Carbon Cable

Sergio Rubio

Carles Paul

Albert Monte

PhYsical PropERTieSCarbon , Copper and Manganine

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Carbon physical Properties – Temperature Coefficient α

-0,0005 ºC-1– Density D

2260 kg/m3– Resistivity ρ

0,000035 Ω m– Specific Heat Ce

710 J/kg m– Coefficient of thermal expansion

∼ 1·10-6 C-1

CARBON PROPERTIESCARBON PROPERTIES

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COPPER PROPERTIES COPPER PROPERTIES

Copper physical Properties – Temperature Coefficient α

0,0043 ºC-1– Density D

8920 kg/m3– Resistivity ρ

0,000000017 Ω m– Specific Heat Ce

384,4 J/kg m– Coefficient of thermal expansion

1,7·10-5 ºC-1

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MANGANINE PROPERTIESMANGANINE PROPERTIES

Manganine is an alloy made from :– 86% Cu, 12% Mn, 2% Ni

Temperature Coefficient can’t be expressed– Density D

8400 kg/m3– Resistivity ρ

4,6·10-7– Specific Heat Ce

408 J/Kg.m– Coefficient of thermal expansion

15·10-6 ºC-1

WHAT IS THE HEAT ?

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HEAT TRANSFERHEAT TRANSFER

When an object or fluid is at a different temperature than another object, transfer of thermal energy, also known as heat transfer, occurs in such a way that the body and the surroundings reach thermal equilibrium.

The Heat is the energy that is transfered as consequence of a temperature difference.

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How the Heat is mesured ?How the Heat is mesured ?

Mesure of the Heat– The Heat is the kinetic energy of the particles. – It is mesured in Joule or calorie– What is a calorie ?

It is the heat energy required to increase the temperature of a gram of watter with 1ºC.

– What is a Joule ? 1 Joule = 0,24 calorie 1 calorie = 4,184 Joules

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Heat transfer mechanismsHeat transfer mechanisms

CONDUCTION– conduction is the transfer of thermal energy

between neighboring molecules in a substance due to a temperature gradient. It always takes place from a region of higher temperature to a region of lower temperature, and acts to equalize temperature differences

– The flow of energy per unit of area per unit of time is called Heat flux and is denoted Φ.

– The Heat flux is proportional with the temperature gradient and with the transfer area.

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Heat transfer mechanisms Heat transfer mechanisms

Fourier's law of Heat conduction k is the is the material's conductivity and is a physical property

of materials. S is the Area is the temperature gradient

Mesured in SI units in W/m·K

dTkSdx

Φ =

dT

dx

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Heat transfer mechanisms Heat transfer mechanisms

CONVECTION– When a fluid (gas or liquid) get in contact with

a solid surface with the temperature different from the fluid’s the heat interchanging process that occures is called convection heat transfer.

– During the convection process upwards currents are generated due to the difference of density resulting from the contact with the solid surface .

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Heat transfer mechanisms Heat transfer mechanisms

Thermal RADIATION– Different from Convection or Conduction in

which case a direct contact between objects is needed , the Radiation is the only form of heat transfer that can occur in the absence of any form of medium.

– The Heat flux is proportional with the square of power at absolute zero temperature.

– The energy is transfered as electromagnetic waves that spreads with

the speed of light.

ElECtric ENERGY AND HEAT

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Basics of electrical engineering Basics of electrical engineering

Electric current I– Represents the flow of electric charge and it is

measured in Ampere A. Potential difference V

– It is the potential difference required to transport an electric charge along a circuit , it is mesured in Volts V

Resistance– The electrical resistance of an object is a

measure of its opposition to the passage of a steady electric current

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Basics of electrical engineering Basics of electrical engineering

Ohm’s law– The relationship between the electric current ,

potential difference and resistance is :

The Resistance of an electrical cable – ρ is the Resistivity– L is the cable’s lenght– S is the cable’s area

V RI=

lR

Sρ=

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Electric currentElectric current

Ohm’s Law is aplicable in any electrical cicuit.– Conecting at the electrical supply the potential

difference is constant 230 V.

Electric current

Resistance

230 V

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Electric ResistivityElectric Resistivity

RESISTIVITY (Ω·M)

CARBON COPPER MANGANINE

3,5·10-5 1,7·10-8 4,6·10-7

• The Carbon has the resistivity 2058 times higher as the copper and 76 times higher as manganine.

• The Manganine has the resistivity 27 times higher as the copper .

• A fundamental carbon property is it’s high resistivity .

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The electric Energy and HeatThe electric Energy and Heat

The electric Cable– The electric current crossing a cable creates it’s

temperature rise.– Therefore a heat transfer to the medium is

produced .

Current

Heat Q

Heat Q

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The electric Energy and Heat The electric Energy and Heat

The amount of Heat generated by an electric cable is proportional with the electric power

The electric Power increases with the conductor rezistance.

The electric Power increases with the square of current that passes the electic cable.

