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Pot-in-Pot refridgerator

Natália Ružičková

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2

Task

The ‘pot-in-pot refrigerator’ is a device that keeps food cool using the principle of

evaporative cooling.It consists of a pot placed inside a bigger pot with the space between them filled with a wet

porous material, e.g. sand.How might one achieve the best cooling

effect?

→ Low temperature→ Fast cooling

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3

Mechanism

vapour

transferedQ

latentQ

fridgeT

Wet porous material:Evaporation latent heat

cooling

Heat transfer from the environment

tenvironmenfridge TT Equillibrium:

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4

Preliminary Experiment

• Porous material: sand

0 20 40 60 80 100 12017

18

19

20

21

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fridgeenviroment

Time [min]

Tem

pera

ture

[°C

]

CT 8,1max

Works, but could be better

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5

Evaporation requirements

Must be wet

(capillarity)

Exposed to air flow

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Big granules: Better airflow Water drains down

Small granules: Can soak with water Little space for airflow

Sand: a granular material6

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Other kind of porous material:Cloth

• Gets soaked with water

• Can be exposed to air flow on sufficient area

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Cloth vs. sand: the difference

0 20 40 60 80 100 12015

16

17

18

19

20

21

22

cloth + sandsandenviroment

Time [min]

Tem

pera

ture

[°C

]

We havea working refrigerator

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9

A working refrigerator

Inner pot

Outer pot

Porous material: cloth

Liquid (water) for evaporation

Content

Airflow

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Task“How might one achieve the best cooling

effect?”

Simple model of the cooling Experimentally verify & optimize

Estimate the best possible cooling

→ Low temperature→ Fast cooling

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MODEL OF THE COOLING

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Model of the cooling effect• Evaporation rate:

related to volatility of the liquid (in air)

• Heat transferredfrom the surroundings:

related to thermal conductivity, capacity of air

Surface areaAir flow speedTemperature difference

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Model of the coolingCalorimetry:

Final temperature drop:

Speed of cooling:

CdTTdtBSvdtASv

tC

BSv

air eB

ATT 1

B

AT

C

BSv

fridge ofcapacity thermalC

heatlatent λ

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EXPERIMENTAL VERIFICATION& INVESTIGATION

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1. High vs. low outer pot

• Terminal temperature:depends on materials only Equal

• Cooling rate:more water bigger slower coolingC

BSv

B

AT

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High vs. low pot: final temperature

0 10 20 30 40 50 60 70 8016

17

18

19

20

21

With outside potWithout outside potEnvironment

Time[min]

Tem

pra

ture

[°C

]

Both models:the same terminal temperature

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0 200 400 600 800 1000 120012

14

16

18

20

22

24

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Low PotHigh Pot

time [s]

T [

°C]

High vs. low pot: rate of cooling

Low outer pot:Less water smaller thermal capacity

faster cooling

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2. Size and shape of the fridgeTerminal temperature:

Independent of size/shape

Speed of cooling:

Independent of size/shape

B

AT

C

BSv

Empty refrigerator:

Proportional to surface area

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Effect of different sizes

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Effect of different size

0 20 40 60 80 100 12013

14

15

16

17

18

19

20

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22

Different sizes

EnvironmentRadius 9,5Radius 7Radius 6Radius 4Radius 3,3

Time[min]

Tem

pra

ture

[C]

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Effect of different shapes

0 50 100 150 200 25013

14

15

16

17

18

19

20

21 EnvironmentRoundElongatedElongated - bigger

Time[min]

Tem

pra

ture

[C]

Size and shape of an empty fridge:No effect on cooling

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3. What’s inside

Terminal temperature:

Independent of content

Speed of cooling:

High capacity slower cooling

B

AT

C

BSv

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Changing heat capacity of the fridge

0 50 100 150 200 250 30013

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15

16

17

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19

20

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EnvironmentWith airWith waterWith sand

Time[min]

Tem

pra

ture

[C]

Air, quick

er

coolin

g

Sand, slower

coolin

g

Water, slowest

coolin

g

Bigger capacity slower cooling

No effect on final temperature

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4. Different liquid

Terminal temperature:

Grows with volatility & latent heat

Speed of cooling:

Independent of liquid(only a small capacity

difference)

B

AT

C

BSv

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Water VS. Etanol:

0 200 400 600 800 1000 12008

10

12

14

16

18

20

22

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ethanolwater

time [s]

T [

°C]

More volatile liquid lower terminal temperature

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Water vs. ethanol: exponential fit

8.14)012.0exp(*6.10 tT 0.10)014.0exp(*4.19 tT

Water Ethanol

Different liquids similar speed of coolingSlight difference: different thermal capacity

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WHAT IS THE BEST POSSIBLE EFFECT?

