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
Wood, k = 0.17150 mm24 °C-11 °Cq″ = ?

A wall of wood is 150 mm thick and has an area of 4 m². Its faces are held at 24 °C and -11 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 150 mmA = 4 m²T1 = 24 °CT2 = -11 °C
q″ = W/m²
2.Easy
Mineral wool, k = 0.04250 mm23 °C-2 °Cq″ = ?

A wall of mineral wool is 250 mm thick and has an area of 10 m². Its faces are held at 23 °C and -2 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 250 mmA = 10 m²T1 = 23 °CT2 = -2 °C
q″ = W/m²
3.Medium
Wood, k = 0.17200 mmGypsum board, k = 0.1725 mm20 °C6 °CTi​ = ?Q̇

A wall is made of 200 mm of wood and 25 mm of gypsum board, with an area of 15 m². The outer faces are at 20 °C and 6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 20 °CT3 = 6 °C
Ti = °C
4.Medium
Glass, k = 0.96100 mmMineral wool, k = 0.0475 mm18 °C-2 °CTi​ = ?Q̇

A wall is made of 100 mm of glass and 75 mm of mineral wool, with an area of 15 m². The outer faces are at 18 °C and -2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 15 m²T1 = 18 °CT3 = -2 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.035150 mmBrick, k = 0.7250 mmroom 21 °Coutside -6 °CQ̇ = ?

A wall of 150 mm expanded polystyrene and 50 mm brick separates a room at 21 °C from outside air at -6 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -6 °C
Q̇ = W
6.Hard
Expanded polystyrene, k = 0.035100 mmWood, k = 0.1725 mmroom 21 °Coutside -2 °CQ̇

A wall of 100 mm expanded polystyrene and 25 mm wood 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 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -2 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 39.67 W/m²
  2. 2. q″ = 4 W/m²
  3. 3. Ti = 7.556 °C
  4. 4. Ti = 16.95 °C
  5. 5. Q̇ = 72.08 W
  6. 6. U = 0.3145 W/(m²·K)

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