### 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 650^{0}C and temperature of the outer wall of the furnace is 150^{0}C.

### Solution

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

As per EnggCyclopedia's heat conduction article,

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

For the given sample problem,

T_{1} = 650^{0}C

T_{2} = 150^{0}C

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 × (T_{1} - T_{2})/L

Q/A = 0.3×(650-150)/0.3048 W/m^{2} = 492.13 W/m^{2}

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