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 = 0.035200 mm18 °C9 °CQ̇ = ?

A wall of expanded polystyrene is 200 mm thick and has an area of 6 m². Its faces are held at 18 °C and 9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 200 mmA = 6 m²T1 = 18 °CT2 = 9 °C
Q̇ = W
2.Easy
Glass, k = 0.9610 mm17 °C-10 °CQ̇ = ?

A wall of glass is 10 mm thick and has an area of 8 m². Its faces are held at 17 °C and -10 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 10 mmA = 8 m²T1 = 17 °CT2 = -10 °C
Q̇ = W
3.Medium
Gypsum board, k = 0.1750 mmMineral wool, k = 0.04150 mm23 °C2 °CTi​ = ?Q̇

A wall is made of 50 mm of gypsum board and 150 mm of mineral wool, with an area of 12 m². The outer faces are at 23 °C and 2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 12 m²T1 = 23 °CT3 = 2 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17250 mmExpanded polystyrene, k = 0.035100 mm15 °C-1 °CTi​ = ?Q̇

A wall is made of 250 mm of gypsum board and 100 mm of expanded polystyrene, with an area of 12 m². The outer faces are at 15 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 12 m²T1 = 15 °CT3 = -1 °C
Ti = °C
5.Hard
Concrete, k = 1.450 mmBrick, k = 0.7250 mmroom 20 °Coutside -1 °CQ̇

A wall of 50 mm concrete and 50 mm brick separates a room at 20 °C from outside air at -1 °C. The convection coefficients are 6 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 = 50 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -1 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.96200 mmConcrete, k = 1.425 mmroom 21 °Coutside 2 °CTs​ = ?Q̇

A wall of 200 mm glass and 25 mm concrete separates a room at 21 °C from outside air at 2 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 8 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 2 °C
Ts = °C

Answer key

  1. 1. Q̇ = 9.45 W
  2. 2. Q̇ = 20736 W
  3. 3. Ti = 21.47 °C
  4. 4. Ti = 9.563 °C
  5. 5. U = 3.277 W/(m²·K)
  6. 6. Ts = 15.08 °C

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