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 = 1.420 mm22 °C4 °CQ̇ = ?

A wall of concrete is 20 mm thick and has an area of 8 m². Its faces are held at 22 °C and 4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 20 mmA = 8 m²T1 = 22 °CT2 = 4 °C
Q̇ = W
2.Easy
Mineral wool, k = 0.04100 mm15 °C1 °CQ̇ = ?

A wall of mineral wool is 100 mm thick and has an area of 6 m². Its faces are held at 15 °C and 1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 100 mmA = 6 m²T1 = 15 °CT2 = 1 °C
Q̇ = W
3.Medium
Gypsum board, k = 0.1750 mmConcrete, k = 1.475 mm22 °C8 °CQ̇ = ?

A wall is made of 50 mm of gypsum board and 75 mm of concrete, with an area of 12 m². The outer faces are at 22 °C and 8 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 12 m²T1 = 22 °CT3 = 8 °C
Q̇ = W
4.Medium
Glass, k = 0.96250 mmExpanded polystyrene, k = 0.03550 mm19 °C-9 °CTi​ = ?Q̇

A wall is made of 250 mm of glass and 50 mm of expanded polystyrene, with an area of 8 m². The outer faces are at 19 °C and -9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 8 m²T1 = 19 °CT3 = -9 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.035250 mmGlass, k = 0.9675 mmroom 20 °Coutside -15 °CTs​ = ?Q̇

A wall of 250 mm expanded polystyrene and 75 mm glass separates a room at 20 °C from outside air at -15 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -15 °C
Ts = °C
6.Hard
Brick, k = 0.72150 mmExpanded polystyrene, k = 0.03525 mmroom 20 °Coutside 2 °CTs​ = ?Q̇

A wall of 150 mm brick and 25 mm expanded polystyrene separates a room at 20 °C from outside air at 2 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 6 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 = 0.035 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = 2 °C
Ts = °C

Answer key

  1. 1. Q̇ = 10080 W
  2. 2. Q̇ = 33.6 W
  3. 3. Q̇ = 483.2 W
  4. 4. Ti = 14.68 °C
  5. 5. Ts = 19.52 °C
  6. 6. Ts = 17.88 °C

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