 # Sample Problem – Heat transfer by conduction across a furnace wall

### Sample Problem Statement

Determine the rate of heat transfer by conduction per unit area, by means of conduction for a furnace wall made of fire clay. Furnace wall thickness is 6" or half a foot. Thermal conductivity of the furnace wall clay is 0.3 W/m·K. The furnace wall temperature can be taken to be same as furnace operating temperature which is 6500C and temperature of the outer wall of the furnace is 1500C.

### Solution Solution to this sample problem is quite straightforward as demonstrated below.

For heat transfer by conduction across a flat wall, the heat transfer rate is expressed by following equation, For the given sample problem,

T1 = 6500C
T2 = 1500C
L = 12" = 12 × 0.0254 m = 0.3048 m
k = 0.3 W/m·K

Hence,

Heat transfer rate per unit area of the wall is calculated as,

Q/A = k × (T1 - T2)/L
Q/A = 0.3×(650-150)/0.3048 W/m2 = 492.13 W/m2

This figure multiplied by the area of the furnace wall, will determine the total heat transfer rate in Joules/sec i.e. Watt.  