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
Concrete, k = 1.4150 mm23 °C-13 °CQ̇ = ?

A wall of concrete is 150 mm thick and has an area of 8 m². Its faces are held at 23 °C and -13 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 150 mmA = 8 m²T1 = 23 °CT2 = -13 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.1720 mm24 °C-12 °Cq″ = ?

A wall of gypsum board is 20 mm thick and has an area of 12 m². Its faces are held at 24 °C and -12 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 20 mmA = 12 m²T1 = 24 °CT2 = -12 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17250 mmMineral wool, k = 0.0425 mm23 °C-15 °CQ̇ = ?

A wall is made of 250 mm of gypsum board and 25 mm of mineral wool, 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 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 4 m²T1 = 23 °CT3 = -15 °C
Q̇ = W
4.Medium
Mineral wool, k = 0.04100 mmConcrete, k = 1.475 mm16 °C-1 °CTi​ = ?Q̇

A wall is made of 100 mm of mineral wool and 75 mm of concrete, with an area of 6 m². The outer faces are at 16 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 6 m²T1 = 16 °CT3 = -1 °C
Ti = °C
5.Hard
Glass, k = 0.9650 mmConcrete, k = 1.475 mmroom 20 °Coutside -4 °CQ̇

A wall of 50 mm glass and 75 mm concrete separates a room at 20 °C from outside air at -4 °C. The convection coefficients are 8 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 = 50 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 6 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -4 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.03550 mmGlass, k = 0.96100 mmroom 21 °Coutside -3 °CQ̇

A wall of 50 mm expanded polystyrene and 100 mm glass separates a room at 21 °C from outside air at -3 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -3 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 2688 W
  2. 2. q″ = 306 W/m²
  3. 3. Q̇ = 72.53 W
  4. 4. Ti = −0.6434 °C
  5. 5. U = 3.563 W/(m²·K)
  6. 6. U = 0.589 W/(m²·K)

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