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
Expanded polystyrene, k = 0.035200 mm24 °C-1 °Cq″ = ?

A wall of expanded polystyrene is 200 mm thick and has an area of 10 m². Its faces are held at 24 °C and -1 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 200 mmA = 10 m²T1 = 24 °CT2 = -1 °C
q″ = W/m²
2.Easy
Glass, k = 0.96100 mm19 °C-11 °CQ̇ = ?

A wall of glass is 100 mm thick and has an area of 6 m². Its faces are held at 19 °C and -11 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 100 mmA = 6 m²T1 = 19 °CT2 = -11 °C
Q̇ = W
3.Medium
Brick, k = 0.72150 mmConcrete, k = 1.4150 mm19 °C4 °CTi​ = ?Q̇

A wall is made of 150 mm of brick and 150 mm of concrete, with an area of 15 m². The outer faces are at 19 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 15 m²T1 = 19 °CT3 = 4 °C
Ti = °C
4.Medium
Concrete, k = 1.4200 mmGypsum board, k = 0.17150 mm18 °C1 °CQ̇ = ?

A wall is made of 200 mm of concrete and 150 mm of gypsum board, with an area of 4 m². The outer faces are at 18 °C and 1 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 4 m²T1 = 18 °CT3 = 1 °C
Q̇ = W
5.Hard
Wood, k = 0.1750 mmConcrete, k = 1.475 mmroom 21 °Coutside -3 °CQ̇

A wall of 50 mm wood and 75 mm concrete separates a room at 21 °C from outside air at -3 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -3 °C
U = W/(m²·K)
6.Hard
Gypsum board, k = 0.17250 mmWood, k = 0.1725 mmroom 20 °Coutside -9 °CTs​ = ?Q̇

A wall of 250 mm gypsum board and 25 mm wood separates a room at 20 °C from outside air at -9 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -9 °C
Ts = °C

Answer key

  1. 1. q″ = 4.375 W/m²
  2. 2. Q̇ = 1728 W
  3. 3. Ti = 9.094 °C
  4. 4. Q̇ = 66.33 W
  5. 5. U = 1.804 W/(m²·K)
  6. 6. Ts = 17.96 °C

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