2-D Heat Transfer Model of A Horizontal U-Tube M. S. Islam 1, A. Fujimoto 2, A. Saida 2 and T....

2-D Heat Transfer Model of A Horizontal U-Tube

M. S. Islam1, A. Fujimoto2, A. Saida2 and T. Fukuhara2


15th International Road Weather ConferenceFebruary 5th - 7th, 2010 in Québec City, Canada

1 Khulna University of Engineering & Technology, Bangladesh2 University of Fukui, Japan


Contents

1. Introduction

2.HUT Road Heating System

3.Numerical Model and Heat Transfer Equations

4. Indoor Experiments

5.Results and Discussions

6.Conclusions


Introduction

A slip accident at specific places such as intersections, bridges, tunnel mouths occurs frequently in winter. because the road surface conditions are remarkably changeable


Road heating system has a significant requirement for reducing winter traffic accidents at the specific places

Introduction


Paying attention to the use of shallow ground heat inside the tunnel, we have been developing Horizontal U-Tube (HUT) road heating system in order to prevent road freezing at tunnel mouth.

Shallow ground heat

Introduction

Horizontal U-Tube (HUT)

Anti-freezing pavement


Tu n n e l l e n g t h = 1 0 4 5 ( m )

Tu n n e l

( = 0 .0 4 m , L = 1 0 0 m )I n v e r t

C e n t r a l p a r t E n t r a n c e

G r o u n d h e a t

R o a d h e a t i n g

P a v e m e n t i n c o r p o r a t i n g h e a t e x c h a n g e p i p e( = 0 . 0 1 5 m , L = 7 0 m )

R o a d h e a t i n g a r e a = 1 7 5 ( m )

7 ( m ) @ 2 5 u n i t s

2

2

S l i p p e r y r o a d

H U T l e n g t h = 5 0 0 ( m )5 0 ( m ) @ 2 0 u n i t s

HIP

HUT Road Heating System

In winter, the HUT fluid is warmed associated with the extraction of the shallow ground heat, while it passes through the HUT and then the extracted heat is supplied to the pavement surface via the HIP.

Since the shallow ground heat has a low energy density, a reliable HUT heat transfer model is required to calculate the extracted ground heat for different tunnel lengths and tunnel ground temperatures


To develop heat transfer models of HUT system.

To examine the validity of the proposed models by indoor experiments.

Specific Aims


1. The temperature gradient of the HUT fluid in the x direction is negligibly small in comparison with the ground temperature gradient in the y or z direction.

2. From the assumption 1), the HUT ground temperature, Tg, is assumed to be uniform in the x direction.

3. From the assumption 2), the heat transfer in ground is applicable in the y-z two-dimensional plane.

Model Assumptions

i = 1

n

i = 1

n Y

j = 1j p n Z

xy

z

G o i n g t u b e

R e t u r n t u b e

T i n T o u t

d y

d z

T g 1

T g n

i p

I n l e t

O u t l e t

T i n T o u t<

G r o u n d h e a t

H U T g r o u n d e l e m e n t ( i p , j p )

x : Longitudinaly : Vertical

z :Transversal


d y

d xd z

x

z

y

G o i n g t u b e

R e t u r n t u b e

q y i n

q y o u t

q x o u t

q ( 2 ) o u t

q ( 2 ) i n

q ( 1 ) o u t

q ( 1 ) i n

E ( 1 )

E

T w (1 )

q x i n

Tw (2 )

q z i n

q z o u tz

z+dz

x+dx( 2 )

x

y + d y

y

Ground surrounding HUT

g

2

1m)m(

gg

gg

gg .E

z

T

zy

T

yt

TC

)m(wg)m( TTE Extracted Heat Flux

[m=1 or 2]

[m=1: for going tube, m= 2: for return tube]

Energy Balance Equations

Tg : ground temperature(ρC)g : heat capacity of groundg : thermal conductivity of groundE(m) : extracted heat flux per unit

circumference- surface area of HUT

ηg : the ratio of the circumference-surface area of HUT to the volume of HUT ground element

: heat transfer coefficient between HUT fluid and HUT ground.

