Theoretical formulas

Thermal

Thermal

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Electric

Electric

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Unit conversion

Unit conversion

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Thermocouples and PT100 sensors

Thermocouples and PT100 sensors

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Thermal

Heating of static products

Heating of static products without change of state:

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Determination of the power required for heating static products, which do not change state when the temperature rises:

  • Legend:
    • P: power (W)
    • m: mass to be heated (kg)
    • Cpm: specific heat (J/kg.K)
    • Ti: initial temperature (°C)
    • Tf: final temperature (°C)
    • Δt: temperature rise time (sec)
    • 1.2: safety factor

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This calculation makes it possible to estimate the theoretical power to be installed to heat the material alone. The parameters taken into account do not take into account the thermal losses of the installation.

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Heating of static products with change of state:

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Determination of the power required for heating static products changing state during the rise in temperature:

  1. Energy requirment to heat the product to the state change temperature:
  2. Amount of heat required to obtain a change of state:
  3. Amount of heat to heat the product to its final temperature:

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  1. Total power:

  • Legend:
    • Q: amount of heat (J)
    • m: mass to be heated (kg)
    • Cpmf: average specific heat, between the initial temperature and the state of change temperature (J/kg.K)
    • Ti: initial temperature (°C)
    • Tc: temperature at change of state (°C)
    • Lf: Latent heat of fusion (J/kg)
    • Cpmi: average specific heat, between the change of state temperature and the final temperature (J/kg.K)
    • Tf: final temperature (°C)
    • Δt: Required warm up time to reach the final temperature (sec)
    • 1.2: safety factor
    • P: power to be installed (W)

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  1. Downloadable calculation in excel
  1. .

This calculation makes it possible to estimate the theoretical power to be installed to heat the material alone. The parameters taken into account do not take into account the thermal losses of the installation.

Heating of circulating liquids

Heating of products in circulation, without change of state:

Determination of the power required for heating liquids in circulation, which do not change state when the temperature rises:

  • Legend:
    • P: power (W)
    • Q: flow (m3/h)
    • ρ: density (kg/m3)
    • Cp: specific heat (J/kg.K)
    • Ti: initial temperature (°C)
    • Tf: final temperature (°C)
    • 1.2: safety factor

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Surface load calculation

Determination of power density on a cylindrical surface:

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This formula can be adapted to collar-type resistors, cartridges, shielded elements, etc.

Collars:

Cartridges:

Shielded elements: DIAGRAM

For flat surface resistors

Electric

Single phase circuit

Calculation of power, intensity and ohmic value:

Equations usable in single-phase alternating current or in direct current, for ohmic resistors

  • Calculations
    • U = Re x I ⇔ Re = U / I ⇔ I = U / Re
    • P = U x I ⇔ U = P / I ⇔ I = P / U
    • P = Re x I² ⇔ Re = P / I² ⇔ I = √(P / Re)
    • P = U² / Re ⇔ Re = U² / P ⇔ U = √(P x Re)
  • Legend:
    U: voltage (V) // Re: equivalent resistance (Ω) // I: current (A) // P: power (W)

Coupling resistors in series:

  • Calculations :
    • Re = R1 + R2 + …
    • I = I1 = I2 = …
    • U = U1 + U2 + …
  • Legend:
    U: voltage (V) // Re: equivalent resistance (Ω) // I: current (A)

Coupling resistors in parallel:

  • Calculations :
    • 1/Re = 1/R1 + 1/R2 + …
    • I = i1 + i2 + …
    • U = U1 = U2 =…
  • Legend:
    U: voltage (V) // Re: equivalent resistance (Ω) // I: current (A)
Three-phase circuit

In the cases below, we will base ourselves on cases with 3 resistors of identical ohmic value, so that each line is balanced.

Triangle connection:

  • Calculations :
    • I = ix √3
    • U = Ur
    • Pglobal = (3 x U²) / R = √3 x U x I = 3 x U xi

  • Legend:
    U: voltage in the line (V) // Ur: voltage by resistance (V)
    R: ohmic value per resistor (Ω)
    I: current in the line (A) // i: current by resistance (A)


Star connection

In the case of 3 resistors of identical ohmic value.

