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
Glass, k = 0.9620 mm22 °C8 °Cq″ = ?

A wall of glass is 20 mm thick and has an area of 8 m². Its faces are held at 22 °C and 8 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 20 mmA = 8 m²T1 = 22 °CT2 = 8 °C
q″ = W/m²
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 8 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 = 8 m²T1 = 21 °CT2 = -6 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.03550 mmMineral wool, k = 0.0450 mm16 °C-13 °CTi​ = ?Q̇

A wall is made of 50 mm of expanded polystyrene and 50 mm of mineral wool, with an area of 4 m². The outer faces are at 16 °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 = 50 mm, k2 = 0.04 W/(m·K)A = 4 m²T1 = 16 °CT3 = -13 °C
Ti = °C
4.Medium
Mineral wool, k = 0.04100 mmGlass, k = 0.9675 mm15 °C2 °CQ̇ = ?

A wall is made of 100 mm of mineral wool and 75 mm of glass, with an area of 20 m². The outer faces are at 15 °C and 2 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 20 m²T1 = 15 °CT3 = 2 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.0450 mmExpanded polystyrene, k = 0.03550 mmroom 20 °Coutside -5 °CTs​ = ?Q̇

A wall of 50 mm mineral wool and 50 mm expanded polystyrene separates a room at 20 °C from outside air at -5 °C. The convection coefficients are 7.7 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 = 50 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -5 °C
Ts = °C
6.Hard
Concrete, k = 1.4150 mmMineral wool, k = 0.0475 mmroom 22 °Coutside -10 °CTs​ = ?Q̇

A wall of 150 mm concrete and 75 mm mineral wool separates a room at 22 °C from outside air at -10 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -10 °C
Ts = °C

Answer key

  1. 1. q″ = 672 W/m²
  2. 2. q″ = 91.8 W/m²
  3. 3. Ti = 0.5333 °C
  4. 4. Q̇ = 100.8 W
  5. 5. Ts = 18.86 °C
  6. 6. Ts = 20.08 °C

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