Question

It is required to insulate a kitchen oven with corkboard (k = 0.043 W/(m K)) so that the heat losses from the oven does not exceed 400 W/m² when the outer surface of the oven is at 225°C and the outer surface of the insulation is at 40°C. The thickness of insulation required is nearly

1. 1 cm
2. 2 cm
3. 3 cm
4. 4 cm

Answer 1

Correct Answer - Option 2 : 2 cm

Concept:

The thickness up to which heat flow increases and after which heat flow decreases is termed as Critical thickness.

\(Q = \frac{{kAdT}}{{dx}}\)

where Q = heat transfer, k = conductivity of board, A = cross-section area, dT = temperature difference, dx = thickness

Calculation:

Given:

Q = 400 W/m², T_i = 225° C, T_o = 40°C, k = 0.043 W/mK

\(\begin{array}{l} Q = \frac{{kAdT}}{{dx}}\\ \Rightarrow 400 = 0.043 \times 1 \times \frac{{\left( {225 - 40} \right)}}{{dx}} \end{array}\)

⇒ dx = 0.0198 m = 1.98 = 2 cm