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
Expanded polystyrene, k = 0.035100 mm23 °C-8 °CQ̇ = ?

A wall of expanded polystyrene is 100 mm thick and has an area of 6 m². Its faces are held at 23 °C and -8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 100 mmA = 6 m²T1 = 23 °CT2 = -8 °C
Q̇ = W
2.Easy
Mineral wool, k = 0.04250 mm18 °C-15 °Cq″ = ?

A wall of mineral wool is 250 mm thick and has an area of 6 m². Its faces are held at 18 °C and -15 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 250 mmA = 6 m²T1 = 18 °CT2 = -15 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.03550 mmGlass, k = 0.9625 mm23 °C-3 °CQ̇ = ?

A wall is made of 50 mm of expanded polystyrene and 25 mm of glass, with an area of 12 m². The outer faces are at 23 °C and -3 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 12 m²T1 = 23 °CT3 = -3 °C
Q̇ = W
4.Medium
Mineral wool, k = 0.0450 mmConcrete, k = 1.450 mm21 °C-15 °CQ̇ = ?

A wall is made of 50 mm of mineral wool and 50 mm of concrete, with an area of 20 m². The outer faces are at 21 °C and -15 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 20 m²T1 = 21 °CT3 = -15 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.0450 mmWood, k = 0.1725 mmroom 20 °Coutside 5 °CTs​ = ?Q̇

A wall of 50 mm mineral wool and 25 mm wood separates a room at 20 °C from outside air at 5 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = 5 °C
Ts = °C
6.Hard
Brick, k = 0.72200 mmExpanded polystyrene, k = 0.035100 mmroom 21 °Coutside -9 °CQ̇

A wall of 200 mm brick and 100 mm expanded polystyrene separates a room at 21 °C from outside air at -9 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 15 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -9 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 65.1 W
  2. 2. q″ = 5.28 W/m²
  3. 3. Q̇ = 214.5 W
  4. 4. Q̇ = 560 W
  5. 5. Ts = 19.02 °C
  6. 6. U = 0.3044 W/(m²·K)

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