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
Mineral wool, k = 0.04200 mm22 °C3 °Cq″ = ?

A wall of mineral wool is 200 mm thick and has an area of 8 m². Its faces are held at 22 °C and 3 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 200 mmA = 8 m²T1 = 22 °CT2 = 3 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.035150 mm15 °C-6 °Cq″ = ?

A wall of expanded polystyrene is 150 mm thick and has an area of 15 m². Its faces are held at 15 °C and -6 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 150 mmA = 15 m²T1 = 15 °CT2 = -6 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035100 mmGypsum board, k = 0.1750 mm20 °C-10 °CQ̇ = ?

A wall is made of 100 mm of expanded polystyrene and 50 mm of gypsum board, with an area of 6 m². The outer faces are at 20 °C and -10 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 20 °CT3 = -10 °C
Q̇ = W
4.Medium
Brick, k = 0.7250 mmExpanded polystyrene, k = 0.03575 mm19 °C6 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 75 mm of expanded polystyrene, with an area of 6 m². The outer faces are at 19 °C and 6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 6 m²T1 = 19 °CT3 = 6 °C
Ti = °C
5.Hard
Mineral wool, k = 0.0450 mmExpanded polystyrene, k = 0.03550 mmroom 20 °Coutside 4 °CQ̇ = ?

A wall of 50 mm mineral wool and 50 mm expanded polystyrene separates a room at 20 °C from outside air at 4 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = 4 °C
Q̇ = W
6.Hard
Expanded polystyrene, k = 0.035250 mmBrick, k = 0.72150 mmroom 20 °Coutside -6 °CTs​ = ?Q̇

A wall of 250 mm expanded polystyrene and 150 mm brick separates a room at 20 °C from outside air at -6 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -6 °C
Ts = °C

Answer key

  1. 1. q″ = 3.8 W/m²
  2. 2. q″ = 4.9 W/m²
  3. 3. Q̇ = 57.12 W
  4. 4. Ti = 18.59 °C
  5. 5. Q̇ = 67.41 W
  6. 6. Ts = 19.43 °C

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