Question 9.1: A resistance-heated furnace is to be designed with following......
A resistance-heated furnace is to be designed with following requirements:
Working space = 30 × 40 × 100 cm
Occasional maximum temperature = 1250°C
Continuous working temperature = 1150°C
Atmosphere = Air
Estimated power = 24 kW
Available voltage = 440 V–3ph
Specific resistivity (average) = 150 × 10^{-6} ohm.cm
Now determine:
1. Material for heating resistors
2. Surface loading
3. Suggest method and material for construction
4. Wire or strip size
5. Element distribution, shape, and construction
6. Heating rate achievable
The furnace atmosphere is oxidizing. Working temperature 1150°C and occasional maximum temperature 1250°C suggest Fe-Cr-Al alloy (Kanthal A1 or Kanthal AF or other similar alloy) having a maximum permissible temperature of 1400°C and a probability of long service life (>1000 h).
We can use nonmetallic elements such as SiC or MoSi_2 (Kanthal Super). They have a much higher temperature capability and are costly. Higher temperatures (> 1250°C) are not specified.
The recommended surface load (q) in the range 1150–1250°C is 1–1.8 W/cm² . For trial, a preliminary load of 1.0 W/cm² is assumed. The chosen alloy is available in both wire and strip form.
For the first trial choose a round wire of diameter d cm.
The power requirement given is 24 kW with a 380 V 3 ph supply. Assume a star connection so that each phase has 24/3 = 8 kW power at 220 V.
Diameter of Wire
Voltage per phase (V) = 220 V
Power dissipated in each phase (P) = 8 kW
Surface loading q = 1.0 W/cm²
Specific resistance = 150 × 10^{-6} ohm.cm
Alternatively,
Resistance R= \frac{V^2}{P} \\ = \frac{220^2}{8000} = 60.5 \ ohm
Surface area = \frac{P}{q} = 8000 \ cm^2 \\ \frac{ohm}{cm^2} = \frac {8000}{6.05} = 1.323 \ cm^2 / ohm
From Table 9.5, nearest wires are
Kanthal A1 – 1550 cm²/ohm – 4.5 mm
Kanthal AF – 1363 cm²/ohm – 4.25 mm
As the diameters determined by both methods are of the same order, we choose Kanthal A1, 4.5 mm diameter wire. This wire has following data:
0.0912 ohm/m at 20°C 113 g/m
Length required for 6.05 ohms is
At 113 gm/m the weight of wire is
66.33 × 113 × 10^{-3} = 7.5 kg
Add 10% for terminals, breakage etc.
Wt = 8.25 kg
Table 9.5 Design Data for Nikrothal (80Ni-20Cr) Heating Wires (Courtesy: Kanthal AB)
Wire mm 6.5–0.02 mm ∅
Resistivity Ω mm² m^{−1} 1.09
Density, gcm^{-3} 8.30
\mathrm{cm}^2 / \Omega \frac{I^2 C_t}{P}I = Current
C_t = Temperature factor
P = Surface load W/cm²
To obtain resistivity at working temperature multiply by the factor C_t in the following table.
