1 isat 413 - module iii: building energy efficiency topic 5:insulation economics heat transfer...

1

ISAT 413 - Module III: Building Energy Efficiency

Topic 5: Insulation Economics

Heat Transfer Fundamentals of Insulation

Case Example on Optimum Insulation

Case Example on Long Steam Pipes

Case Example on Water Tanks

2

• Insulation is one of the most obvious and basic ways of recovering energy. The annual fuel cost is reduced as the thickness of the insulation is increased but the capital cost of the insulation increases with the thickness and hence the financial saving must be off-set against the capital cost.

• For a typical write-off period there will normally be an economic thickness of insulation for a particular case.

Economic Thickness of Insulation

3

Thermal Resistance of Cylinder Wall

kL

r

rln

TTQ

TTkLr

rlnQ

dTkLr

drQ

i

o

oicond

oii

ocond

oT

iT

or

ir

cond

2

2

2

kL

r

rln

R i

o

2

dr

dTrLkQcond 2

as written

be can surfaces alcylinderic for

Conduction Heat ofLaw sFourier'

4

Optimum Radius of Insulation

The refrigerant of a heat pump is circulating through a thin walled copper tube of radius ri = 6 mm as shown in the Figure at left. The refrigerant temperature is Ti, ambient temperature is To, and Ti<To. The outside convection heat transfer coefficient is ho = 7 W/m2.K. What would the optimum thickness of the insulation, assuming the thermal conductivity of the insulation material is k = 0.06 W/m.K.

5

In the thermal analysis of radius systems, we must keep in mind that there are competing effects associated with changing the thickness of insulation. Increasing the insulation thickness increases the conduction resistance; however, the area available for convection heat transfer increases as well, resulting in reduced convection resistance.

To find the optimum radius for insulation, we first identify the major resistance in the path of heat flow. Our assumptions are that (1) the tube wall thickness is small enough that conduction resistance can be ignored, (2) heat transfer occurs at steady state, (3) insulation has uniform properties, and (4) radial heat transfer is one-dimension.

Optimum Radius of Insulation (continued)

6


The resistances per unit length are

where r , the outer radius of insulation, is unknown. The total resistance is

The optimum thickness of the insulation is obtained when the total resistance is maximized. By differentiating Rt with respect to r, we have

o

i

rhR

k

r/rlnR

2

1 and

2 21

o

it rhk

r/rlnRRR

2

1

221

m.K.m/W

K.m/W.

h

kr

hrrkdr

dR

oc

o

t 008607

060

2

1

2

122

7


minimum. a is Therefore, . 02

1

2

13

2

322

2

to

ooo

t Rk

h

hhk

hk

kdr

Rd

m.rc 00860

InsulationThickness (m)

OuterRadius(m)

TotalResistanceper Length(K/W)

0 0.0060 3.79

0.0010 0.0070 3.66

0.0020 0.0080 3.60

0.0025 0.0085 3.59

0.0040 0.0100 3.63

0.0060 0.0120 3.73

8

Example 1. Insulation on Long Steam PipesA steel pipe carries wet steam from a gas-fired boiler through a small workshop to a process plant. It is proposed to insulate the pipe using a glass fiber insulation with an aluminum alloy casing. Using the data below making suitable assumptions, determine: (i) the most economic thickness of insulation; (ii) the simple pay-back period for this thickness.

%C

C

W/m.K..K W/m

mm.

o

o

80 efficiencyboiler 15 pin workshoair of etemperatur

200 re temperatusteam

070 insulation ofty conductivi thermal10 insulation of

surface outsidefor t coefficienfer heat trans360 diameter outside pipe

2

Data:

9

years 5 period off-write1280 1007 763 632 531 476 length/p metreper cost

60 50 38 32 25 19 /mminsulation of thickness:insulation ofcost

Example 1 (continued)

W

K.m

x..x.DLh

L

Ah.LR.L

xW

K.m

.

x.ln

.

.x.

ln

k

rr

ln

R.L

Solutions:

ooo

ik

03317018941

1

10236010

11is surface outside on the film fluid theof resistance thermalthe

mm.in insulation theof thickness theis where440

0331701

07023602360

2

is insulation theof resisance thermalThe

3

10


m

p

L

Q../

J.

p.

hr

sechrs

m

W

L

Q

p/MJ.

hours

m

W

x...

x.lnLR

T

L

Q

0548001001

3036003000

:bygiven is lossheat

theofcost annual the therefore,30 is loss thisproduce to

gas theofcost theand ,3000 is timeoperating annual the

03317018941

1

440

0337101152001

as calculated becan length unit per fer heat trans The

6

Thickness (mm)

Capital cost (p/m)

Heat loss (W/m)

Annual fuel cost (p/m)

0 0 350.5 1419.1 19 476 129.0 522.5 25 531 111.4 451.2 32 632 97.4 394.5 50 1007 76.4 309.4 60 1280 69.4 281.1

11


below table the give to cost capital the

of years)5 period off-(write to cost fuel annual the addingby

obtained be can cost annual total the inflation and ondepreciati ignoring

one-fifth

Thickness (mm)

0 19 25 32 50 60

Total annual cost (p/m)

1419 618 557 521 510.8 537

months 10.9 years 0.907 309.4)-.11007/(1419 periodpayback i.e.

