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
Gypsum board, k = 0.17100 mm16 °C6 °Cq″ = ?

A wall of gypsum board is 100 mm thick and has an area of 8 m². Its faces are held at 16 °C and 6 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 8 m²T1 = 16 °CT2 = 6 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03550 mm21 °C4 °Cq″ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 12 m². Its faces are held at 21 °C and 4 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 12 m²T1 = 21 °CT2 = 4 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04250 mmWood, k = 0.17150 mm22 °C4 °CTi​ = ?Q̇

A wall is made of 250 mm of mineral wool and 150 mm of wood, with an area of 6 m². The outer faces are at 22 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 22 °CT3 = 4 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035200 mmWood, k = 0.17100 mm25 °C6 °CQ̇ = ?

A wall is made of 200 mm of expanded polystyrene and 100 mm of wood, with an area of 8 m². The outer faces are at 25 °C and 6 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 25 °CT3 = 6 °C
Q̇ = W
5.Hard
Expanded polystyrene, k = 0.035100 mmGlass, k = 0.96100 mmroom 20 °Coutside -15 °CQ̇

A wall of 100 mm expanded polystyrene and 100 mm glass separates a room at 20 °C from outside air at -15 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 4 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -15 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.035200 mmGypsum board, k = 0.1725 mmroom 20 °Coutside -6 °CQ̇ = ?

A wall of 200 mm expanded polystyrene and 25 mm gypsum board 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 8 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 8 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -6 °C
Q̇ = W

Answer key

  1. 1. q″ = 17 W/m²
  2. 2. q″ = 11.9 W/m²
  3. 3. Ti = 6.227 °C
  4. 4. Q̇ = 24.12 W
  5. 5. U = 0.32 W/(m²·K)
  6. 6. Q̇ = 34.7 W

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