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 mm18 °C-13 °Cq″ = ?

A wall of glass is 50 mm thick and has an area of 15 m². Its faces are held at 18 °C and -13 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 15 m²T1 = 18 °CT2 = -13 °C
q″ = W/m²
2.Easy
Wood, k = 0.1710 mm22 °C8 °CQ̇ = ?

A wall of wood is 10 mm thick and has an area of 6 m². Its faces are held at 22 °C and 8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 6 m²T1 = 22 °CT2 = 8 °C
Q̇ = W
3.Medium
Gypsum board, k = 0.17150 mmGlass, k = 0.9650 mm20 °C7 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 50 mm of glass, with an area of 8 m². The outer faces are at 20 °C and 7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 8 m²T1 = 20 °CT3 = 7 °C
Ti = °C
4.Medium
Concrete, k = 1.4250 mmBrick, k = 0.7250 mm16 °C9 °CTi​ = ?Q̇

A wall is made of 250 mm of concrete and 50 mm of brick, with an area of 15 m². The outer faces are at 16 °C and 9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 15 m²T1 = 16 °CT3 = 9 °C
Ti = °C
5.Hard
Concrete, k = 1.4150 mmExpanded polystyrene, k = 0.03550 mmroom 22 °Coutside -13 °CQ̇ = ?

A wall of 150 mm concrete and 50 mm expanded polystyrene separates a room at 22 °C from outside air at -13 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 15 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -13 °C
Q̇ = W
6.Hard
Gypsum board, k = 0.17250 mmGlass, k = 0.9625 mmroom 20 °Coutside -7 °CQ̇

A wall of 250 mm gypsum board and 25 mm glass separates a room at 20 °C from outside air at -7 °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 overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -7 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 595.2 W/m²
  2. 2. Q̇ = 1428 W
  3. 3. Ti = 7.725 °C
  4. 4. Ti = 10.96 °C
  5. 5. Q̇ = 299.6 W
  6. 6. U = 0.6135 W/(m²·K)

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