# 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
3. Suggest method and material for construction
4. Wire or strip size
5. Element distribution, shape, and construction
6. Heating rate achievable

Step-by-Step
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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 MoS$i_2$ (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
Specific resistance = 150 × $10^{-6}$ ohm.cm

\begin{aligned}d & =0.74 \sqrt[3]{\left[\frac{8000}{220}\right]^2 \times \frac{150 \times 10^{-6}}{1.0}} \\& =0.43 \ \mathrm{~cm} \ ( 4.3 \mathrm{~mm})\end{aligned}

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

$\frac{6.05}{0.0912} = 66.33 \ m \ (663 \ cm)$

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

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

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