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 mm21 °C7 °Cq″ = ?

A wall of expanded polystyrene is 100 mm thick and has an area of 4 m². Its faces are held at 21 °C and 7 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 100 mmA = 4 m²T1 = 21 °CT2 = 7 °C
q″ = W/m²
2.Easy
Mineral wool, k = 0.04200 mm19 °C9 °CQ̇ = ?

A wall of mineral wool is 200 mm thick and has an area of 12 m². Its faces are held at 19 °C and 9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 200 mmA = 12 m²T1 = 19 °CT2 = 9 °C
Q̇ = W
3.Medium
Expanded polystyrene, k = 0.035100 mmConcrete, k = 1.450 mm22 °C1 °CTi​ = ?Q̇

A wall is made of 100 mm of expanded polystyrene and 50 mm of concrete, with an area of 8 m². The outer faces are at 22 °C and 1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 8 m²T1 = 22 °CT3 = 1 °C
Ti = °C
4.Medium
Mineral wool, k = 0.04100 mmGypsum board, k = 0.17150 mm24 °C-13 °CTi​ = ?Q̇

A wall is made of 100 mm of mineral wool and 150 mm of gypsum board, with an area of 8 m². The outer faces are at 24 °C and -13 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 24 °CT3 = -13 °C
Ti = °C
5.Hard
Concrete, k = 1.4200 mmExpanded polystyrene, k = 0.03525 mmroom 20 °Coutside -6 °CQ̇

A wall of 200 mm concrete and 25 mm expanded polystyrene separates a room at 20 °C from outside air at -6 °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 overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -6 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.035150 mmBrick, k = 0.7250 mmroom 20 °Coutside 0 °CQ̇ = ?

A wall of 150 mm expanded polystyrene and 50 mm brick separates a room at 20 °C from outside air at 0 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 0 °C
Q̇ = W

Answer key

  1. 1. q″ = 4.9 W/m²
  2. 2. Q̇ = 24 W
  3. 3. Ti = 1.259 °C
  4. 4. Ti = −3.348 °C
  5. 5. U = 1.01 W/(m²·K)
  6. 6. Q̇ = 44.31 W

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