Heat Transfer Process Design Solved Sample Problems

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.

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,

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.

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