt

[ ]

G r a p h 5 . P ressu re loss coe f f i c i en t ove r 5 .5m semic i rcu la r hea t exchanger ve r sus Reyno lds

number fo r the hor izon ta l p la te o r ien ta t ion

For the other semicircular heat exchangers the results are similar and

the results of the trendline equations are listed in Table 3. In each case the

section 1 or 2 refers to either side of the heat exchanger where there is not

supposed to be a difference in the results, but due to manufacturing

differences there are slight differences. These results are represented in

21

Graph 6. The graphs have similar trends to those of normal round tube- in-

tube heat exchangers (Appendix G).

T a b l e 3 . Equa t ions fo r p ressure loss coe f f i c i en t fo r d i f f e ren t semic i rcu la r hea t exchanger

sec t ions

CP Standard

deviation

Circular CP = 70.757Re -0.2117 0.9963

Horizontal I CP = 40.585Re -0.1216 0.8305

Horizontal II CP = 52.671Re -0.1543 0.9698

Vertical I CP = 35.17Re -0.1064 0.4429

Vertical II CP = 56.62Re -0.1545 0.8735

Spiral inside CP = 16.698Re -0.028 0.4355

Spiral outside CP = 13.939Re -0.022 0.2499

S-shape I CP = 21.447Re -0.0545 0.7976

S-shape II CP = 22.956Re -0.0649 0.9192

22

6

7

8

9

10

11

12

13

14

15

16

0 10000 20000 30000 40000 50000 60000 70000 80000

Reynolds number [ ]

Pre

ssur

e lo

ss c

oeff

icie

nt [

]

Circular Horizontal I Horizontal IIVertical I Vertical II Spiral insideSpiral outside S-shape I S-shape II

G r a p h 6 . P ressure loss coef f i c i en t over 5 .5m semic i rcu la r hea t exchanger ve r sus Reyno lds

number fo r d i f f e ren t semic i rcu la r hea t exchanger sec t ions

In Graph 6 all the trendlines are similar except that of the flow for the

water on the outside spiral. This is also emphasised by the low trendline

correlation of the flow in the outside spiral (Tab le 3). The reason for the

deviation in results is air in the pressure measuring connection points.

However, the experiments could not be repeated , since this experimental set-

up had been altered at the point where this was noticed. The pressure loss

coefficient correlates directly with that of the increase in Nusselt number.

The highest increase in pressure loss coefficient was obtained with the flow in

the inner spiral and similar results were produced for the three different

straight semicircular he at exchangers.

23

3.3 Heat transfer and pressure loss

In order to compare the different semicircular heat exchangers with one

another and with a normal round inner tube of a tube- in- tube heat exchanger

the enhancement factor [21] (Eq. 3) and pressure factor (Eq. 4 ) were

calculated for each of the different semicircular heat exchangers. From

literature it was found that the enhancement factor is defined as the ratio of

the heat transfer coefficient of the enhanced surface to that of a plain surface.

A decis ion was made to use the definition of Webb [21] instead , since it gives

a better indication of the true enhancement obtained only by the improved

heat transfer coefficient and not the area of heat transfer. The enhancement

and pressure factors were calcula ted in comparison to a smooth round tube

with equal hydraulic diameter and heat exchange length. The results are given

in Table 4 .

EFhAhA

Semicircular

Inner tube

= (3)

PFCPCP

Semicircular

Inner tube

= (4)

24

T a b l e 4 . Enhancement f ac to r and p ressu re f ac to r fo r d i f f e ren t semic i rcu la r hea t

exchangers

Water Heating Pr = 6

EF PF

Plate vertical 1.524 1.492

Plate horizontal hot water bottom 1.726 1.429

Plate horizontal hot water top 1.604 1.429

Spiral hot water outside 2.172 1.653

Spiral hot water inside 1.714 1.470

S-shape 1.973 1.570

Water Cooling Pr = 6

EF PF

Plate vertical 1.713 1.492

Plate horizontal hot water bottom 1.671 1.429

Plate horizontal hot water top 1.649 1.429

Spiral hot water outside 1.872 1.470

Spiral hot water inside 2.081 1.653

S-shape 1.943 1.570

Table 4 is calculated at a Reynolds number of 40 000 and a Prandtl

number of 6. In Table 4 the payoff for increase in heat transfer (enhancement

factor) can clearly be observed in the increase in pressure loss coefficient

(pressure factor). There is a direct correlation, since as the enhancement

factor increase s, the pressure factor increase s as well. The highest

enhancement factor (2.081) was obtained with hot water flowing in the inside

25

spiral but the highest pressure factor (1.653) was also obtained with this

configuration.

