# Carbon Cable. Sergio Rubio Carles Paul Albert Monte

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1 Carbon Cable Sergio Rubio Carles Paul Albert Monte

2 Carbon, Copper and Manganine PhYsical PropERTieS

3 CARBON PROPERTIES Carbon physical Properties Temperature Coefficient α -0,0005 ºC-1 Density D 2260 kg/m3 Resistivity ρ 0, Ω m Specific Heat Ce 710 J/kg m Coefficient of thermal expansion C-1 3

4 COPPER PROPERTIES Copper physical Properties Temperature Coefficient α 0,0043 ºC-1 Density D 8920 kg/m3 Resistivity ρ 0, Ω m Specific Heat Ce 384,4 J/kg m Coefficient of thermal expansion 1, ºC-1 4

5 MANGANINE 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, Specific Heat Ce 408 J/Kg.m Coefficient of thermal expansion ºC-1 5

6 WHAT IS THE HEAT?

7 HEAT 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. 7

8 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 8

9 Heat 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. 9

10 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 dt is the temperature gradient dx Mesured in SI units in W/m K Φ = dt ks dx 10

11 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. 11

12 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. 12

13 ElECtric ENERGY AND HEAT

14 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 14

15 Basics of electrical engineering Ohm s law The relationship between the electric current, potential difference and resistance is : V = RI The Resistance of an electrical cable ρ is the Resistivity L is the cable s lenght S is the cable s area R = ρ l S 15

16 Electric 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 16

17 Electric Resistivity RESISTIVITY (Ω M) CARBON COPPER MANGANINE 3, , , 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. 17

18 The 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 Heat Q produced. Current Heat Q 18

19 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. 19

20 Electric energy and Heat Equation for any type of energy Electric energy Ee Ee = 2 Ri t Heat energy Q Q = mc t e Transfered energy given by Fourier Law Ef E = ks T t f 20

21 Specific Heat SPECIFIC HEAT (J/Kg K) CARBON COPPER MANGANINE ,4 408 Carbon s specific Heat is higher. Specific Heat for liquid watter is

22 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. 22

23 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. 23

24 The Temperature Coefficient, α TEMPERATURE COEFFICIENT(ºC-1) CARBON COPPER MANGANINE -0,0005 0,0039 0, 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. 24

25 The Resistance and the Temperature The Resistance depends on Temperature R = R0 (1+α T) The equation for energy without Heat transfer: Ri2t = mce T ( ) 2 α R + T i t = mc T 0 1 e Do we really need this equation??? 25

26 Ohm 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 V = RI R I 26

27 Resistance 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. Current intensity, A Voltage V 27

28 The Model of the Carbon resistance Graph obtained experimentally At first glance it seems to be a line but in reality it is a parable. 28

29 1 I = av + bv + c 2 2 Carbon resistance model We can obtained the parabolic curve equation based on the experimental obtained values. Obtained values a = b = 28, c = 5, I = av + bv + c The values a and c can be neglected The resistance may be considerate constant

30 Resistance of the carbon Cable Linear dependence I = 28, V Value of one meter carbon cable resistance, obteined by mesuring. R = 35,46 Ω Theoretic calculation of the resistance R l 5 1 = ρ = 3, 510 = 35 Ω 6 S 10 The experimental and theoretical values are the same. 30

31 The resistance of any carbon cable The carbon cable is composed by multiple carbon fibres. The studied cable containes carbon fibers. 31

32 The carbon cable with filaments Resistance calculation Starting from experimental results: I =29, V R = 1/ 29, = 33,5 Ω We obtain the value of 35 Ω The area calculations S l 1 = ρ = 0, 0035 = 0, m R

33 The carbon cable with 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. 33

34 The carbon cable with filaments Cable s section is 1 mm2 There are carbon filaments in one mm2 S1 S d d1 34

35 The carbon cable with filaments The fililament s diameter 2 d S 1 S = π d 2 2 1, 13mm 4 = π = π = Carbon filament s diameter The filament s section is 2 1mm = 8, 3310 mm 5 2 The diameter is dfilament 5 8, 3310 = 2 = 0, 01mm π 35

