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 = 0.03520 mm15 °C5 °CQ̇ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 15 m². Its faces are held at 15 °C and 5 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 15 m²T1 = 15 °CT2 = 5 °C
Q̇ = W
2.Easy
Glass, k = 0.9650 mm19 °C9 °Cq″ = ?

A wall of glass is 50 mm thick and has an area of 4 m². Its faces are held at 19 °C and 9 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 4 m²T1 = 19 °CT2 = 9 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.1750 mmBrick, k = 0.7250 mm23 °C-10 °CTi​ = ?Q̇

A wall is made of 50 mm of gypsum board and 50 mm of brick, with an area of 20 m². The outer faces are at 23 °C and -10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 20 m²T1 = 23 °CT3 = -10 °C
Ti = °C
4.Medium
Brick, k = 0.72100 mmWood, k = 0.17150 mm19 °C3 °CQ̇ = ?

A wall is made of 100 mm of brick and 150 mm of wood, with an area of 15 m². The outer faces are at 19 °C and 3 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 19 °CT3 = 3 °C
Q̇ = W
5.Hard
Concrete, k = 1.4200 mmExpanded polystyrene, k = 0.035150 mmroom 22 °Coutside -6 °CQ̇

A wall of 200 mm concrete and 150 mm expanded polystyrene separates a room at 22 °C from outside air at -6 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -6 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.96150 mmGypsum board, k = 0.17100 mmroom 20 °Coutside -2 °CTs​ = ?Q̇

A wall of 150 mm glass and 100 mm gypsum board separates a room at 20 °C from outside air at -2 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -2 °C
Ts = °C

Answer key

  1. 1. Q̇ = 262.5 W
  2. 2. q″ = 192 W/m²
  3. 3. Ti = −3.697 °C
  4. 4. Q̇ = 235 W
  5. 5. U = 0.2189 W/(m²·K)
  6. 6. Ts = 16.98 °C

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