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
Concrete, k = 1.410 mm15 °C1 °CQ̇ = ?

A wall of concrete is 10 mm thick and has an area of 6 m². Its faces are held at 15 °C and 1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 10 mmA = 6 m²T1 = 15 °CT2 = 1 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.1710 mm19 °C-11 °CQ̇ = ?

A wall of gypsum board is 10 mm thick and has an area of 20 m². Its faces are held at 19 °C and -11 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 20 m²T1 = 19 °CT2 = -11 °C
Q̇ = W
3.Medium
Concrete, k = 1.4100 mmBrick, k = 0.72150 mm16 °C4 °CQ̇ = ?

A wall is made of 100 mm of concrete and 150 mm of brick, with an area of 8 m². The outer faces are at 16 °C and 4 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 8 m²T1 = 16 °CT3 = 4 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035200 mmBrick, k = 0.72100 mm19 °C-8 °CTi​ = ?Q̇

A wall is made of 200 mm of expanded polystyrene and 100 mm of brick, with an area of 15 m². The outer faces are at 19 °C and -8 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 15 m²T1 = 19 °CT3 = -8 °C
Ti = °C
5.Hard
Glass, k = 0.9650 mmBrick, k = 0.7275 mmroom 21 °Coutside -7 °CTs​ = ?Q̇

A wall of 50 mm glass and 75 mm brick separates a room at 21 °C from outside air at -7 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 15 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -7 °C
Ts = °C
6.Hard
Brick, k = 0.72100 mmConcrete, k = 1.4150 mmroom 22 °Coutside -1 °CQ̇

A wall of 100 mm brick and 150 mm concrete separates a room at 22 °C from outside air at -1 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 20 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -1 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 11760 W
  2. 2. Q̇ = 10200 W
  3. 3. Q̇ = 343.1 W
  4. 4. Ti = −7.359 °C
  5. 5. Ts = 8.141 °C
  6. 6. U = 2.473 W/(m²·K)

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