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 = 0.04250 mm19 °C-9 °CQ̇ = ?

A wall of mineral wool is 250 mm thick and has an area of 15 m². Its faces are held at 19 °C and -9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 250 mmA = 15 m²T1 = 19 °CT2 = -9 °C
Q̇ = W
2.Easy
Brick, k = 0.72250 mm18 °C10 °Cq″ = ?

A wall of brick is 250 mm thick and has an area of 6 m². Its faces are held at 18 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 250 mmA = 6 m²T1 = 18 °CT2 = 10 °C
q″ = W/m²
3.Medium
Wood, k = 0.17200 mmConcrete, k = 1.475 mm23 °C-15 °CQ̇ = ?

A wall is made of 200 mm of wood and 75 mm of concrete, with an area of 4 m². The outer faces are at 23 °C and -15 °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 = 4 m²T1 = 23 °CT3 = -15 °C
Q̇ = W
4.Medium
Wood, k = 0.1750 mmBrick, k = 0.7225 mm15 °C-4 °CTi​ = ?Q̇

A wall is made of 50 mm of wood and 25 mm of brick, with an area of 4 m². The outer faces are at 15 °C and -4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 4 m²T1 = 15 °CT3 = -4 °C
Ti = °C
5.Hard
Concrete, k = 1.450 mmWood, k = 0.1725 mmroom 20 °Coutside -14 °CTs​ = ?Q̇

A wall of 50 mm concrete and 25 mm wood separates a room at 20 °C from outside air at -14 °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 temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -14 °C
Ts = °C
6.Hard
Glass, k = 0.96250 mmMineral wool, k = 0.0450 mmroom 20 °Coutside -12 °CQ̇

A wall of 250 mm glass and 50 mm mineral wool separates a room at 20 °C from outside air at -12 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -12 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 67.2 W
  2. 2. q″ = 23.04 W/m²
  3. 3. Q̇ = 123.6 W
  4. 4. Ti = −1.994 °C
  5. 5. Ts = 7.824 °C
  6. 6. U = 0.579 W/(m²·K)

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