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
Glass, k = 0.9650 mm21 °C7 °Cq″ = ?

A wall of glass is 50 mm thick and has an area of 10 m². Its faces are held at 21 °C and 7 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 10 m²T1 = 21 °CT2 = 7 °C
q″ = W/m²
2.Easy
Glass, k = 0.96100 mm24 °C-5 °CQ̇ = ?

A wall of glass is 100 mm thick and has an area of 4 m². Its faces are held at 24 °C and -5 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 100 mmA = 4 m²T1 = 24 °CT2 = -5 °C
Q̇ = W
3.Medium
Gypsum board, k = 0.17150 mmExpanded polystyrene, k = 0.03575 mm21 °C1 °CQ̇ = ?

A wall is made of 150 mm of gypsum board and 75 mm of expanded polystyrene, with an area of 10 m². The outer faces are at 21 °C and 1 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 10 m²T1 = 21 °CT3 = 1 °C
Q̇ = W
4.Medium
Concrete, k = 1.450 mmMineral wool, k = 0.0475 mm20 °C5 °CTi​ = ?Q̇

A wall is made of 50 mm of concrete and 75 mm of mineral wool, with an area of 10 m². The outer faces are at 20 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 10 m²T1 = 20 °CT3 = 5 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17200 mmConcrete, k = 1.4150 mmroom 20 °Coutside 4 °CTs​ = ?Q̇

A wall of 200 mm gypsum board and 150 mm concrete separates a room at 20 °C from outside air at 4 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 6 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 4 °C
Ts = °C
6.Hard
Gypsum board, k = 0.17100 mmConcrete, k = 1.450 mmroom 20 °Coutside 5 °CQ̇ = ?

A wall of 100 mm gypsum board and 50 mm concrete separates a room at 20 °C from outside air at 5 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 4 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = 5 °C
Q̇ = W

Answer key

  1. 1. q″ = 268.8 W/m²
  2. 2. Q̇ = 1114 W
  3. 3. Q̇ = 66.11 W
  4. 4. Ti = 19.72 °C
  5. 5. Ts = 18.61 °C
  6. 6. Q̇ = 74.64 W

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