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Minimal temperature estimationAnalogical phenomenon:

Assman psychrometer

• Wet and dry thermometer

• Wet is cooler due to evaporation

• Equilibrium state:

• Solution: Sufficient airflow

latenttransfered dQdQ

)(])([ fridgeairpairfridgelatm

air TTceTEp

M

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0 2 4 6 8 10 12 14 16 18 2014

16

18

20

22

24

26

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30

Fridge tempera-ture

wet bulb tempera-ture

time [min]

Te

mp

era

ture

[°C

]

Wet bulb vs. refrigerator

We can get closeto the theoretical

minimum

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Minimal achievable temperature

0 0.090.180.270.360.450.540.630.720.81 0.9 0.99101520253035404550

10 1112 1314 1516 1718 1920 2122 2324 2526 2728 2930 3132 3334 3536 3738 39

CTair

humidityRelative

CT fridge :Colour

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Best cooling effect

tC

BSv

air eB

ATT 1

Sufficient air flow

volatile liquid with low

concentration in air (eg. Ethanol)Minimise thermal

capacity of the fridge (eg. Low outer pot)

Maximize the area

of evaporati

on

speed

Minimal temperatur

e

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0 0.090.180.270.360.450.540.630.720.81 0.9 0.99101520253035404550

10 1112 1314 1516 1718 1920 2122 2324 2526 2728 2930 3132 3334 3536 3738 39

Thank you for your attention

CTair

humidityRelative

CT fridge :Colour

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APPENDICES

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Assman psychrometer theory

Assumptions:• Air cools to Tfridge; vapor pressure saturates

(thanks to fast airflow)• Equilibrium of heat flow:

• Numerically solve for(complicated function )

latenttransfered dQdQ

fridgeT)(TE

Wet bulb

)(])([ fridgeairpairfridgelatm

air TTceTEp

M

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EXTRA MEASUREMENTS

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Airflow importance

0 20 40 60 80 100 120 14013

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15

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enviromentno fanfan

Time [min]

Tem

pera

ture

[°C

]

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Water vs. ethanol:Rate of evaporation

0 200 400 600 800 1000 120027293133353739414345

ethanolewater

time [s]

mass [

g]

Ethanol: more volatile

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Do we need cloth or not?

0 20 40 60 80 100 12015.5

16.5

17.5

18.5

19.5

20.5

21.5

Cloth

Cloth, Sand, Wa-ter

Sand and a lot of water

Sand and a little of water

Environment

Only water

Time [min]

Tem

pra

ture

[°C

]

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What is the best material for cloth?

0 20 40 60 80 100 120 14013

14

15

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Fluffy clothNormal clothenviroment

time [min]

Te

mp

era

ture

[°C

]

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Why the type of cloth does NOT matter?

1) Water fills gaps

• Water fills gaps.

• The surface of water = the area of evaporation

The same as normal cloth

Area of evaporation

=

area through which heat gets in

• Equilibrium temperature doesn’t change

2) Water soaks

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Effect of different sizes

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Effect of different shapes

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Our refrigerator

tC

BSv

air eB

ATT 1

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Covered VS uncovered areas

Height of

cloth

• Uncovered areas heat gets in

• Covered areas Evaporation + heat gets in

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Does area of cloth matter?

0 1 2 3 4 5 6 7 8 9 1013

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The height of cloth

Height of cloth[cm]

TER

MIN

AL T

em

pra

ture

[°C

]

Whole fridge must be covered

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Why istn’s the second pot needed?

Area of evaporation

= area through which heat expands

We do not need the second pot

only requirement for fridge’s surface

…ISOLATED AREAS MUST BE UNCOVERED WITH

CLOTH

So that area of evaporation

= area trough heat gets in

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Speed of cooling

tcm

Svk

vair

efftotalek

LkTT

2

12

1

Svdtkdmwater 1

CdTdtTTSvkdtSvLk fridgeairV )(21

efftotalpotpotww cmcmcmC

k1= ability of liquid to evaporate [kg/m3]k2= part of air which cools down [J/Km3]

Temperature difference

1/tauProperties of liquid

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Assman psychrometer: theory

Equillibriumof heat flow:

Air cools to Tfridge; vapor pressure saturates:

fridgeairairairtransfered TTcdmdQ

vwaterlatent LdmdQ

latenttransfered dQdQ

eTEp

nMdQ fridgelatent

fridgeairptransfered TTncdQ

)(])([ fridgeairpairfridgelatm

air TTceTEp

M

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Assman psychrometer: theory

Surrounding air:– Transfers heat

to the cloth:

– Absorbs water vapor(heat used for evaporation)

Equilibrium (terminal temperature):

fridgeairairairtransfered TTcdmdQ

vwaterlatent LdmdQ

latenttransfered dQdQ

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Minimal T: theoretical estimation

Terminal temperature:

Numerically solved for (complicated function )

)(])([ fridgeairpairfridgelatm

air TTceTEp

M

)( fridgeairairairT

transferedlatent

TTcdmdmL

dQdQ

fridgeT

)(TE

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Conclusion – What should the most effective refrigerator look like?

• Minimal temperature:– sufficient air flow, maximize evaporation area– volatile liquid with low concentration in air (eg.

Ethanol)

• Fastest cooling:– Fast air flow– Minimise thermal capacity of the fridge (eg. Low

outer pot)

• Prediction of minimal temperature

tC

BSv

air eB

ATT 1