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 = 0.7210 mm24 °C-1 °Cq″ = ?

A wall of brick is 10 mm thick and has an area of 15 m². Its faces are held at 24 °C and -1 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 10 mmA = 15 m²T1 = 24 °CT2 = -1 °C
q″ = W/m²
2.Easy
Concrete, k = 1.4150 mm22 °C-7 °CQ̇ = ?

A wall of concrete is 150 mm thick and has an area of 20 m². Its faces are held at 22 °C and -7 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 150 mmA = 20 m²T1 = 22 °CT2 = -7 °C
Q̇ = W
3.Medium
Wood, k = 0.17100 mmConcrete, k = 1.4150 mm18 °C-14 °CTi​ = ?Q̇

A wall is made of 100 mm of wood and 150 mm of concrete, with an area of 8 m². The outer faces are at 18 °C and -14 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 8 m²T1 = 18 °CT3 = -14 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035100 mmConcrete, k = 1.425 mm20 °C4 °CTi​ = ?Q̇

A wall is made of 100 mm of expanded polystyrene and 25 mm of concrete, with an area of 8 m². The outer faces are at 20 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 8 m²T1 = 20 °CT3 = 4 °C
Ti = °C
5.Hard
Concrete, k = 1.4250 mmBrick, k = 0.7275 mmroom 22 °Coutside -10 °CQ̇

A wall of 250 mm concrete and 75 mm brick separates a room at 22 °C from outside air at -10 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -10 °C
U = W/(m²·K)
6.Hard
Wood, k = 0.1750 mmExpanded polystyrene, k = 0.03550 mmroom 22 °Coutside -9 °CTs​ = ?Q̇

A wall of 50 mm wood and 50 mm expanded polystyrene separates a room at 22 °C from outside air at -9 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 10 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -9 °C
Ts = °C

Answer key

  1. 1. q″ = 1800 W/m²
  2. 2. Q̇ = 5413 W
  3. 3. Ti = −9.069 °C
  4. 4. Ti = 4.099 °C
  5. 5. U = 2.311 W/(m²·K)
  6. 6. Ts = 19.87 °C

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