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 = 0.7220 mm20 °C6 °CQ̇ = ?

A wall of brick is 20 mm thick and has an area of 4 m². Its faces are held at 20 °C and 6 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 20 mmA = 4 m²T1 = 20 °CT2 = 6 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.03520 mm24 °C-9 °Cq″ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 6 m². Its faces are held at 24 °C and -9 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 6 m²T1 = 24 °CT2 = -9 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035100 mmConcrete, k = 1.4100 mm22 °C-5 °CQ̇ = ?

A wall is made of 100 mm of expanded polystyrene and 100 mm of concrete, with an area of 6 m². The outer faces are at 22 °C and -5 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 6 m²T1 = 22 °CT3 = -5 °C
Q̇ = W
4.Medium
Mineral wool, k = 0.04100 mmBrick, k = 0.72150 mm22 °C-2 °CTi​ = ?Q̇

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 22 °C and -2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 8 m²T1 = 22 °CT3 = -2 °C
Ti = °C
5.Hard
Concrete, k = 1.450 mmBrick, k = 0.72150 mmroom 22 °Coutside -1 °CQ̇

A wall of 50 mm concrete and 150 mm brick separates a room at 22 °C from outside air at -1 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 8 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -1 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.96200 mmExpanded polystyrene, k = 0.035150 mmroom 20 °Coutside -12 °CTs​ = ?Q̇

A wall of 200 mm glass and 150 mm expanded polystyrene separates a room at 20 °C from outside air at -12 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -12 °C
Ts = °C

Answer key

  1. 1. Q̇ = 2016 W
  2. 2. q″ = 57.75 W/m²
  3. 3. Q̇ = 55.32 W
  4. 4. Ti = −0.1538 °C
  5. 5. U = 2.604 W/(m²·K)
  6. 6. Ts = 19.14 °C

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