# Question 9.2: A muffle furnace is to be designed for silicon carbide heate......

A muffle furnace is to be designed for silicon carbide heaters.

Size of heating space (nominal)     28 (W) × 22 (H) × 120 (D) cm

Maximum temperature     1400°C

Atmosphere     Air

Estimated power     15 kW

Power supply     380 V, 3 phase

Heating elements to be situated at the top across the width.

Now determine:

Number of heating elements required.
Size of elements.
Current and resistance of elements.
Transformer required.

Step-by-Step
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The width of the chamber is 28 cm. The heating element chosen must have a hot (central) zone about 28 cm.

According to Figure 9.8 the permissible surface loading (P) at 1400°C and in air atmosphere is

P = 6 W/cm²
Element temperature ~ 1,475°C
Total heating surface required

= $\frac{1,5000}{6}$ = 2,500 cm²

For equal distribution in three phases the number of elements must be divisible by 3.
For trial consider 18 elements so that power per element will be

$=\frac{15,000}{18}$ = 833 W/element

Hot surface for each element

=$\frac{2,500}{18}$ = 138.89 ~ 140 cm²

Referring to Table 9.7 it can be seen that the nearest resistor has a heating length 305 mm for furnace width 279 mm.

The surface area required per element is 140 cm² . The nearest area of the heating zone is 152 cm² for a 15.8 mm diameter rod.

We have no information about the thickness of the insulation. There are four options available. They are 76, 127, 166, 191, and 229 mm. Assume a wall thickness of about 200 mm.
The nearest size is 191 mm.
The element chosen has following specifications:
Heating length      305 mm
Furnace width      279 mm
Element diameter      15.8 mm
Resistance      1.63 ohm
Let us try a combination of six elements in parallel. The total resistance in each phase will be

\begin{aligned}& \frac{1}{R}=\frac{6}{1.63} \\& \therefore R=\frac{1.63}{6}=0.271 \ \mathrm{ohm}\end{aligned}

Current = $\sqrt{5000 / 0.271}=136 \ \mathrm{~A} / \text { phase }$

Voltage = 136 × 0.271 = 36.8 V/Phase

kVA = 5 kW
Primary voltage 380/$\sqrt{3}$ = 220 V

The transformer required is 380 V, 3 ph, 30 amp-primary; and 20, 30, 40, 50, 80 V taps on secondary with current 200 A, kVA ~ 20–25

Table 9.7 Extract from Specification Data for Silicon Carbide Heaters (Norton)

 Effective heating length (mm) Width of furance chamber (mm) Diameter Nominal radiating surface ($mm^2$) Thickness of furance wall (mm) Overall length (mm) Nominal resistances (ohm) – – 9.5 9,120 $76 \\ 127 \\ 165 \\ 76$ $483 \\ 584 \\ 600\\ 438$ $4.55\\ 4.62\\ 4.87\\ 3.24$ – – 11.1 10,639 $127 \\ 165 \\ 191 \\ 229 \\ 76$ $584\\ 600\\ 711\\ 787 \\ 483$ $3.40\\ 3.43\\ 3.46\\ 3.50\\ 2.50$ 305 279 12.7 12,161 $127 \\ 165 \\ 191 \\ 229 \\ 76$ $584\\ 600\\ 711\\ 787 \\ 508$ $2.54\\ 2.57 \\ 2.59\\ 2.62\\ 1.57$ – – 15.8 15,201 $127 \\ 165 \\ 191 \\ 229 \\ 76$ $610\\ 686\\ 737\\ 813 \\ 508$ $1.60\\ 1.62\\ 1.63\\ 1.65\\ 1.07$ – – 19 18,239 $127 \\ 165 \\ 191 \\ 229 \\ 191$ $610\\ 686\\ 737\\ 813\\ 787$ $1.08\\ 1.10\\ 1.11\\ 1.12\\ 0.063$ 25.4 24,323 $229 \\ 343$ $864\\ 1,092$ $0.064\\ 0.066$

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