Heat conduction worksheet with answers

Free printable Heat conduction worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
Brick, k = 0.72200 mm24 °C-6 °CQ̇ = ?

A wall of brick is 200 mm thick and has an area of 4 m². Its faces are held at 24 °C and -6 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 200 mmA = 4 m²T1 = 24 °CT2 = -6 °C
Q̇ = W
2.Easy
Mineral wool, k = 0.0450 mm16 °C3 °CQ̇ = ?

A wall of mineral wool is 50 mm thick and has an area of 12 m². Its faces are held at 16 °C and 3 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 50 mmA = 12 m²T1 = 16 °CT2 = 3 °C
Q̇ = W
3.Medium
Glass, k = 0.96150 mmBrick, k = 0.72100 mm24 °C7 °CTi​ = ?Q̇

A wall is made of 150 mm of glass and 100 mm of brick, with an area of 20 m². The outer faces are at 24 °C and 7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 20 m²T1 = 24 °CT3 = 7 °C
Ti = °C
4.Medium
Mineral wool, k = 0.04250 mmConcrete, k = 1.475 mm24 °C-14 °CTi​ = ?Q̇

A wall is made of 250 mm of mineral wool and 75 mm of concrete, with an area of 8 m². The outer faces are at 24 °C and -14 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 8 m²T1 = 24 °CT3 = -14 °C
Ti = °C
5.Hard
Glass, k = 0.96200 mmExpanded polystyrene, k = 0.035150 mmroom 22 °Coutside -9 °CQ̇ = ?

A wall of 200 mm glass and 150 mm expanded polystyrene separates a room at 22 °C from outside air at -9 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -9 °C
Q̇ = W
6.Hard
Glass, k = 0.9650 mmMineral wool, k = 0.04150 mmroom 21 °Coutside -1 °CTs​ = ?Q̇

A wall of 50 mm glass and 150 mm mineral wool separates a room at 21 °C from outside air at -1 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -1 °C
Ts = °C

Answer key

  1. 1. Q̇ = 432 W
  2. 2. Q̇ = 124.8 W
  3. 3. Ti = 15 °C
  4. 4. Ti = −13.68 °C
  5. 5. Q̇ = 40.2 W
  6. 6. Ts = 20.31 °C

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