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
Concrete, k = 1.4200 mm19 °C7 °Cq″ = ?

A wall of concrete is 200 mm thick and has an area of 6 m². Its faces are held at 19 °C and 7 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 200 mmA = 6 m²T1 = 19 °CT2 = 7 °C
q″ = W/m²
2.Easy
Wood, k = 0.1750 mm21 °C-3 °Cq″ = ?

A wall of wood is 50 mm thick and has an area of 12 m². Its faces are held at 21 °C and -3 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 12 m²T1 = 21 °CT2 = -3 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04100 mmGypsum board, k = 0.17100 mm21 °C8 °CQ̇ = ?

A wall is made of 100 mm of mineral wool and 100 mm of gypsum board, with an area of 12 m². The outer faces are at 21 °C and 8 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 12 m²T1 = 21 °CT3 = 8 °C
Q̇ = W
4.Medium
Concrete, k = 1.450 mmMineral wool, k = 0.04100 mm17 °C-6 °CQ̇ = ?

A wall is made of 50 mm of concrete and 100 mm of mineral wool, with an area of 12 m². The outer faces are at 17 °C and -6 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 12 m²T1 = 17 °CT3 = -6 °C
Q̇ = W
5.Hard
Brick, k = 0.72150 mmGlass, k = 0.9625 mmroom 21 °Coutside -12 °CTs​ = ?Q̇

A wall of 150 mm brick and 25 mm glass separates a room at 21 °C from outside air at -12 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -12 °C
Ts = °C
6.Hard
Concrete, k = 1.4250 mmGlass, k = 0.9675 mmroom 22 °Coutside -5 °CQ̇

A wall of 250 mm concrete and 75 mm glass separates a room at 22 °C from outside air at -5 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -5 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 84 W/m²
  2. 2. q″ = 81.6 W/m²
  3. 3. Q̇ = 50.51 W
  4. 4. Q̇ = 108.8 W
  5. 5. Ts = 8.806 °C
  6. 6. U = 2.291 W/(m²·K)

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