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 = 1.420 mm23 °C-4 °CQ̇ = ?

A wall of concrete is 20 mm thick and has an area of 8 m². Its faces are held at 23 °C and -4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 20 mmA = 8 m²T1 = 23 °CT2 = -4 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.1750 mm21 °C-6 °Cq″ = ?

A wall of gypsum board is 50 mm thick and has an area of 15 m². Its faces are held at 21 °C and -6 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 15 m²T1 = 21 °CT2 = -6 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.03550 mmWood, k = 0.17150 mm22 °C-13 °CTi​ = ?Q̇

A wall is made of 50 mm of expanded polystyrene and 150 mm of wood, with an area of 15 m². The outer faces are at 22 °C and -13 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 22 °CT3 = -13 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17200 mmGlass, k = 0.96150 mm19 °C4 °CQ̇ = ?

A wall is made of 200 mm of gypsum board and 150 mm of glass, with an area of 15 m². The outer faces are at 19 °C and 4 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 15 m²T1 = 19 °CT3 = 4 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.04250 mmWood, k = 0.17150 mmroom 22 °Coutside 1 °CTs​ = ?Q̇

A wall of 250 mm mineral wool and 150 mm wood separates a room at 22 °C from outside air at 1 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = 1 °C
Ts = °C
6.Hard
Concrete, k = 1.4250 mmMineral wool, k = 0.04150 mmroom 21 °Coutside 0 °CQ̇

A wall of 250 mm concrete and 150 mm mineral wool separates a room at 21 °C from outside air at 0 °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 overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = 0 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 15120 W
  2. 2. q″ = 91.8 W/m²
  3. 3. Ti = 0.3636 °C
  4. 4. Q̇ = 168.8 W
  5. 5. Ts = 21.71 °C
  6. 6. U = 0.2462 W/(m²·K)

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