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
Expanded polystyrene, k = 0.035100 mm25 °C0 °Cq″ = ?

A wall of expanded polystyrene is 100 mm thick and has an area of 10 m². Its faces are held at 25 °C and 0 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 100 mmA = 10 m²T1 = 25 °CT2 = 0 °C
q″ = W/m²
2.Easy
Wood, k = 0.17150 mm19 °C6 °Cq″ = ?

A wall of wood is 150 mm thick and has an area of 10 m². Its faces are held at 19 °C and 6 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 150 mmA = 10 m²T1 = 19 °CT2 = 6 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035150 mmMineral wool, k = 0.04150 mm21 °C10 °CTi​ = ?Q̇

A wall is made of 150 mm of expanded polystyrene and 150 mm of mineral wool, with an area of 20 m². The outer faces are at 21 °C and 10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 20 m²T1 = 21 °CT3 = 10 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17250 mmGlass, k = 0.96150 mm24 °C4 °CQ̇ = ?

A wall is made of 250 mm of gypsum board and 150 mm of glass, with an area of 15 m². The outer faces are at 24 °C and 4 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 15 m²T1 = 24 °CT3 = 4 °C
Q̇ = W
5.Hard
Gypsum board, k = 0.17200 mmMineral wool, k = 0.0450 mmroom 20 °Coutside -3 °CTs​ = ?Q̇

A wall of 200 mm gypsum board and 50 mm mineral wool separates a room at 20 °C from outside air at -3 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 6 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -3 °C
Ts = °C
6.Hard
Brick, k = 0.72250 mmExpanded polystyrene, k = 0.035100 mmroom 20 °Coutside -1 °CQ̇

A wall of 250 mm brick and 100 mm expanded polystyrene separates a room at 20 °C from outside air at -1 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 6 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -1 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 8.75 W/m²
  2. 2. q″ = 14.73 W/m²
  3. 3. Ti = 15.13 °C
  4. 4. Q̇ = 184.4 W
  5. 5. Ts = 18.89 °C
  6. 6. U = 0.2959 W/(m²·K)

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