4. Discussion of results

4.1 Heat transfer

There is a significant increase in heat transfer for a semicircular heat

exchanger above a normal round tube of equal hydraulic diameter. This can be

attributed to conduction, which is much higher than convection. With the

semicircular heat exchanger an extended fin (Fig. 11.) forms , which increase s

the heat transfer characteristics.

Flowarea

Good the rmalconnect ion for

conduct ion

Extended f in incontact wi thother f lu id

F i g . 1 1 . Ex tended f in fo rmed wi th semic i rcu la r h e a t e xchanger conf igura t ion

By combining Graphs 1 and 2 the difference between the hot and cold

water is represented for each of the different semicircular heat exchangers.

This combination is given in Graph s 7 – 10 for each of the different

semicircular heat exchangers.

26

Vertical Pr = 6

50

100

150

200

250

300

350

400

450

10000 20000 30000 40000 50000 60000 70000

Reynolds number [ ]

Nus

selt

num

ber

[ ]

Plate vertical hot waterPlate vertical cold water Inner tube-in-tube Sieder and Tate cold waterInner tube-in-tube Sieder and Tate hot water

G r a p h 7 . Nusse l t number ve r sus Reyno lds number fo r semic i rcu la r hea t exchanger wi th

separa t ing p la te in ve r t i ca l o r i en ta t ion

Horizontal Pr = 6

50

100

150

200

250

300

350

400

450

500

10000 20000 30000 40000 50000 60000 70000

Reynolds number [ ]

Nus

selt

num

ber

[ ]

Plate horizontal cold water TopPlate horizontal cold water bottomPlate horizontal hot water bottomPlate horizontal hot water topInner tube-in-tube Sieder and Tate cold waterInner tube-in-tube Sieder and Tate hot water

G r a p h 8 . Nusse l t number ve r sus Reyno lds number fo r semic i rcu la r hea t exchanger wi th

separa t ing p la te in hor izon ta l o r ien ta t ion

27

S-Shape Pr = 6

50

150

250

350

450

550

10000 20000 30000 40000 50000 60000 70000

Reynolds number [ ]

Nus

selt

num

ber

[ ]S-shape cold waterS-shape hot waterInner tube-in-tube Sieder and Tate cold waterInner tube-in-tube Sieder and Tate hot water

G r a p h 9 . Nusse l t number ve r sus Reyno lds number fo r S -shaped semic i r cu la r hea t

exchange r

Spiral Pr = 6

50

150

250

350

450

550

650

10000 20000 30000 40000 50000 60000 70000

Reynolds number [ ]

Nus

selt

num

ber

[ ]

Spiral cold water insideSpiral hot water insideSpiral hot water outsideSpiral cold water outsideInner tube-in-tube Sieder and Tate cold waterInner tube-in-tube Sieder and Tate hot water

G r a p h 1 0 . Nusse l t number ve r sus Reyno lds number fo r sp i r a l l ed semic i r cu la r hea t

exchange r

28

From the Sieder- Tate equation there should not be a difference in the

C-value for the hot and cold water in the different semicircular sections. The

C-value only change s for different flow geometries. This can be observed in

Graph s 7 – 9, where there is a small difference between the hot and cold

water results. The differences can be attributed to experimental errors and

manufacturing differences, since the hot and cold water flowed in opposite

directions in the same semicircular section. The results for the normal smooth

round tube (Graphs 7 – 10) also show a difference between the hot and cold

water because for the hot water the copper wall temperature is cold and the

inverse is true for the cold water. In Table 5 the percentage difference in the

Nusselt number at a Reynolds number of 40 000 for hot and cold water in

different semicircular heat exchangers is given.

