In a furnace the heat loss through the 150 mm thick refractory wall lining is estimated to be 50 W/m². If the average thermal conductivity of the refractory material is 0.05 W/mK, the temperature drop across the wall will be:

Concept:

According to Fourier’s law, the rate of heat flow, Q through a homogeneous solid is directly proportional to the area A, of the section at the right angles to the direction of the heat flow, and to the temperature difference dT along the path of heat flow.

\(Q = - kA\frac{{dT}}{{dx}}\;\)

Calculation:

Given:

dx = 150 mm = 0.15 m, k = 0.05 W/mK, Q = 50 W/m²

^{\(Q = - kA\frac{{dT}}{{dx}}\;\)}

\(50 = 0.05 \times \frac{{dT}}{{0.15}}\)

\(dT = \frac{{50 \times 0.15}}{{0.05}} = 150^\circ C\)