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
Glass, k = 0.9650 mm24 °C-6 °CQ̇ = ?

A wall of glass is 50 mm thick and has an area of 15 m². Its faces are held at 24 °C and -6 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 15 m²T1 = 24 °CT2 = -6 °C
Q̇ = W
2.Easy
Brick, k = 0.7210 mm19 °C-13 °CQ̇ = ?

A wall of brick is 10 mm thick and has an area of 6 m². Its faces are held at 19 °C and -13 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 10 mmA = 6 m²T1 = 19 °CT2 = -13 °C
Q̇ = W
3.Medium
Expanded polystyrene, k = 0.035250 mmGlass, k = 0.9650 mm16 °C-14 °CTi​ = ?Q̇

A wall is made of 250 mm of expanded polystyrene and 50 mm of glass, with an area of 10 m². The outer faces are at 16 °C and -14 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 10 m²T1 = 16 °CT3 = -14 °C
Ti = °C
4.Medium
Wood, k = 0.1750 mmGypsum board, k = 0.1775 mm18 °C-14 °CTi​ = ?Q̇

A wall is made of 50 mm of wood and 75 mm of gypsum board, with an area of 6 m². The outer faces are at 18 °C and -14 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 18 °CT3 = -14 °C
Ti = °C
5.Hard
Wood, k = 0.17150 mmGlass, k = 0.9625 mmroom 22 °Coutside -3 °CTs​ = ?Q̇

A wall of 150 mm wood and 25 mm glass separates a room at 22 °C from outside air at -3 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -3 °C
Ts = °C
6.Hard
Expanded polystyrene, k = 0.03550 mmBrick, k = 0.72100 mmroom 22 °Coutside -14 °CQ̇

A wall of 50 mm expanded polystyrene and 100 mm brick separates a room at 22 °C from outside air at -14 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -14 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 8640 W
  2. 2. Q̇ = 13824 W
  3. 3. Ti = −13.78 °C
  4. 4. Ti = 5.2 °C
  5. 5. Ts = 19.02 °C
  6. 6. U = 0.5778 W/(m²·K)

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