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Electric energy and HeatElectric energy and Heat

Equation for any type of energy– Electric energy Ee

– Heat energy Q

– Transfered energy given by Fourier’Law Ef

2eE Ri t=

eQ mc t=

fE kS T t= ∆

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Specific Heat Specific Heat

SPECIFIC HEAT (J/Kg·K)

CARBON COPPER MANGANINE

710 384,4 408

• Carbon’s specific Heat is higher .

• Specific Heat for liquid watter is 4180.

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Carbon Cable Carbon Cable

The Temperature coefficient shows that the resistance depends on the temperature .

Carbon resistance decreases when the Temperature increase .

In Copper’s case the resistance increases when the Temperature increase .

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Electric Resistance Electric Resistance

The Resistance variation depends on the Temperature

– R = R0 (1+α(T – T0))– R, resistance at temperature T– R0, resistance at temperature T0– α, temperature coefficient

In the case of metallic conductors the resistance increases when temperature increases and for dielectric materials the resistance decreases when temperature increases.

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The Temperature Coefficient, αThe Temperature Coefficient, α

TEMPERATURE COEFFICIENT(ºC-1)CARBON COPPER MANGANINE

-0,0005 0,0039 0,000015

• The Carbon has a negativ temperature coefficient.

• In carbon’s case the resistance decreases when temperature increase and it can be considered a low conductive material in opposition with other materials that are good conductors.

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The Resistance and the TemperatureThe Resistance and the Temperature

The Resistance depends on Temperature– R = R0 (1+α∆T)

The equation for energy without Heat transfer:– Ri2t = mce ∆T

Do we really need this equation ???

( ) 201

eR T i t mc Tα+ ∆ = ∆

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Ohm’s LawOhm’s Law

Ohm’s Law establishes a linear relationship between supply voltage and current intensity.

– The graph of the relationship between the current and the voltage is a straight one .

– The angle is given be the Resistance R.V

I

R

V RI=

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Resistance of the carbon CableResistance of the carbon Cable

Mesured Resistance at the carbon’s cable– The taken mesurements on the supply votage

and on current indicate the existance of a light parabolic dependence , this coincides with the amount of negative temperature coefficient.

Voltage V

Current intensity, A

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The Model of the Carbon resistanceThe Model of the Carbon resistance

Graph obtained experimentally– At first glance it seems to be a line but in reality

it is a parable.

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Carbon resistance model Carbon resistance model

We can obtained the parabolic curve equation based on the experimental obtained values.

Obtained values– a = 137·10-12– b = 28,2·10-3– c = 5,73·10-9

The values “a” and “c” can be neglected The resistance may be considerate constant

21

2I aV bV c= + +

21

2I aV bV c= + +

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Resistance of the carbon Cable Resistance of the carbon Cable

Linear dependence– I = 28,2·10-3 V

Value of one meter carbon cable resistance , obteined by mesuring.

– R = 35,46 Ω Theoretic calculation of the resistance

The experimental and theoretical values are the same .

5

6

13 510 35

10, ·l

RS

ρ −−

= = = Ω

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The resistance of any carbon cableThe resistance of any carbon cable

The carbon cable is composed by multiple carbon fibres.

The studied cable containes 12000 carbon fibers .

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The carbon cable with 12000 filamentsThe carbon cable with 12000 filaments

Resistance calculation– Starting from experimental results:– I =29,8·10-3 V– R = 1/ 29,8·10-3 = 33,5 Ω– We obtain the value of 35 Ω

The area calculations

210 0035 0 000001

35, ,l

S mR

ρ= = =

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The carbon cable with 12000 filaments The carbon cable with 12000 filaments

The resistance of carbon , copper , manganine– For cables 1 m long one of carbon , one of

copper and anotherone of manganine– Carbon resistance

35 Ω– Copper resistance

0,017 Ω– Manganine resistance

0,42 Ω ThE carbon caBLE has a RESISTANCE MUCH

HIGHER THAN THE COPPER or manganine CABLE .

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The carbon cable with 12000 filaments The carbon cable with 12000 filaments

Cable’s section is 1 mm2 There are 12000 carbon filaments in one mm2

dd1

S

S1

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The carbon cable with 12000 filamentsThe carbon cable with 12000 filaments

The fililament’s diameter

Carbon filament’s diameter– The filament’s section is

– The diameter is

2 12 2 1 13

4,d S

S d mmππ π

= → = = =

25 21

8 331012000

, ·mmmm−=

58 33102 0 01, · ,

filamentd mm

π

−

= =

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The carbon cable with 12000 filaments at 230 V The carbon cable with 12000 filaments at 230 V

Carbon cable– current 6,57 A

Copper cable– current 13529,4 A

Manganine cable– current 547,6 A

The Carbon Cable consumes less Current as other cables .

– In the same geometric condITions

230 V

current

Resistance

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The filament resistanceThe filament resistance

Carbon cable with N filaments– Considering N carbon fibers connected in

parallel

N

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Carbon cable Carbon cable

Resistors in paralel

– R1 = 12000·35 = 420000 Ω The equation to find the resistance of a carbon

cable composed by N fibers.

