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 = 0.72150 mm15 °C9 °CQ̇ = ?

A wall of brick is 150 mm thick and has an area of 10 m². Its faces are held at 15 °C and 9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 150 mmA = 10 m²T1 = 15 °CT2 = 9 °C
Q̇ = W
2.Easy
Glass, k = 0.9610 mm21 °C6 °Cq″ = ?

A wall of glass is 10 mm thick and has an area of 6 m². Its faces are held at 21 °C and 6 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 10 mmA = 6 m²T1 = 21 °CT2 = 6 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17200 mmConcrete, k = 1.425 mm16 °C-3 °CTi​ = ?Q̇

A wall is made of 200 mm of gypsum board and 25 mm of concrete, with an area of 6 m². The outer faces are at 16 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 6 m²T1 = 16 °CT3 = -3 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17150 mmWood, k = 0.1750 mm15 °C-3 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 50 mm of wood, with an area of 6 m². The outer faces are at 15 °C and -3 °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 = 0.17 W/(m·K)A = 6 m²T1 = 15 °CT3 = -3 °C
Ti = °C
5.Hard
Glass, k = 0.96200 mmGypsum board, k = 0.17100 mmroom 21 °Coutside -2 °CQ̇ = ?

A wall of 200 mm glass and 100 mm gypsum board separates a room at 21 °C from outside air at -2 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -2 °C
Q̇ = W
6.Hard
Gypsum board, k = 0.17100 mmWood, k = 0.1775 mmroom 21 °Coutside -13 °CTs​ = ?Q̇

A wall of 100 mm gypsum board and 75 mm wood separates a room at 21 °C from outside air at -13 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 15 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -13 °C
Ts = °C

Answer key

  1. 1. Q̇ = 288 W
  2. 2. q″ = 1440 W/m²
  3. 3. Ti = −2.716 °C
  4. 4. Ti = 1.5 °C
  5. 5. Q̇ = 230.8 W
  6. 6. Ts = 17.44 °C

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