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
Brick, k = 0.7220 mm23 °C-4 °Cq″ = ?

A wall of brick is 20 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 = 0.72 W/(m·K)L = 20 mmA = 6 m²T1 = 23 °CT2 = -4 °C
q″ = W/m²
2.Easy
Brick, k = 0.72200 mm18 °C-5 °Cq″ = ?

A wall of brick is 200 mm thick and has an area of 4 m². Its faces are held at 18 °C and -5 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 200 mmA = 4 m²T1 = 18 °CT2 = -5 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035150 mmGlass, k = 0.96150 mm23 °C-4 °CTi​ = ?Q̇

A wall is made of 150 mm of expanded polystyrene and 150 mm of glass, with an area of 10 m². The outer faces are at 23 °C and -4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 10 m²T1 = 23 °CT3 = -4 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17150 mmGlass, k = 0.9675 mm25 °C-1 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 75 mm of glass, with an area of 8 m². The outer faces are at 25 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 8 m²T1 = 25 °CT3 = -1 °C
Ti = °C
5.Hard
Wood, k = 0.1750 mmGlass, k = 0.96100 mmroom 21 °Coutside -4 °CQ̇

A wall of 50 mm wood and 100 mm glass separates a room at 21 °C from outside air at -4 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 8 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 8 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -4 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.035250 mmGypsum board, k = 0.1775 mmroom 21 °Coutside 4 °CQ̇ = ?

A wall of 250 mm expanded polystyrene and 75 mm gypsum board separates a room at 21 °C from outside air at 4 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = 4 °C
Q̇ = W

Answer key

  1. 1. q″ = 972 W/m²
  2. 2. q″ = 82.8 W/m²
  3. 3. Ti = −3.05 °C
  4. 4. Ti = 1.115 °C
  5. 5. U = 1.824 W/(m²·K)
  6. 6. Q̇ = 8.804 W

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