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
Brick, k = 0.7210 mm23 °C-14 °Cq″ = ?

A wall of brick is 10 mm thick and has an area of 8 m². Its faces are held at 23 °C and -14 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 10 mmA = 8 m²T1 = 23 °CT2 = -14 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.035100 mm19 °C-9 °Cq″ = ?

A wall of expanded polystyrene is 100 mm thick and has an area of 20 m². Its faces are held at 19 °C and -9 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 100 mmA = 20 m²T1 = 19 °CT2 = -9 °C
q″ = W/m²
3.Medium
Wood, k = 0.17250 mmExpanded polystyrene, k = 0.035150 mm19 °C8 °CQ̇ = ?

A wall is made of 250 mm of wood and 150 mm of expanded polystyrene, with an area of 20 m². The outer faces are at 19 °C and 8 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 20 m²T1 = 19 °CT3 = 8 °C
Q̇ = W
4.Medium
Brick, k = 0.7250 mmGlass, k = 0.96150 mm16 °C4 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 150 mm of glass, with an area of 4 m². The outer faces are at 16 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 4 m²T1 = 16 °CT3 = 4 °C
Ti = °C
5.Hard
Wood, k = 0.17200 mmConcrete, k = 1.4100 mmroom 21 °Coutside 5 °CQ̇

A wall of 200 mm wood and 100 mm concrete separates a room at 21 °C from outside air at 5 °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 overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 5 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4200 mmMineral wool, k = 0.0475 mmroom 21 °Coutside -12 °CQ̇

A wall of 200 mm concrete and 75 mm mineral wool separates a room at 21 °C from outside air at -12 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 10 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -12 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 2664 W/m²
  2. 2. q″ = 9.8 W/m²
  3. 3. Q̇ = 38.22 W
  4. 4. Ti = 12.31 °C
  5. 5. U = 0.7004 W/(m²·K)
  6. 6. U = 0.4571 W/(m²·K)

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