36 The carbon cable with filaments at 230 V Carbon cable current 6,57 A Copper cable current 13529,4 A Manganine cable current 547,6 A current Resistance The Carbon Cable consumes less Current as other cables. In the same geometric conditions 230 V 36

37 The filament resistance Carbon cable with N filaments Considering N carbon fibers connected in parallel N 37

38 Carbon cable Resistors in paralel N 1 1 T N = = R = 1 i = 1 i 1 R R R NR T R1 = = Ω The equation to find the resistance of a carbon cable composed by N fibers. R N = N 38

39 THermAL BEHAVIOR

40 Carbon cable with filaments The resistive behavior for materials, without Fourier heat transfer. Ohm Law V = R I Joule s Law Ri2t = mce T Equations i 2 DS ce T = ρ t V Dc l T t 2 = ρ e 40

41 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. 41

42 Carbon Cable The necessary energy for raising the temperature with 50ºC is for Carbon Copper Q = 80,23 J Q = 171,44 J The energetic carbon-copper relationship: 80, , 44 RQCar = = Cu 80, 23 1, 13 42

43 Carbon Cable THE carbon requires less energy than copper to reach the same temperature. 43

44 The thermal behavior Thermal conduction Fourier s Law Energy conservation Ri 2 dt = mc dt + KS ( T T ) dt e l 0 ( ) t T = T + T T 1 exp 0 f 0 τ τ = mc ks e l 44

45 The thermal behavior The theoretical graph for the relationship between temperature and time : Transitory Stationary 45

46 The thermal behavior The temperature-time obtained experimentally for a carbon cable 46

47 The temperaturetime graph for the PANEL MULTILAYER system ThermalTechnology The time to reach the stationary regim is 10 minute. The thermal behavior

48 EnergY AND HEAT

49 Energy 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. dt 2 Ri t = mc dt + KS t e dx 49

50 Internal 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

51 Internal Energy COPPER MANGANINE CARBON

52 Specific heat capacity The specific heat capacity is the relationship between the heat flow that enters in the system relative to the increase of temperature Q mce T = = DSlc e 52

53 Specific heat capacity SPECIFIC HEAT CAPACITY(J/K) CARBON COPPER MANGANINE 1,6 3,4 3,36 Considering a cable 1 m long with the section of 10-6 m2 53

54

55 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. 55

56 Comparing conduction energy Comparing two watter deposits = + Electric Energy Absorbed Heat Released Heat 56

57 CONDUCTION HEAT TransmisiON

58 The carbon cable structure 58

59 Heat 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 Φ = dt ks dr 59

60 Heat Transmission In stationary equilibrium the heat flow is: Φ = T 2π kl 1 2 The value of the time constant in transitory regime is : ln R R T 2 1 τ = ( 2 2 ) D R R R ln 2k R

61 Thermal Conductivity Thermal resistance R 2 = ln Thermal conductivity T 1 2π kl R R 1 k = V 2 2π Rl T ln R R

62 Thermal conductivity k Let s find the value of k starting from the experimental results for diferent lengths. 62

63 Thermal conductivity We obtain the value k = 0,086 W/m K Thermal conductivity 0,1 0, Cable lenght Lineare () 63

64 Carbon cable efficiency Results obtained Electric power used: 155,58 W Transmited caloric power : 101,82 W The carbon fiber efficiency η KS T 101, 82 = = = 2 R i 155, 58 0, 65 The efficiency is approximate 0,7. 64

65 Carbon Cable 65

66 Cablul de carbon 66

67 Carbon Cable 67

68 Carbon Cable 68

69 Carbon Cable 69

70 Carbon Cable 70

71 Carbon Cable 71

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