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 mm23 °C-14 °CQ̇ = ?

A wall of brick is 10 mm thick and has an area of 6 m². Its faces are held at 23 °C and -14 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 10 mmA = 6 m²T1 = 23 °CT2 = -14 °C
Q̇ = W
2.Easy
Concrete, k = 1.450 mm16 °C-2 °Cq″ = ?

A wall of concrete is 50 mm thick and has an area of 4 m². Its faces are held at 16 °C and -2 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 50 mmA = 4 m²T1 = 16 °CT2 = -2 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035100 mmConcrete, k = 1.475 mm25 °C-11 °CQ̇ = ?

A wall is made of 100 mm of expanded polystyrene and 75 mm of concrete, with an area of 8 m². The outer faces are at 25 °C and -11 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 8 m²T1 = 25 °CT3 = -11 °C
Q̇ = W
4.Medium
Gypsum board, k = 0.17100 mmBrick, k = 0.72150 mm20 °C-15 °CTi​ = ?Q̇

A wall is made of 100 mm of gypsum board and 150 mm of brick, with an area of 6 m². The outer faces are at 20 °C and -15 °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 = 0.72 W/(m·K)A = 6 m²T1 = 20 °CT3 = -15 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.035200 mmWood, k = 0.17150 mmroom 21 °Coutside -9 °CQ̇

A wall of 200 mm expanded polystyrene and 150 mm wood separates a room at 21 °C from outside air at -9 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -9 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4250 mmBrick, k = 0.72100 mmroom 22 °Coutside -8 °CQ̇

A wall of 250 mm concrete and 100 mm brick separates a room at 22 °C from outside air at -8 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -8 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 15984 W
  2. 2. q″ = 504 W/m²
  3. 3. Q̇ = 98.94 W
  4. 4. Ti = −5.846 °C
  5. 5. U = 0.1468 W/(m²·K)
  6. 6. U = 2.011 W/(m²·K)

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