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
Wood, k = 0.17100 mm22 °C-15 °CQ̇ = ?

A wall of wood is 100 mm thick and has an area of 15 m². Its faces are held at 22 °C and -15 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 15 m²T1 = 22 °CT2 = -15 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.03520 mm22 °C10 °Cq″ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 4 m². Its faces are held at 22 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 4 m²T1 = 22 °CT2 = 10 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04100 mmGlass, k = 0.9650 mm20 °C-9 °CQ̇ = ?

A wall is made of 100 mm of mineral wool and 50 mm of glass, with an area of 20 m². The outer faces are at 20 °C and -9 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 20 m²T1 = 20 °CT3 = -9 °C
Q̇ = W
4.Medium
Brick, k = 0.7250 mmGypsum board, k = 0.1750 mm24 °C-9 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 50 mm of gypsum board, with an area of 6 m². The outer faces are at 24 °C and -9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 24 °CT3 = -9 °C
Ti = °C
5.Hard
Glass, k = 0.96150 mmGypsum board, k = 0.1725 mmroom 21 °Coutside -8 °CTs​ = ?Q̇

A wall of 150 mm glass and 25 mm gypsum board separates a room at 21 °C from outside air at -8 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 8 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -8 °C
Ts = °C
6.Hard
Concrete, k = 1.4250 mmWood, k = 0.1750 mmroom 22 °Coutside 0 °CQ̇

A wall of 250 mm concrete and 50 mm wood separates a room at 22 °C from outside air at 0 °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 overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = 0 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 943.5 W
  2. 2. q″ = 21 W/m²
  3. 3. Q̇ = 227.3 W
  4. 4. Ti = 17.7 °C
  5. 5. Ts = 14.46 °C
  6. 6. U = 1.532 W/(m²·K)

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