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
Gypsum board, k = 0.1750 mm25 °C-10 °Cq″ = ?

A wall of gypsum board is 50 mm thick and has an area of 4 m². Its faces are held at 25 °C and -10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 4 m²T1 = 25 °CT2 = -10 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.17250 mm25 °C0 °CQ̇ = ?

A wall of gypsum board is 250 mm thick and has an area of 20 m². Its faces are held at 25 °C and 0 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 250 mmA = 20 m²T1 = 25 °CT2 = 0 °C
Q̇ = W
3.Medium
Brick, k = 0.7250 mmWood, k = 0.1725 mm17 °C-8 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 25 mm of wood, with an area of 8 m². The outer faces are at 17 °C and -8 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 17 °CT3 = -8 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17150 mmWood, k = 0.1775 mm17 °C4 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 75 mm of wood, with an area of 8 m². The outer faces are at 17 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 17 °CT3 = 4 °C
Ti = °C
5.Hard
Concrete, k = 1.4200 mmWood, k = 0.1775 mmroom 22 °Coutside -11 °CTs​ = ?Q̇

A wall of 200 mm concrete and 75 mm wood separates a room at 22 °C from outside air at -11 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -11 °C
Ts = °C
6.Hard
Brick, k = 0.7250 mmConcrete, k = 1.475 mmroom 20 °Coutside -5 °CQ̇

A wall of 50 mm brick and 75 mm concrete separates a room at 20 °C from outside air at -5 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 15 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -5 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 119 W/m²
  2. 2. Q̇ = 340 W
  3. 3. Ti = 8.981 °C
  4. 4. Ti = 8.333 °C
  5. 5. Ts = 15.13 °C
  6. 6. U = 2.944 W/(m²·K)

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