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 = 0.04200 mm18 °C5 °Cq″ = ?

A wall of mineral wool is 200 mm thick and has an area of 6 m². Its faces are held at 18 °C and 5 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 200 mmA = 6 m²T1 = 18 °CT2 = 5 °C
q″ = W/m²
2.Easy
Glass, k = 0.96200 mm22 °C10 °Cq″ = ?

A wall of glass is 200 mm thick and has an area of 10 m². Its faces are held at 22 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 200 mmA = 10 m²T1 = 22 °CT2 = 10 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035100 mmGlass, k = 0.9625 mm18 °C5 °CTi​ = ?Q̇

A wall is made of 100 mm of expanded polystyrene and 25 mm of glass, with an area of 6 m². The outer faces are at 18 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 6 m²T1 = 18 °CT3 = 5 °C
Ti = °C
4.Medium
Wood, k = 0.17200 mmConcrete, k = 1.475 mm23 °C3 °CQ̇ = ?

A wall is made of 200 mm of wood and 75 mm of concrete, with an area of 10 m². The outer faces are at 23 °C and 3 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 10 m²T1 = 23 °CT3 = 3 °C
Q̇ = W
5.Hard
Glass, k = 0.9650 mmExpanded polystyrene, k = 0.03525 mmroom 22 °Coutside -6 °CQ̇

A wall of 50 mm glass and 25 mm expanded polystyrene separates a room at 22 °C from outside air at -6 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -6 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4250 mmExpanded polystyrene, k = 0.035150 mmroom 20 °Coutside -10 °CQ̇ = ?

A wall of 250 mm concrete and 150 mm expanded polystyrene separates a room at 20 °C from outside air at -10 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -10 °C
Q̇ = W

Answer key

  1. 1. q″ = 2.6 W/m²
  2. 2. q″ = 57.6 W/m²
  3. 3. Ti = 5.117 °C
  4. 4. Q̇ = 162.6 W
  5. 5. U = 1.017 W/(m²·K)
  6. 6. Q̇ = 64.9 W

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