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 = 0.96250 mm22 °C0 °CQ̇ = ?

A wall of glass is 250 mm thick and has an area of 10 m². Its faces are held at 22 °C and 0 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 250 mmA = 10 m²T1 = 22 °CT2 = 0 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.17200 mm24 °C-10 °Cq″ = ?

A wall of gypsum board is 200 mm thick and has an area of 15 m². Its faces are held at 24 °C and -10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 15 m²T1 = 24 °CT2 = -10 °C
q″ = W/m²
3.Medium
Wood, k = 0.17100 mmGypsum board, k = 0.1775 mm21 °C-11 °CTi​ = ?Q̇

A wall is made of 100 mm of wood and 75 mm of gypsum board, with an area of 20 m². The outer faces are at 21 °C and -11 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 20 m²T1 = 21 °CT3 = -11 °C
Ti = °C
4.Medium
Brick, k = 0.72100 mmExpanded polystyrene, k = 0.03525 mm24 °C4 °CTi​ = ?Q̇

A wall is made of 100 mm of brick and 25 mm of expanded polystyrene, with an area of 6 m². The outer faces are at 24 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 6 m²T1 = 24 °CT3 = 4 °C
Ti = °C
5.Hard
Brick, k = 0.72100 mmMineral wool, k = 0.04150 mmroom 20 °Coutside 0 °CQ̇

A wall of 100 mm brick and 150 mm mineral wool separates a room at 20 °C from outside air at 0 °C. The convection coefficients are 7.7 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 = 100 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 8 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = 0 °C
U = W/(m²·K)
6.Hard
Mineral wool, k = 0.04100 mmConcrete, k = 1.4100 mmroom 21 °Coutside 4 °CTs​ = ?Q̇

A wall of 100 mm mineral wool and 100 mm concrete separates a room at 21 °C from outside air at 4 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = 4 °C
Ts = °C

Answer key

  1. 1. Q̇ = 844.8 W
  2. 2. q″ = 28.9 W/m²
  3. 3. Ti = 2.714 °C
  4. 4. Ti = 20.74 °C
  5. 5. U = 0.2458 W/(m²·K)
  6. 6. Ts = 20.37 °C

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