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 = 1.450 mm17 °C-6 °Cq″ = ?

A wall of concrete is 50 mm thick and has an area of 15 m². Its faces are held at 17 °C and -6 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 50 mmA = 15 m²T1 = 17 °CT2 = -6 °C
q″ = W/m²
2.Easy
Brick, k = 0.7250 mm19 °C-9 °Cq″ = ?

A wall of brick is 50 mm thick and has an area of 10 m². Its faces are held at 19 °C and -9 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 50 mmA = 10 m²T1 = 19 °CT2 = -9 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04100 mmGypsum board, k = 0.1750 mm17 °C-14 °CQ̇ = ?

A wall is made of 100 mm of mineral wool and 50 mm of gypsum board, with an area of 8 m². The outer faces are at 17 °C and -14 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 17 °CT3 = -14 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035150 mmGlass, k = 0.9625 mm24 °C-8 °CQ̇ = ?

A wall is made of 150 mm of expanded polystyrene and 25 mm of glass, with an area of 20 m². The outer faces are at 24 °C and -8 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 20 m²T1 = 24 °CT3 = -8 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.04200 mmConcrete, k = 1.4100 mmroom 21 °Coutside 1 °CQ̇

A wall of 200 mm mineral wool and 100 mm concrete separates a room at 21 °C from outside air at 1 °C. The convection coefficients are 10 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 = 200 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 1 °C
U = W/(m²·K)
6.Hard
Mineral wool, k = 0.04200 mmConcrete, k = 1.450 mmroom 21 °Coutside -13 °CTs​ = ?Q̇

A wall of 200 mm mineral wool and 50 mm concrete separates a room at 21 °C from outside air at -13 °C. The convection coefficients are 6 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 = 0.04 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -13 °C
Ts = °C

Answer key

  1. 1. q″ = 644 W/m²
  2. 2. q″ = 403.2 W/m²
  3. 3. Q̇ = 88.76 W
  4. 4. Q̇ = 148.4 W
  5. 5. U = 0.1915 W/(m²·K)
  6. 6. Ts = 19.92 °C

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