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 = 0.035150 mm22 °C-15 °Cq″ = ?

A wall of expanded polystyrene is 150 mm thick and has an area of 20 m². Its faces are held at 22 °C and -15 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 150 mmA = 20 m²T1 = 22 °CT2 = -15 °C
q″ = W/m²
2.Easy
Concrete, k = 1.4100 mm21 °C-6 °CQ̇ = ?

A wall of concrete is 100 mm thick and has an area of 15 m². Its faces are held at 21 °C and -6 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 100 mmA = 15 m²T1 = 21 °CT2 = -6 °C
Q̇ = W
3.Medium
Concrete, k = 1.4250 mmMineral wool, k = 0.0425 mm25 °C-5 °CTi​ = ?Q̇

A wall is made of 250 mm of concrete and 25 mm of mineral wool, with an area of 10 m². The outer faces are at 25 °C and -5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 10 m²T1 = 25 °CT3 = -5 °C
Ti = °C
4.Medium
Glass, k = 0.96250 mmConcrete, k = 1.4150 mm17 °C7 °CQ̇ = ?

A wall is made of 250 mm of glass and 150 mm of concrete, with an area of 10 m². The outer faces are at 17 °C and 7 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 10 m²T1 = 17 °CT3 = 7 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.0450 mmBrick, k = 0.72100 mmroom 21 °Coutside -14 °CQ̇ = ?

A wall of 50 mm mineral wool and 100 mm brick separates a room at 21 °C from outside air at -14 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -14 °C
Q̇ = W
6.Hard
Concrete, k = 1.450 mmWood, k = 0.1775 mmroom 20 °Coutside -6 °CTs​ = ?Q̇

A wall of 50 mm concrete and 75 mm wood separates a room at 20 °C from outside air at -6 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -6 °C
Ts = °C

Answer key

  1. 1. q″ = 8.633 W/m²
  2. 2. Q̇ = 5670 W
  3. 3. Ti = 18.33 °C
  4. 4. Q̇ = 272.1 W
  5. 5. Q̇ = 88.11 W
  6. 6. Ts = 14.72 °C

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