Tw : HUT fluid temperature


d y

d xd z

x

z

y

G o i n g t u b e

R e t u r n t u b e

q y i n

q y o u t

q x o u t

q ( 2 ) o u t

q ( 2 ) i n

q ( 1 ) o u t

q ( 1 ) i n

E ( 1 )

E

T w (1 )

q x i n

Tw (2 )

q z i n

q z o u tz

z+dz

x+dx( 2 )

x

y + d y

y

Heat Carrier Fluid of HUT (HUT fluid)

Energy Balance Equations

(ρC)w : heat capacity of HUT fluidw : thermal conductivity of HUT fluidV : velocity of HUT fluidHp : ratio of circumference-surface area to volume of

HUT

p

2

1m)m(

)m(ww

)m(ww

)m(ww .E

x

TVC

x

T

xt

TC


Indoor Experiments

T h erm ocou p les a t th ree d ifferen t section s

C o n sta n t tem p era tu re b a th

C o o lin g w a ter ta n k

S o il b ox in c lu d in g a m in ia tu re H U T

In flo w p ip e

O u tflo w p ip e

D a ta loggers

F lo w co n tro l v a lv es

D a ta lo g g ers

M in ia tu re H U T

0 .4 0 5 m

1.2

m0 .3 0 5 m

0.2

m0 .

2 m

0 .4

m

S ectio n 3

S ectio n 2

S ectio n 1

Air temperature : 25ºC

HUT fluid temperature : 10ºC

Constant temperature bath

Miniature HUT

0.15m

45mm

1.0m

Soil box


Pipe pitch: 4.5 cm Pipe pitch: 12 cm1.5 cm

4 0 .5 cm 4 0 .5 cm

30.5

cm

1 .5 cm 1 .5 cm

R etu rn tu b eG o in g tu b e G o in g tu b e R etu rn tu b e 1.5

cm

x: P o sition o f th erm o-cou p leH U T p itch = 12 cmH U T p itch = 4 .5 cm

Thermo-couples position


Experimental Conditions

CaseNo.

Room conditionsFlow rate

(m3/sec × 10-7)Ta

(oC)

RHa

(%)

1

25 50

7.0

2 12.4

3 20.8

4 25.7

5 47.6


2

D i s t a n c e f r o m t h e i n l e t o f H U T ( m )

Q = 1 2 . 1 04 × -7 m 3 /sec

Longitudinal profile of HUT fluid temperature

Flow rate: 47.6×10-7 m3/sec

Inlet of HUT

2 hours after beginning experiment

Going pipe

Return pipe

Distance from the inlet of HUT (m)

HU

T f

luid

te

mp

era

ture

(ºC

)

Outlet of HUT


0 .0 0 .2 5 0 .5 0 .7 5 1 1 .2 5 1 .5 1 .7 5 28

1 0

1 2

1 4

1 6

1 8

2 0

2 2

2 4

2 6

E la p sed tim e , t (h r.)

Flu

idte

mp

erat

ure

,Tin

,Tou

t(o C

)

Q = 1 2 . 1 04 × -7 m 3 /sec

Inlet of HUT


Elapsed time (hour)

HU

T f

luid

te

mp

era

ture

(ºC

)

Outlet of HUT

Measured

Calculated

Time change of HUT fluid temperature

= 46 W/m2K)


1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 60 .3 0

0 .2 5

0 .2 0

0 .1 5

0 .1 0

0 .0 5

0 .0

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 61 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

S ectio n -1 (c-c)

= 5 8 (W /m2K )

Ver

t ic a

l dep

t hm

) S ectio n -2 (c-c)

= 5 8 (W /m2K )

S ectio n -3 (c-c)

= 5 8 (W /m2K )

O b s. C a l.

In itia l tem p .

A fte r 1 5 m in s .


A fte r 1 .5 h rs .

a ) C a se-2

b ) C a se-5

H U T

G rou n d tem p era tu re ( C )o

G rou n d tem p era tu re ( C )oG rou n d tem p era tu re ( C )o

O b s. C a l.

In itia l tem p .



A fte r 2 h rs .1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 61 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

S ectio n -1 (c-c)

= 4 6 (W /m 2K )

S ectio n -2 (c-c)

= 4 6 (W /m 2K )

S ectio n -3 (c-c)

= 4 6 (W /m 2K )


H U T

G rou n d tem p era tu re ( C )o G rou n d tem p era tu re ( C )o

0 .3 0

0 .2 5

0 .2 0

0 .1 5

0 .1 0

0 .0 5

0 .0

Ve r

tica l

dep t

hm

) Vertical ground temperature

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 60 .3 0

0 .2 5

0 .2 0

0 .1 5

0 .1 0

0 .0 5

0 .0

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 61 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

S ectio n -1 (c-c)

= 5 8 (W /m2K )

Ver

t ical

dep t

hm


= 5 8 (W /m2K )

S ectio n -3 (c-c)

= 5 8 (W /m2K )

O b s. C a l.

