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 = 0.17250 mm20 °C-4 °CQ̇ = ?

A wall of gypsum board is 250 mm thick and has an area of 15 m². Its faces are held at 20 °C and -4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 250 mmA = 15 m²T1 = 20 °CT2 = -4 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.1710 mm16 °C10 °Cq″ = ?

A wall of gypsum board is 10 mm thick and has an area of 6 m². Its faces are held at 16 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 6 m²T1 = 16 °CT2 = 10 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.0450 mmExpanded polystyrene, k = 0.03550 mm18 °C-12 °CTi​ = ?Q̇

A wall is made of 50 mm of mineral wool and 50 mm of expanded polystyrene, with an area of 6 m². The outer faces are at 18 °C and -12 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 6 m²T1 = 18 °CT3 = -12 °C
Ti = °C
4.Medium
Concrete, k = 1.4200 mmBrick, k = 0.7225 mm20 °C4 °CQ̇ = ?

A wall is made of 200 mm of concrete and 25 mm of brick, with an area of 20 m². The outer faces are at 20 °C and 4 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 20 m²T1 = 20 °CT3 = 4 °C
Q̇ = W
5.Hard
Glass, k = 0.96200 mmWood, k = 0.1775 mmroom 20 °Coutside -3 °CTs​ = ?Q̇

A wall of 200 mm glass and 75 mm wood separates a room at 20 °C from outside air at -3 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -3 °C
Ts = °C
6.Hard
Gypsum board, k = 0.17150 mmGlass, k = 0.9625 mmroom 22 °Coutside -4 °CQ̇

A wall of 150 mm gypsum board and 25 mm glass separates a room at 22 °C from outside air at -4 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 8 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 8 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -4 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 244.8 W
  2. 2. q″ = 102 W/m²
  3. 3. Ti = 4 °C
  4. 4. Q̇ = 1802 W
  5. 5. Ts = 16.47 °C
  6. 6. U = 0.9332 W/(m²·K)

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