---
title: "Nichrome strip width for 40 kW 3-phase oven"
subject: "Utilization of Electrical Energy"
chapter: 5
key: "semester_7/utilization_of_electrical_energy:nichrome-strip-40kw-oven-width"
source: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/nichrome-strip-40kw-oven-width
site: BCT Engineering
---

# Nichrome strip width for 40 kW 3-phase oven

Utilization of Electrical Energy · Chapter 5: Electric Heating

- Asked in: 2080 Baisakh, 8 marks
- Video: [ELECTRICAL HEATING  - PART - 03 - THREE PROBLEMS IN DESIGN OF HEATING ELEMENT](https://www.youtube.com/watch?v=4tFLfZXrAeM) — zenmurali Sachithanandam
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/nichrome-strip-40kw-oven-width
- Whole chapter: https://www.bctengineer.com/md/semester_7/utilization_of_electrical_energy/chapter-5

## Question

A 40 kW, 3-phase, 400 V resistance oven is to employ nickel-chrome strip 0.0025 cm thick for the three phase star connected heating elements. If the wire temperature is to be 1,100°C and that of charge is to be 700°C, estimate a suitable width for the strip. Assume radiating efficiency as 0.6 and emissivity as 0.9. The specific resistance of the nichrome-alloy is 1.03×10⁻⁶ Ω-m.

## Short answer

Per phase R = 4 ohm and heat dissipation H = 82,082 W/m². For the strip, l/w = 97.09 and wl = 0.08122 m², giving width about 28.9 mm and length about 2.81 m per phase.

## Answer

For a thin strip, the radiating surface is both faces, $2wl$ (edges neglected), and the cross-section is $wt$.

**Given:** $P = 40$ kW, 3-phase, 400 V, star connected; $t = 0.0025$ cm $= 2.5 \times 10^{-5}$ m; $T_1 = 1100 + 273 = 1373$ K; $T_2 = 700 + 273 = 973$ K; $k = 0.6$; $e = 0.9$; $\rho = 1.03 \times 10^{-6}\ \Omega$m.

#### Per-phase values
$$
\begin{aligned}
P_{ph} &= \frac{40\,000}{3} = 13\,333\ \text{W}, \quad V_{ph} = \frac{400}{\sqrt3} = 230.94\ \text{V} \\
R &= \frac{V_{ph}^2}{P_{ph}} = \frac{230.94^2}{13\,333} = 4.0\ \Omega
\end{aligned}
$$

#### Heat dissipated per m² (Stefan's law)
$$
\begin{aligned}
H &= 5.72\,e\,k\left[\left(\frac{T_1}{100}\right)^4 - \left(\frac{T_2}{100}\right)^4\right] \\
&= 5.72 \times 0.9 \times 0.6 \times (13.73^4 - 9.73^4) \\
&= 3.0888 \times (35\,537 - 8\,963) = 82\,082\ \text{W/m}^2
\end{aligned}
$$

#### Equations for the strip
$$
\begin{aligned}
R = \frac{\rho l}{w t} &\Rightarrow \frac{l}{w} = \frac{R t}{\rho} = \frac{4 \times 2.5\times10^{-5}}{1.03\times10^{-6}} = 97.09 \quad (1) \\
P_{ph} = 2wlH &\Rightarrow wl = \frac{13\,333}{2 \times 82\,082} = 0.08122\ \text{m}^2 \quad (2)
\end{aligned}
$$

#### Solving
$$
\begin{aligned}
w^2 &= \frac{0.08122}{97.09} = 8.365 \times 10^{-4} \\
w &= 0.02892\ \text{m} = 28.9\ \text{mm} \\
l &= 97.09 \times 0.02892 = 2.81\ \text{m (per phase)}
\end{aligned}
$$

**Answer:** Strip width $\approx 28.9$ mm (about 2.9 cm), with length $\approx 2.81$ m per phase.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For star-connected elements, what is the per-phase voltage and resistance?
   A. 400 V, R = 12 Ω
   B. 230.9 V, R = 4 Ω
   C. 230.9 V, R = 12 Ω
   D. 133 V, R = 1.3 Ω
   Answer: B. V_ph = 400/sqrt3 = 230.9 V and P_ph = 13,333 W, so R = 230.9^2/13,333 = 4 Ω. (Key point: Per-phase resistance)

2. For a thin strip of width w and length l, the radiating surface used is:
   A. w x l
   B. 2 w l (both faces, edges neglected)
   C. π w l
   D. w t
   Answer: B. Both faces radiate, so P_ph = 2 w l H. (Key point: Radiating surface of a strip)

3. Which relations are solved together?
   A. l/d^2 = πR/4ρ only
   B. l/w = R t/ρ and w l = P_ph/(2H)
   C. w = t only
   D. l/w = P/H
   Answer: B. R = ρ l/(w t) gives l/w = 97.09, and the heat condition gives wl = 0.0812 m^2. (Key point: Strip equations)

4. Strip width obtained is about:
   A. 2.89 mm
   B. 28.9 mm
   C. 289 mm
   D. 97 mm
   Answer: B. w^2 = 0.08122/97.09 = 8.365x10^-4, so w = 0.0289 m = 28.9 mm. (Key point: Result)

## Close variants set in other exams

- [Nichrome strip width for 30 kW 3-phase oven](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Anichrome-strip-30kw-oven-width) — Utilization of Electrical Energy, chapter 5, asked 2×

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