Question

In a furnace, the wall thickness is 60 cm and is 100 cm wide by 150 cm height made of material with thermal conductivity 0.4 W/mK. The temperature inside and outside are 1000°C and 4°C respectively. The thermal resistance is  
1. 1 K/W
2. 2 K/W
3. 18 K/W
4. 15 K/W

Answer 1

Correct Answer - Option 1 : 1 K/W

Concept:

According to the Fourier's law of conduction heat transfer through a slab of thickness 't' is given by.

Q = \(\frac{{{\rm{KA}}\left( {{{\rm{T}}_1} - {{\rm{T}}_2}} \right)}}{{\rm{t}}}\) where, K = thermal conductivity, A = area perpendicular to the heat transfer, t = thickness of the slab, (T₁ - T₂) is the temperature difference between inside and outside the slab.

The conduction resistance through the slab is given by

R_th = \(\frac{{{{\rm{T}}_1} - {{\rm{T}}_2}}}{{\rm{Q}}} = \frac{{\rm{t}}}{{{\rm{KA}}}}\) K/W

Calculation:

Given:

Thickness (t) = 60 cm = 0.6 m, Width (b) = 100 cm = 1 m, Height (h) = 150 cm = 1.5 m

K = 0.4 W/mK, T₁ = 1000°C, T₂ = 4°C

R_th = \(\frac{{\rm{t}}}{{{\rm{KA}}}}\)

R_th = \(\frac{{0.6}}{{0.4 \times 1.5}} = 1\;{\bf{K}}/ {\bf{W}} \)