11 1

1 1N

TiT i

NR NR

R R R== = ⇒ =∑

420000NR

N=

THermAL BEHAVIOR

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Carbon cable with 12000 filamentsCarbon cable with 12000 filaments

The resistive behavior for materials , without Fourier heat transfer .

– Ohm’ Law V = R I

– Joule’s Law Ri2t = mce ∆T

– Equations

2e

DS c Ti

tρ ∆=

2e

TV Dc l

tρ

∆=

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Carbon Cable Carbon Cable

Necessary time to raise the temperature at 50ºC, with 1 A. (without thermal transfer – Fourier’s Law)

For carbon cable– 2,3 s

For copper cable– 10084,8 s

The CarboN CaBle heats up much faster than a metallic conductor .

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Carbon Cable Carbon Cable

The necessary energy for raising the temperature with 50ºC is for

– Carbon Q = 80,23 J

– Copper Q = 171,44 J

The energetic carbon-copper relationship:

80 23 171 441 13

80 23

, ,,

,Car CuRQ −

−= =

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Carbon Cable Carbon Cable

THE carbon requires less energy than copper to reach the same temperature .

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The thermal behaviorThe thermal behavior

Thermal conduction –Fourier’s Law Energy conservation

20

( )e l

Ri dt mc dT KS T T dt= + −

( )0 01 exp

f

tT T T T

τ

= + − − ÷ ÷ e

l

mc

kSτ =

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The thermal behavior The thermal behavior

The theoretical graph for the relationship between temperature and time :

Transitory Stationary

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The thermal behavior The thermal behavior

The temperature-time obtained experimentally for a carbon cable

The thermal behavior

The temperature-time graph for the PANEL MULTILAYER system

ThermalTechnology– The time to reach

the stationary regim is

10 minute.

EnergY AND HEAT

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Energy TransferEnergy Transfer

Electric energy = internal energy + conduction energy

– Electric energy is influenced be the cabel is used

– Internal energy is the one that the cable is retaining

– Conduction energy is the one that the cable releases .

2e

dTRi t mc dT KS t

dx= +

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Internal EnergyInternal Energy

The relationship between the absorbed heat and the one released

The absorbed heat depends on the de product mce Q=mce ∆T = (DSl)ce ∆T

Despite the fact it has a higher speciffic heat the carbon has a lower density .

DENSITY (Kg/m3)

CARBON COPPER MANGANINE

2260 8920 8400

Internal Energy

CARBON

MANGANINE

COPPER

1604600 3360000 3428848

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Specific heat capacitySpecific heat capacity

The specific heat capacity is the relationship between the heat flow that enters in the system relative to the increase of temperature

e e

Qmc DSlc

T= =

∆

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Specific heat capacity Specific heat capacity

Considering a cable 1 m long with the section of 10-6 m2

SPECIFIC HEAT CAPACITY(J/K)

CARBON COPPER MANGANINE

1,6 3,4 3,36

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Carbon Cable Carbon Cable

The carbon combines two optimal conditions: High specific heat capacity

It can store a large amount of heat– Lower density

It can easily release the heat Theese features gives it a high specific heat .

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Comparing conduction energyComparing conduction energy

Comparing two watter deposits

= +

Electric Energy Absorbed Heat Released Heat

CONDUCTION HEAT TransmisiON

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The carbon cable structureThe carbon cable structure

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Heat TransmissionHeat Transmission

The temperature inside a cable dependes on it’s radius.

– T= T(r) The heat flow that crosses the cylindrical

section depends on the temperature gradient . It is called the heat conduction by Fourier’s

Law

dTkSdr

Φ =

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Heat Transmission Heat Transmission

In stationary equilibrium the heat flow is:

The value of the time constant in transitory regime is :

1 2

2

1

2

ln

T Tkl

R

R

π−

Φ =

( )2 22 1 2

12

lnD R R R

k Rτ

−=

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Thermal Conductivity Thermal Conductivity

Thermal resistance

Thermal conductivity

2

1

1

2ln

T

RR

kl Rπ

= ÷ ÷

22

12

lnRV

kRl T Rπ

=∆

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Thermal conductivity kThermal conductivity k

Let’s find the value of k starting from the experimental results for diferent lengths.

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Thermal conductivity Thermal conductivity

We obtain the value k = 0,086 W/m·K

0 1 2 3 4 5 60

0,05

0,1

Lineare ()

Cable lenght

Thermal conductivity

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Carbon cable efficiency Carbon cable efficiency

Results obtained – Electric power used: 155,58 W– Transmited caloric power : 101,82 W

The carbon fiber efficiency

The efficiency is approximate 0,7.

2

101 820 65

155 58

, ,,

KS T

Riη ∆= = =

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Carbon CableCarbon Cable

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Cablul de carbonCablul de carbon

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Carbon CableCarbon Cable

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Carbon CableCarbon Cable

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Carbon CableCarbon Cable

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Carbon CableCarbon Cable

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Carbon CableCarbon Cable