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
Glass, k = 0.96100 mm23 °C-15 °Cq″ = ?

A wall of glass is 100 mm thick and has an area of 20 m². Its faces are held at 23 °C and -15 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 100 mmA = 20 m²T1 = 23 °CT2 = -15 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.035150 mm19 °C4 °CQ̇ = ?

A wall of expanded polystyrene is 150 mm thick and has an area of 6 m². Its faces are held at 19 °C and 4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 150 mmA = 6 m²T1 = 19 °CT2 = 4 °C
Q̇ = W
3.Medium
Concrete, k = 1.450 mmGypsum board, k = 0.1775 mm23 °C-7 °CTi​ = ?Q̇

A wall is made of 50 mm of concrete and 75 mm of gypsum board, with an area of 8 m². The outer faces are at 23 °C and -7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 23 °CT3 = -7 °C
Ti = °C
4.Medium
Brick, k = 0.72200 mmWood, k = 0.17150 mm19 °C5 °CQ̇ = ?

A wall is made of 200 mm of brick and 150 mm of wood, with an area of 15 m². The outer faces are at 19 °C and 5 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 19 °CT3 = 5 °C
Q̇ = W
5.Hard
Concrete, k = 1.4100 mmBrick, k = 0.72100 mmroom 22 °Coutside -15 °CTs​ = ?Q̇

A wall of 100 mm concrete and 100 mm brick separates a room at 22 °C from outside air at -15 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -15 °C
Ts = °C
6.Hard
Expanded polystyrene, k = 0.035200 mmWood, k = 0.1725 mmroom 20 °Coutside -4 °CTs​ = ?Q̇

A wall of 200 mm expanded polystyrene and 25 mm wood separates a room at 20 °C from outside air at -4 °C. The convection coefficients are 6 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 = 200 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -4 °C
Ts = °C

Answer key

  1. 1. q″ = 364.8 W/m²
  2. 2. Q̇ = 21 W
  3. 3. Ti = 20.75 °C
  4. 4. Q̇ = 181 W
  5. 5. Ts = 11.44 °C
  6. 6. Ts = 19.34 °C

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