.insulatingby cost fuelin saving annual by thecost capital thedivingby found is periodback pay simple The (ii)

)( mm. 50 around is insulation of thicknesseconomic theabove,shown table the toAccording (i)

next slideot on the see the pl

12

Example 1 (conclusion)

Insulation Cost against Thickness

0

250

500

750

1000

1250

1500

0 10 20 30 40 50 60 70

Thickness (mm)

An

nua

l Cos

t (p

/m)

The economic thickness of insulation is about 50 mm.

13

Example 2. Insulation on Water Tanks

A factory has five steel tanks used for dip cleaning a product; each tank is 2 m long by 1 m high by 1.5 m wide. The detergent solution in the tanks is heated to a temperature of 65oC by steam in tubes immersed in the liquid; the steam is provided by a boiler with an efficiency, including steam distribution losses, of 60%. Using the additional data below, assuming that the heat loss through the floor of the tanks is negligible and neglecting the thermal resistance of the steel tank walls, calculate: (i) the annual cash saving if the tank walls are insulated using a 25 mm thick slab of insulating material; (ii) the annual cash saving if a double layer of Allplas balls is applied to the liquid surfaces; (iii) the simple pay-back period if the measure in (i) and (ii) are both implemented.

14


annum hours per/mL

L/mL

p/MJ..K/W m.

W/m

W/m.K. W/m

.K W/m

.K W/m

.K W/m

Co

4800 input heat of rategiven at the timeeffective60 balls Allplas ofcost

Pound)English ,( 12 cost insulation

30 boiler in used fuel ofcost 20 balls Allplas todue resistance thermaladditional

1500 balls Allplas with tanksfromn evaporatioby lossheat

0350 material insulating ofty conductivi thermal8000 surfaces liquid fromn evaporatioby lossheat

500 tank wallof inside toliquid fromt coefficienfer heat trans

10 air ambient tosurface liquidfor t coeeficienfer heat trans

10 surfaces tank allfor t coefficienfer heat trans

15 mperatureambient te

2

2

2

2

2

2

2

2

Data:

15


W

WK.m

.

Kmm.mm

R.A

T.A

R

TQ

W

K.m.

W

K.m.

K.mW

.

m..

k

LR.A

W

WK.m

.

Kmm.mm

R.A

T.A

R

TQ

W

K.m.

hR.A

hAR

tt

t

429

8160

15652151212is wallsh thefer througheat trans the

816010200350

02501020

is resistance thermal total theinsulated, tank With the

3431

1020

15652151212as calculated becan lossheat then the

102010

1

500

111

is resistance thermal the tank,duninsulatean For (i)

2

22

2

2

16


Pound)English 1297 (i.e., 129725943230

savingcash annual theyieldswhich

25943236004800

55003

insulatingby saving Annaul Hence

on.distributi steam plusboiler of efficiency overallgiven for the,5003603002 ofper tank input energy fuel a represents This

30024293431 is lossheat in reduction and

LMJ,MJ

p.

MJ,hr

sec

yr

hrskstan

Tank

W

W./ W-

17


kW.

WK.m

.

Km.m

WK.m

.

T.AW

K.m

.kW.m.mm

W

kW.Km.mK.m

Wm.m

m

W

ThAQQQQ evapconvevapT

50

30

1565512

30

by given now is

surface liquid thefrom lossheat thehence and , 0.30.210

1

toincreased is surface theof resistance thermal theAlso

545120015 becomes

nevaporatioby lossheat theballs Allplas ofon introducti After the

5251565512105128000

surface thefrom convectionplusn evaporatio todue is surface liquid thefrom lossheat the(ii)

22

2

2

22

18

Example 2 (conclusion)

months . ./.L

;L

Lm

.L.

.LMJ.MJ

p.

MJ.hr

sec

yr

hrskstan

Tank

W

kW....

42666101320 periodback -pay theTherefore,1320 900420 cost capital Total

90053m60 balls Allplas ofCost

; 4205712 iscost Insulation

66610653131297 is measuresboth for savingcash Total (iii)

Pound)English 5313.6 (i.e., 65313107712130

savingcash annual theyieldswhich

107712136004800

520500

insulatingby saving Annaul Hence

5205054525isper tank balls Allplas usingby energy in saving total thethus

2

2

7

7

1 isat 413 - module iii: building energy efficiency topic 5:insulation economics heat transfer...

Documents