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 = 1.4250 mm24 °C-5 °Cq″ = ?

A wall of concrete is 250 mm thick and has an area of 20 m². Its faces are held at 24 °C and -5 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 250 mmA = 20 m²T1 = 24 °CT2 = -5 °C
q″ = W/m²
2.Easy
Wood, k = 0.17250 mm22 °C-14 °Cq″ = ?

A wall of wood is 250 mm thick and has an area of 6 m². Its faces are held at 22 °C and -14 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 250 mmA = 6 m²T1 = 22 °CT2 = -14 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035150 mmBrick, k = 0.72150 mm17 °C1 °CTi​ = ?Q̇

A wall is made of 150 mm of expanded polystyrene and 150 mm of brick, with an area of 15 m². The outer faces are at 17 °C and 1 °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 = 0.72 W/(m·K)A = 15 m²T1 = 17 °CT3 = 1 °C
Ti = °C
4.Medium
Brick, k = 0.72100 mmGypsum board, k = 0.17150 mm16 °C9 °CTi​ = ?Q̇

A wall is made of 100 mm of brick and 150 mm of gypsum board, with an area of 8 m². The outer faces are at 16 °C and 9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 16 °CT3 = 9 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17200 mmGlass, k = 0.96100 mmroom 22 °Coutside 4 °CQ̇ = ?

A wall of 200 mm gypsum board and 100 mm glass separates a room at 22 °C from outside air at 4 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = 4 °C
Q̇ = W
6.Hard
Expanded polystyrene, k = 0.03550 mmMineral wool, k = 0.0450 mmroom 22 °Coutside 1 °CTs​ = ?Q̇

A wall of 50 mm expanded polystyrene and 50 mm mineral wool separates a room at 22 °C from outside air at 1 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = 1 °C
Ts = °C

Answer key

  1. 1. q″ = 162.4 W/m²
  2. 2. q″ = 24.48 W/m²
  3. 3. Ti = 1.742 °C
  4. 4. Ti = 15.05 °C
  5. 5. Q̇ = 186.1 W
  6. 6. Ts = 21.26 °C

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