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
Wood, k = 0.1720 mm23 °C0 °CQ̇ = ?

A wall of wood is 20 mm thick and has an area of 4 m². Its faces are held at 23 °C and 0 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 20 mmA = 4 m²T1 = 23 °CT2 = 0 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.035150 mm21 °C-2 °CQ̇ = ?

A wall of expanded polystyrene is 150 mm thick and has an area of 10 m². Its faces are held at 21 °C and -2 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 150 mmA = 10 m²T1 = 21 °CT2 = -2 °C
Q̇ = W
3.Medium
Concrete, k = 1.450 mmGlass, k = 0.96100 mm25 °C-5 °CTi​ = ?Q̇

A wall is made of 50 mm of concrete and 100 mm of glass, with an area of 4 m². The outer faces are at 25 °C and -5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 4 m²T1 = 25 °CT3 = -5 °C
Ti = °C
4.Medium
Concrete, k = 1.4100 mmExpanded polystyrene, k = 0.03575 mm25 °C8 °CQ̇ = ?

A wall is made of 100 mm of concrete and 75 mm of expanded polystyrene, with an area of 10 m². The outer faces are at 25 °C and 8 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 10 m²T1 = 25 °CT3 = 8 °C
Q̇ = W
5.Hard
Glass, k = 0.96150 mmConcrete, k = 1.475 mmroom 22 °Coutside -10 °CQ̇ = ?

A wall of 150 mm glass and 75 mm concrete separates a room at 22 °C from outside air at -10 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 20 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -10 °C
Q̇ = W
6.Hard
Mineral wool, k = 0.04100 mmBrick, k = 0.72100 mmroom 20 °Coutside -13 °CTs​ = ?Q̇

A wall of 100 mm mineral wool and 100 mm brick separates a room at 20 °C from outside air at -13 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -13 °C
Ts = °C

Answer key

  1. 1. Q̇ = 782 W
  2. 2. Q̇ = 53.67 W
  3. 3. Ti = 17.34 °C
  4. 4. Q̇ = 76.77 W
  5. 5. Q̇ = 1686 W
  6. 6. Ts = 18.53 °C

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