In itia l tem p .



A fte r 1 .5 h rs .

a ) C a se-2

b ) C a se-5

H U T



O b s. C a l.

In itia l tem p .



A fte r 2 h rs .1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 61 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

S ectio n -1 (c-c)

= 4 6 (W /m 2K )

S ectio n -2 (c-c)

= 4 6 (W /m 2K )

S ectio n -3 (c-c)

= 4 6 (W /m 2K )


H U T


0 .3 0

0 .2 5

0 .2 0

0 .1 5

0 .1 0

0 .0 5

0 .0

Ve r

tica l

dep t

hm

)

26

InitialAfter

15 mins.

After 30 mins.

After 2 hrs.

c-c section

Soil temperature (ºC)

Ve

rtic

al d

ep

th (

m)

= 46 W/m2K


0 5 0 1 0 0 1 5 0 2 0 0 2 5 00

1

2

3

4

5

6

H U T R ey n o ld s n u m b er, R e

N u = 1 .1 5 R e0 .2 1 + 1 .5

R = 0 .9 5

HU

T N

uss

elt

nu

mb

er, N

u

Relation between Nu and Re

HUT Reynolds number, Re

HU

T N

us

selt

nu

mb

er, N

u

Nu = 1.15 Re + 1.5(for 30 < Re <230)

0.21


Conclusions

1. The relation between the HUT Nusselt number and the HUT Reynolds number is given by a power function and Nu increases with Re.

2. The indoor experimental results allowed the proposed model to reasonably predict the extracted ground heat.

A simplified heat transfer theory of a Horizontal U-Tube (HUT) is proposed and the applicability of the proposed model was discussed in comparison with experimental results using a miniature HUT


Thank You

2-D Heat Transfer Model of A Horizontal U-TubeEnvironmental Heat and Hydraulics Lab.

A Dissertation Submitted to the University of Fukui for the Degree of Doctor of Engineering

2.3 Initial & Boundary Conditions for Indoor Examination

Fig. 9 Boundary conditions for indoor examination

Heat Transfer Model of Horizontal U-Tube (HUT) Road Heating System

T (t)right

T (t)bot

T (t)left

T (t)surf

Miniature HUT

T (t)in T (t)out

CL

CL

C L

C L

Soil

Initial Conditions

• Horizontal and vertical soil temperature

•Fluid temperature at the inlet of HUT

Boundary Conditions

• Room temperature = 25 oC

• Relative Humidity = 50 %

• Time variations of the boundary soil temperatures were interpolated from the observed data obtained at an interval of 30 seconds.



3.2 Results of Indoor Experiments

Fig. 18 Observed and calculated isothermal contours after 1.5 hours system operation (Case-5)


Observed


8

1 0

1 2

1 4

1 6

1 8

2 0

2 2

2 4

2 6

= 5 8 (W /m 2K )

R etu rn tu b eG oin g tu b e

S ectio n -1 (a -a )

W id th (m )


G oin g tu b e R etu rn tu b e

= 5 8 (W /m 2K )

W id th (m )



= 5 8 (W /m 2K )

W id th (m )

0 .0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .41 0

1 2

1 4

1 6

1 8

2 0

2 2

2 4

2 6

S ectio n -1 (a -a ) = 4 6 (W /m 2K )

R etu rn tu b eG oin g tu b e

W id th (m )



= 4 6 (W /m 2K )

W id th (m )



= 4 6 (W /m 2K )

W id th (m )

a ) C a se-2

b ) C a se-5

Gro

und

tem

pera

tur e

(C

)o

Gro

un

d te

mpe

ratu

re (

C)

o

0 .0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4

0 .0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .40 .0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4

O b s. C a l.

In itia l A fte r 1 5 m in s .

A fte r 3 0 m in s A fte r 2 h rs . (C ase -2 )

O b s. C a l.

A fte r 1 .5 h rs . (C a se -5 )

O b s. C a l.

Horizontal ground temperature

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 60 .3 0

0 .2 5

0 .2 0

0 .1 5

0 .1 0

0 .0 5

0 .0

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 61 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

S ectio n -1 (c-c)

= 5 8 (W /m2K )

Ver

t ic a

l dep

t hm


= 5 8 (W /m2K )

S ectio n -3 (c-c)

= 5 8 (W /m2K )

O b s. C a l.

