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 = 1.450 mm19 °C-13 °Cq″ = ?

A wall of concrete is 50 mm thick and has an area of 10 m². Its faces are held at 19 °C and -13 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 50 mmA = 10 m²T1 = 19 °CT2 = -13 °C
q″ = W/m²
2.Easy
Brick, k = 0.72100 mm21 °C5 °Cq″ = ?

A wall of brick is 100 mm thick and has an area of 8 m². Its faces are held at 21 °C and 5 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 100 mmA = 8 m²T1 = 21 °CT2 = 5 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035150 mmWood, k = 0.1750 mm21 °C5 °CTi​ = ?Q̇

A wall is made of 150 mm of expanded polystyrene and 50 mm of wood, with an area of 6 m². The outer faces are at 21 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 21 °CT3 = 5 °C
Ti = °C
4.Medium
Concrete, k = 1.4100 mmWood, k = 0.1750 mm19 °C-14 °CQ̇ = ?

A wall is made of 100 mm of concrete and 50 mm of wood, with an area of 10 m². The outer faces are at 19 °C and -14 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 10 m²T1 = 19 °CT3 = -14 °C
Q̇ = W
5.Hard
Brick, k = 0.7250 mmGypsum board, k = 0.1725 mmroom 21 °Coutside -6 °CTs​ = ?Q̇

A wall of 50 mm brick and 25 mm gypsum board separates a room at 21 °C from outside air at -6 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -6 °C
Ts = °C
6.Hard
Glass, k = 0.96100 mmBrick, k = 0.7275 mmroom 22 °Coutside -3 °CTs​ = ?Q̇

A wall of 100 mm glass and 75 mm brick separates a room at 22 °C from outside air at -3 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -3 °C
Ts = °C

Answer key

  1. 1. q″ = 896 W/m²
  2. 2. q″ = 115.2 W/m²
  3. 3. Ti = 6.028 °C
  4. 4. Q̇ = 902.8 W
  5. 5. Ts = 11.77 °C
  6. 6. Ts = 14.68 °C

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