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
Mineral wool, k = 0.0450 mm21 °C4 °Cq″ = ?

A wall of mineral wool is 50 mm thick and has an area of 10 m². Its faces are held at 21 °C and 4 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 50 mmA = 10 m²T1 = 21 °CT2 = 4 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03550 mm23 °C8 °Cq″ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 10 m². Its faces are held at 23 °C and 8 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 10 m²T1 = 23 °CT2 = 8 °C
q″ = W/m²
3.Medium
Wood, k = 0.17200 mmMineral wool, k = 0.04150 mm25 °C5 °CTi​ = ?Q̇

A wall is made of 200 mm of wood and 150 mm of mineral wool, with an area of 15 m². The outer faces are at 25 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 15 m²T1 = 25 °CT3 = 5 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17200 mmExpanded polystyrene, k = 0.035100 mm25 °C-13 °CQ̇ = ?

A wall is made of 200 mm of gypsum board and 100 mm of expanded polystyrene, with an area of 6 m². The outer faces are at 25 °C and -13 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 6 m²T1 = 25 °CT3 = -13 °C
Q̇ = W
5.Hard
Concrete, k = 1.4150 mmBrick, k = 0.72150 mmroom 20 °Coutside 0 °CTs​ = ?Q̇

A wall of 150 mm concrete and 150 mm brick separates a room at 20 °C from outside air at 0 °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 = 150 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = 0 °C
Ts = °C
6.Hard
Concrete, k = 1.4200 mmGlass, k = 0.9675 mmroom 20 °Coutside -5 °CQ̇

A wall of 200 mm concrete and 75 mm glass separates a room at 20 °C from outside air at -5 °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 overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -5 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 13.6 W/m²
  2. 2. q″ = 10.5 W/m²
  3. 3. Ti = 20.22 °C
  4. 4. Q̇ = 56.53 W
  5. 5. Ts = 14.9 °C
  6. 6. U = 2.77 W/(m²·K)

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