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T a b l e 5 . Pe rcen tage d i f fe rence in Nusse l t number a t Reyno lds number o f 40 000 fo r ho t

and co ld wa te r in d i f fe ren t semic i rcu la r hea t exchangers

Nu Nu

Water heating

cold water

Water cooling

hot water

% difference

Inner tube Sieder and Tate 240.4 230.6 4.2

Plate vertical 273.5 294.8 7.5

Plate horizontal hot water bottom 309.7 287.7 7.4

Plate horizontal hot water top 287.9 283.8 1.4

Outside spiral 307.6 322.3 4.7

Inside spiral 389.7 358.2 8.4

S-shape 354.0 334.5 5.7

There is , however, a significant difference in the heat transfer if the

water passes in the inside or outside spiral of the spiralled heat exchanger

(Graph 10 ). In each case for hot and cold water the heat transfer is increased

with the flow in the inside spiral. This can be explained in Fig. 12. In this

figure it is clear that the flow in the inner spiral is always forced against the

heat transfer surface. This differs from the flow in the outer spiral which is

always forced against the outer surface where heat is not directly transferred

but still by means of the extended fin. This is the reason for the increase in

heat transfer of the spiralled heat exchanger over that of a straight

semicircular heat exchanger.

30

Fi g . 1 2 . F low cha rac te r i s t i c s o f (ou te r and inne r ) sp i r a ll ed semic i rcu la r hea t exchanger

The reason for the results of the S-shaped semicircular heat exchanger

being in the middle of the results of the two spiralled heat exchangers is

clear, since the fluid is in the inner and outer spiral for different sections of

the heat exchanger.

4.2 Pressure loss

The reason for the increase in pressure loss coefficient for the

semicircular heat exchanger over that of a normal round tube is the sharp

corners of the semicircular heat exchanger. The pressure loss results are very

similar to the heat transfer results. Similarly, there is no significant

difference between the vertical and horizontal separating plate orientation.

When the fluid is in the inside spiral, the pressure loss is higher since the

fluid is pushed into the sharp corners all the time. S imilarly, the results of the

S-shaped semicircular heat exchanger regarding pressure loss also lie between

those of the two spiralled heat exchangers.

Flow in outer spiral forced against outer

surface

Flow in inner spiral forced against

inner heat transfer surface

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5. Conclusio n

In this study expressions for heat transfer coefficients and pressure loss

coefficients, for a semicircular geometry in different orientations, were

determined. The research focuses on semicircular heat exchangers with

turbulent flow in order to make the design of a rotary lobe condenser pump

possible.

There is a significant increase in heat transfer for semicircular heat

exchangers ove r the inner tube of a normal tube- in- tube heat exchanger with

equal hydraulic diameter. Quanti tat ively the averag e increase in the Nusselt

number is 33% for water being heated and 36% for water being cooled at a

Reynolds number of 40 000 and Prandtl number of 6. Unfortunately, the

pressure loss increase s by an equal amount. The highest enhancement factor

(highest increase in heat transfer coefficient) and pressure factor (highest

increase in pressure loss coefficient) were obtained with the flow of water in

the inner spiral of the spiralled semicircular heat exchanger.

Due to the equal increase in heat transfer coeffic ient and pressure loss

coefficient, it can be concluded that it would not be viable to use semicircular

heat exchangers instead of normal round tube- in- tube heat exchangers in

normal situations. This is mainly due to a difficult manufacturing process.

Use of semicircular heat exchangers could , however, be made much easier

with an extrusion process, for example .

32

Semicircular heat exchange channels would be very suitable for

combined condenser pumps, with the increase in heat transfer. There is an

increase in pressure loss but the determining gain is a much smaller system.

For the design of the combined condenser pump more experiments need to be

conducted with refrigerant in a semicircular heat exchanger. For the practical

application it is believed that a conservative practical answer can be obtained

by using the theory for normal round tubes. With this approach the design of

such a combined condenser pump would be possible.

The results obtained in this study could be used to verify a

computational fluid dynamics (CFD) model. Then CFD model could then be

expanded to different diameters of pipe and even more configurations of

semicircular heat exchangers.

This research could also be expanded to the combined evaporator or

condenser fan to either cool or heat air that is being blown by a fan.

33

6. References

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34

[12] Hu X & Jacobi AM. Local heat transfer behaviour and its impact on a

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