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 = 0.03510 mm21 °C-10 °CQ̇ = ?

A wall of expanded polystyrene is 10 mm thick and has an area of 10 m². Its faces are held at 21 °C and -10 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 10 mmA = 10 m²T1 = 21 °CT2 = -10 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.035250 mm15 °C-14 °Cq″ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 12 m². Its faces are held at 15 °C and -14 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 12 m²T1 = 15 °CT2 = -14 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04100 mmBrick, k = 0.72150 mm17 °C2 °CQ̇ = ?

A wall is made of 100 mm of mineral wool and 150 mm of brick, with an area of 8 m². The outer faces are at 17 °C and 2 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 8 m²T1 = 17 °CT3 = 2 °C
Q̇ = W
4.Medium
Brick, k = 0.72150 mmExpanded polystyrene, k = 0.035100 mm24 °C-9 °CTi​ = ?Q̇

A wall is made of 150 mm of brick and 100 mm of expanded polystyrene, with an area of 15 m². The outer faces are at 24 °C and -9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 15 m²T1 = 24 °CT3 = -9 °C
Ti = °C
5.Hard
Glass, k = 0.96250 mmMineral wool, k = 0.0425 mmroom 21 °Coutside 2 °CQ̇

A wall of 250 mm glass and 25 mm mineral wool separates a room at 21 °C from outside air at 2 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = 2 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4100 mmGlass, k = 0.96100 mmroom 21 °Coutside -11 °CQ̇

A wall of 100 mm concrete and 100 mm glass separates a room at 21 °C from outside air at -11 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -11 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 1085 W
  2. 2. q″ = 4.06 W/m²
  3. 3. Q̇ = 44.31 W
  4. 4. Ti = 21.76 °C
  5. 5. U = 0.9752 W/(m²·K)
  6. 6. U = 3.237 W/(m²·K)

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