In itia l tem p .



A fte r 1 .5 h rs .

a ) C a se-2

b ) C a se-5

H U T



O b s. C a l.

In itia l tem p .



A fte r 2 h rs .1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 61 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

S ectio n -1 (c-c)

= 4 6 (W /m 2K )

S ectio n -2 (c-c)

= 4 6 (W /m 2K )

S ectio n -3 (c-c)

= 4 6 (W /m 2K )


H U T


0 .3 0

0 .2 5

0 .2 0

0 .1 5

0 .1 0

0 .0 5

0 .0

Ve r

tica l

dep t

hm

)

a-a section



3.2 Results of Indoor Experiments

Fig. 20 Extracted heat flow with elapsed time


Case-2 Case-5

00 0.25 0.5 0.75 1 1.25 1.5 1.75 2

50

100

150

200

250

300

Elapsed time, t (hr.)

Observed Calculated

00

Ext

ract

ed h

eat

flo

w, H

(W

)ex

t

R = 60 e

0 0.25 0.5 0.75 1 1.25 1.50

50

100

150

200

250

300

Elapsed time, t (hr.)

Observed Calculated

00

R = 230 e

Ext

ract

ed h

eat

flo

w, H

(W

)ex

t



3.2 Results of Indoor ExperimentsHeat Transfer Model of Horizontal U-Tube (HUT) Road Heating System

Fig. 16 Model verification based on the horizontal ground temperature profile

0 .0 0 .05 0 .1 0 .15 0 .2 0 .25 0 .3 0 .35 0 .410

12

14

16

18

20

22

24

26

S ection -1 (a -a ) = 4 6 (W /m 2K )

R etu rn tu b eG o in g tu b e

W id th (m )

S ection -2 (a -a )

G o in g tu b e R etu rn tu b e

= 4 6 (W /m 2K )

W id th (m )

S ection -3 (a -a )

G o in g tu b e R etu rn tu b e

= 4 6 (W /m 2K )

W id th (m )

Gro

und

te m

per

a tur

e (

C)

o

0 .0 0 .05 0 .1 0 .15 0 .2 0 .25 0 .3 0 .35 0 .4 0 .0 0 .05 0 .1 0 .15 0 .2 0 .25 0 .3 0 .35 0 .4

O b s. C a l.

In itia l t = 1 5 m in s .t = 3 0 m in s .

t = 2 h rs . (C ase -2 ) O b s. C a l.

t = 1 .5 h rs . (C a se -5 )

O b s. C a l.

Case-2



3.2 Results of Indoor ExperimentsHeat Transfer Model of Horizontal U-Tube (HUT) Road Heating System

Fig. 15 Model verification based on the vertical ground temperature profile

O b s. C a l.

In itia l tem p .

t = 1 5 m in s .

t = 3 0 m in s .

t = 2 h rs .1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 61 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

S ectio n -1 (c-c)

= 4 6 (W /m 2K )

S ectio n -2 (c-c)

= 4 6 (W /m 2K )

S ectio n -3 (c-c)

= 4 6 (W /m 2K )


H U T


0 .3 0

0 .2 5

0 .2 0

0 .1 5

0 .1 0

0 .0 5

0 .0

Ve r

tica l

dep t

hm

)

Case-2


0 . 0 0 . 1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 . 9 1 . 05

6

7

8

9

1 0

11

1 2

1 3

1 4

0 .0 0

0 .0 5

0 .1 0

0 .1 5

0 .2 0

0 .2 5

0 .3 0

0 .3 5

R e t u r n t u b eO u t l e t o f H U T

I n l e t o f H U T

H U T g r o u n d

G o i n g t u b e

D i s t a n c e f r o m t h e i n l e t o f H U T ( m )

O b s e r v e d C a l c u l a t e d

A f t e r 1 . 5 h r s .

= 5 8 ( W / m 2K )

E x t r a c t e d h e a t f l u x

2

Q = 47 .6 10× -7 m 3 /sec

Longitudinal profile of HUT fluid temperature


Inlet of HUT

After 2 hours after beginning of experiment

Going pipe

Return pipe

Distance from the inlet of HUT (m)

HU

T f

luid

te

mp

era

ture

(ºC

)

Outlet of HUT

2-D Heat Transfer Model of A Horizontal U-Tube M. S. Islam 1, A. Fujimoto 2, A. Saida 2 and T....

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