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
Brick, k = 0.72150 mm19 °C7 °CQ̇ = ?

A wall of brick is 150 mm thick and has an area of 6 m². Its faces are held at 19 °C and 7 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 150 mmA = 6 m²T1 = 19 °CT2 = 7 °C
Q̇ = W
2.Easy
Glass, k = 0.96100 mm16 °C1 °CQ̇ = ?

A wall of glass is 100 mm thick and has an area of 4 m². Its faces are held at 16 °C and 1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 100 mmA = 4 m²T1 = 16 °CT2 = 1 °C
Q̇ = W
3.Medium
Brick, k = 0.72150 mmExpanded polystyrene, k = 0.035100 mm21 °C-6 °CTi​ = ?Q̇

A wall is made of 150 mm of brick and 100 mm of expanded polystyrene, with an area of 15 m². The outer faces are at 21 °C and -6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 15 m²T1 = 21 °CT3 = -6 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17250 mmExpanded polystyrene, k = 0.03525 mm16 °C7 °CTi​ = ?Q̇

A wall is made of 250 mm of gypsum board and 25 mm of expanded polystyrene, with an area of 10 m². The outer faces are at 16 °C and 7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 10 m²T1 = 16 °CT3 = 7 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.035200 mmConcrete, k = 1.4100 mmroom 22 °Coutside 0 °CQ̇

A wall of 200 mm expanded polystyrene and 100 mm concrete separates a room at 22 °C from outside air at 0 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 8 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = 0 °C
U = W/(m²·K)
6.Hard
Gypsum board, k = 0.1750 mmConcrete, k = 1.4150 mmroom 22 °Coutside -15 °CTs​ = ?Q̇

A wall of 50 mm gypsum board and 150 mm concrete separates a room at 22 °C from outside air at -15 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -15 °C
Ts = °C

Answer key

  1. 1. Q̇ = 345.6 W
  2. 2. Q̇ = 576 W
  3. 3. Ti = 19.17 °C
  4. 4. Ti = 9.942 °C
  5. 5. U = 0.1666 W/(m²·K)
  6. 6. Ts = 15.29 °C

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