  • Calculations :
    • I = i
    • U = Ur x √3
    • Pglobal = U² / R = (3 x Ur²) / R = √3 x U x I

  • Legend:
    U: voltage in the line (V) // Ur: voltage by resistance (V)
    R: ohmic value per resistor (Ω)
    I: current in the line (A) // i: current by resistance (A)

Unit conversion

Temperature

Kelvin………… K = °C + 273

Celsius………. °C = K – 273

Energy

1 joule = 0.24 calories

1 calorie = 4.18 joules

Joules: J

calories: calories

Volume

1 liter = 1 dm3 = 0.001 m3

1m3 = 1000 liters

Specific heat

1 cal/kg. K = 4.18 J/ kg.K

1 J/ kg.K = 0.238 cal/kg.K

Thermocouples and probes

Thermocouples

Standard colors of thermocouple cables

Couple

International NF EN IEC 60584-3

France NF C 42-324

England BS 1843

Germany DIN 43714

Japan JISC1610

USA ANSI/MC96.1

J Pole+
Pole-
K Pole+
Pole-

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Table of Electromotive Force FEM of thermocouples J

According to standard NF EN IEC 60584-1
Alloy: Positive pole = iron /// Negative pole = copper – nickel
Theoretical operating temperature range: -200°C to + 750°C

FEM, for a cold junction (reference point) at 0°C.
EMF in millivots, temperature in celsius.

°C0102030405060708090
00,0000,5071,0191,5362,0582,5853,1153,6494,1864,725
1005,2685,8126,3596,9077,4578,0088,5609,1139,66710,222
20010,77711,33211,88712,44212,99813,55314,10814,66315,21715,771
30016,32516,87917,43217,98418,53719,08919,64020,19220,74321,295
40021,84622,39722,94923,50124,05424,60725,16125,71626,27226,829
50027,38827,94928,51129,07529,64230,21030,78231,35631,93332,513
60033,09633,68334,27334,86735,46436,06636,67137,28037,89338,510
70039,13039,75440,38241,01341,64742,283

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Table of EMF Electromotive Force of K thermocouples

According to standard NF EN IEC 60584-1
Alloy: Positive pole = nickel-chrome /// Negative pole = nickel-aluminum
Theoretical operating temperature range: -200°C to + 1100°C

FEM, for a cold junction (reference point) at 0°C.
EMF in millivots, temperature in celsius

°C

0102030405060708090
00,0000,3970,7901,2031,6112,0222,4362,8503,2663,681
1004,0954,5084,9195,3275,7336,1376,5396,9397,3387,737
2008,1378,5378,9389,3419,74510,15110,56010,96911,38111,793
30012,20712,62313,03913,45613,87414,29214,71215,13215,55215,974
40016,39516,81817,24117,66418,08818,51318,93819,36319,78820,214
50020,64021,06621,49321,91922,34622,77223,19823,62424,05024,476
60024,90225,32725,75126,17626,59927,02227,44527,86728,28828,709

700

29,12829,54729,96530,38330,79931,21431,62932,04232,45332,866
80033,27733,68634,09534,50234,90935,31435,71836,12136,52436,925
90037,32537,72438,12238,51938,91539,31039,70340,09640,48840,879
100041,26941,65742,04542,43242,81743,20243,58543,96844,34944,729
1100 45.108
PT100 probe

Table of the ohmic value of PT100 probes, depending on the temperature:
According to standard NF EN IEC 60751

°C

0

10

20

30

40

50

60

70

80

90

0

100,00

103,90

107,79

111,67

115,54

119,40

123,24

127,07

130,89

134,70

100

138,50

142,28

146,06

149,82

153,57

157,32

161,04

164,76

168,47

172,16

200

175,84

179,51

183,17

186,82

190,46

194,08

197,70

201,30

204,88

208,46

300

212,03

215,58

219,13

222,66

226,18

229,69

233,19

236,67

240,15

243,61

400

247,06

250,50

253,93

257,31

260,75

264,14

267,52

270,89

274,25

277,60

500

280,93

284,26

287,57

290,87

294,16

297,43

300,70

303,95

307,20

310,43

600

313,65

316,86

320,05

323,24

326,41

329,57

332,72

335,86

338,99

342,10

700

345,21

348,30

351,38

354,45

357,51

360,55

363,59

366,61

369,62

372,62

800

375,61

378,59

381,55

384,50

387,45

390,38

°C

0

10

20

30

40

50

60

70

80

90

0

100,00

103,90

107,79

111,67

115,54

119,40

123,24

127,07

130,89

134,70

100

138,50

142,28

146,06

149,82

153,57

157,32

161,04

164,76

168,47

172,16

200

175,84

179,51

183,17

186,82

190,46

194,08

197,70

201,30

204,88

208,46

300

212,03

215,58

219,13

222,66

226,18

229,69

233,19

236,67

240,15

243,61

400

247,06

250,50

253,93

257,31

260,75

264,14

267,52

270,89

274,25

277,60

500

280,93

284,26

287,57

290,87

294,16

297,43

300,70

303,95

307,20

310,43

600

313,65

316,86

320,05

323,24

326,41

329,57

332,72

335,86

338,99

342,10

700

345,21

348,30

351,38

354,45

357,51

360,55

363,59

366,61

369,62

372,62

800

375,61

378,59

381,55

384,50

387,45

390,38