| °C | 20 | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 | 1400 |
| C_t | 1 | 1.01 | 1.02 | 1.03 | 1.04 | 1.05 | 1.04 | 1.04 | 1.04 | 1.04 | 1.05 | 1.06 | 1.07 |
| Diameter mm | Resistance Ω/m 20°C | cm²/Ω 20°C | Weight g/m | Surface area cm²/m | Cross-sect. area mm² | Diameter mm |
| 6.5 | 0.0328 | 6220 | 275 | 204 | 33.2 | 6.5 |
| 6 | 0.0386 | 4890 | 235 | 188 | 28.3 | 6 |
| 5.5 | 0.0459 | 3770 | 197 | 173 | 23.8 | 5.5 |
| 5 | 0.0555 | 3770 | 163 | 157 | 19.6 | 5 |
| 4.75 | 0.0615 | 2430 | 147 | 149 | 17.7 | 4.75 |
| 4.5 | 0.0685 | 2060 | 132 | 141 | 15.9 | 4.5 |
| 4.25 | 0.0768 | 1740 | 118 | 134 | 14.2 | 4.25 |
| 4 | 0.0867 | 1450 | 104 | 126 | 12.6 | 4 |
| 3.75 | 0.0987 | 1190 | 91.7 | 118 | 11 | 3.75 |
| 3.5 | 0.113 | 971 | 79.9 | 110 | 9.62 | 3.5 |
| 3.25 | 0.131 | 777 | 68.9 | 102 | 8.3 | 3.25 |
| 3 | 0.154 | 611 | 58.7 | 94.2 | 7.07 | 3 |
| 2.8 | 0.177 | 497 | 51.1 | 88 | 6.16 | 2.8 |
| 2.5 | 0.222 | 354 | 40.7 | 78.5 | 4.91 | 2.5 |
| 2.25 | 0.274 | 258 | 33 | 70.7 | 3.98 | 2.25 |
| 2 | 0.347 | 181 | 26.1 | 62.8 | 3.14 | 2 |
| 1.8 | 0.428 | 132 | 21.1 | 56.5 | 2.54 | 1.8 |
| 1.7 | 0.48 | 111 | 18.8 | 53.4 | 2.27 | 1.7 |
| 1.6 | 0.542 | 92.7 | 16.7 | 50.3 | 2.01 | 1.6 |
| 1.5 | 0.617 | 76.4 | 14.7 | 47.1 | 1.77 | 1.5 |
| 1.4 | 0.708 | 62.4 | 12.8 | 44 | 1.54 | 1.4 |
| 1.3 | 0.821 | 49.7 | 11 | 40.8 | 1.33 | 1.3 |
| 1.2 | 0.964 | 39.1 | 9.39 | 37.7 | 1.13 | 1.2 |
| 1.1 | 1.15 | 30.1 | 7.89 | 34.6 | 0.95 | 1.1 |
| 1 | 1.39 | 22.6 | 6.52 | 31.4 | 0.785 | 1 |
| 0.95 | 1.54 | 19.4 | 5.88 | 29.8 | 0.709 | 0.95 |
| 0.9 | 1.71 | 16.5 | 5.28 | 28.3 | 0.636 | 0.9 |
| 0.85 | 1.92 | 13.9 | 4.71 | 26.7 | 0.567 | 0.85 |
| 0.8 | 2.17 | 11.6 | 4.17 | 25.1 | 0.503 | 0.8 |
| 0.75 | 2.47 | 9.55 | 3.67 | 23.6 | 0.442 | 0.75 |
| 0.7 | 2.83 | 7.76 | 3.19 | 22 | 0.385 | 0.7 |
| 0.65 | 3.28 | 6.22 | 2.75 | 20.4 | 0.332 | 0.65 |
| 0.6 | 3.86 | 4.89 | 2.35 | 18.8 | 0.283 | 0.6 |
| 0.55 | 4.59 | 3.77 | 1.97 | 17.3 | 0.238 | 0.6 |
| 0.5 | 5.55 | 2.83 | 1.63 | 15.7 | 0.196 | 0.5 |
| 0.475 | 6.15 | 2.43 | 1.47 | 14.9 | 0.177 | 0.475 |
| 0.45 | 6.85 | 2.06 | 1.32 | 14.1 | 0.159 | 0.45 |
| 0.425 | 7.68 | 1.74 | 1.18 | 13.4 | 0.142 | 0.425 |
| 0.4 | 8.67 | 1.45 | 1.04 | 12.6 | 0.126 | 0.4 |
| 0.375 | 9.87 | 1.19 | 0.917 | 11.8 | 0.11 | 0.375 |
| 0.35 | 11.3 | 0.971 | 0.799 | 11 | 0.0962 | 0.35 |
| 0.325 | 13.1 | 0.777 | 0.689 | 10.2 | 0.083 | 0.325 |
| 0.3 | 15.4 | 0.611 | 0.587 | 9.42 | 0.0707 | 0.3 |
| 0.28 | 17.7 | 0.497 | 0.511 | 8.8 | 0.0616 | 0.28 |
| 0.26 | 20.5 | 0.398 | 0.441 | 8.17 | 0.0531 | 0.26 |