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 mm20 °C1 °Cq″ = ?

A wall of expanded polystyrene is 150 mm thick and has an area of 15 m². Its faces are held at 20 °C and 1 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 150 mmA = 15 m²T1 = 20 °CT2 = 1 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03510 mm23 °C4 °Cq″ = ?

A wall of expanded polystyrene is 10 mm thick and has an area of 6 m². Its faces are held at 23 °C and 4 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 10 mmA = 6 m²T1 = 23 °CT2 = 4 °C
q″ = W/m²
3.Medium
Wood, k = 0.1750 mmGypsum board, k = 0.1725 mm21 °C-8 °CTi​ = ?Q̇

A wall is made of 50 mm of wood and 25 mm of gypsum board, with an area of 4 m². The outer faces are at 21 °C and -8 °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 = 0.17 W/(m·K)A = 4 m²T1 = 21 °CT3 = -8 °C
Ti = °C
4.Medium
Concrete, k = 1.4150 mmMineral wool, k = 0.0475 mm23 °C-7 °CQ̇ = ?

A wall is made of 150 mm of concrete and 75 mm of mineral wool, with an area of 4 m². The outer faces are at 23 °C and -7 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 4 m²T1 = 23 °CT3 = -7 °C
Q̇ = W
5.Hard
Gypsum board, k = 0.17150 mmConcrete, k = 1.4150 mmroom 22 °Coutside -14 °CQ̇ = ?

A wall of 150 mm gypsum board and 150 mm concrete separates a room at 22 °C from outside air at -14 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -14 °C
Q̇ = W
6.Hard
Wood, k = 0.17100 mmExpanded polystyrene, k = 0.035150 mmroom 20 °Coutside -4 °CQ̇

A wall of 100 mm wood and 150 mm expanded polystyrene separates a room at 20 °C from outside air at -4 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -4 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 4.433 W/m²
  2. 2. q″ = 66.5 W/m²
  3. 3. Ti = 1.667 °C
  4. 4. Q̇ = 60.54 W
  5. 5. Q̇ = 192.4 W
  6. 6. U = 0.1997 W/(m²·K)

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