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 = 0.035250 mm24 °C-13 °CQ̇ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 4 m². Its faces are held at 24 °C and -13 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 4 m²T1 = 24 °CT2 = -13 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.17150 mm25 °C-13 °Cq″ = ?

A wall of gypsum board is 150 mm thick and has an area of 10 m². Its faces are held at 25 °C and -13 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 150 mmA = 10 m²T1 = 25 °CT2 = -13 °C
q″ = W/m²
3.Medium
Brick, k = 0.72250 mmGlass, k = 0.9675 mm23 °C9 °CTi​ = ?Q̇

A wall is made of 250 mm of brick and 75 mm of glass, with an area of 8 m². The outer faces are at 23 °C and 9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 8 m²T1 = 23 °CT3 = 9 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035250 mmWood, k = 0.17150 mm23 °C4 °CTi​ = ?Q̇

A wall is made of 250 mm of expanded polystyrene and 150 mm of wood, with an area of 8 m². The outer faces are at 23 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 23 °CT3 = 4 °C
Ti = °C
5.Hard
Brick, k = 0.72150 mmMineral wool, k = 0.0425 mmroom 21 °Coutside -11 °CQ̇

A wall of 150 mm brick and 25 mm mineral wool separates a room at 21 °C from outside air at -11 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -11 °C
U = W/(m²·K)
6.Hard
Wood, k = 0.17250 mmMineral wool, k = 0.04100 mmroom 22 °Coutside -13 °CTs​ = ?Q̇

A wall of 250 mm wood and 100 mm mineral wool separates a room at 22 °C from outside air at -13 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -13 °C
Ts = °C

Answer key

  1. 1. Q̇ = 20.72 W
  2. 2. q″ = 43.07 W/m²
  3. 3. Ti = 11.57 °C
  4. 4. Ti = 6.089 °C
  5. 5. U = 1.034 W/(m²·K)
  6. 6. Ts = 21.15 °C

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