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 = 0.9610 mm19 °C-1 °CQ̇ = ?

A wall of glass is 10 mm thick and has an area of 4 m². Its faces are held at 19 °C and -1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 10 mmA = 4 m²T1 = 19 °CT2 = -1 °C
Q̇ = W
2.Easy
Brick, k = 0.72250 mm25 °C4 °CQ̇ = ?

A wall of brick is 250 mm thick and has an area of 20 m². Its faces are held at 25 °C and 4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 250 mmA = 20 m²T1 = 25 °CT2 = 4 °C
Q̇ = W
3.Medium
Gypsum board, k = 0.1750 mmConcrete, k = 1.475 mm20 °C-9 °CQ̇ = ?

A wall is made of 50 mm of gypsum board and 75 mm of concrete, with an area of 4 m². The outer faces are at 20 °C and -9 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 4 m²T1 = 20 °CT3 = -9 °C
Q̇ = W
4.Medium
Concrete, k = 1.4200 mmGlass, k = 0.96100 mm20 °C2 °CTi​ = ?Q̇

A wall is made of 200 mm of concrete and 100 mm of glass, with an area of 6 m². The outer faces are at 20 °C and 2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 6 m²T1 = 20 °CT3 = 2 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.03550 mmBrick, k = 0.72100 mmroom 21 °Coutside -15 °CQ̇ = ?

A wall of 50 mm expanded polystyrene and 100 mm brick separates a room at 21 °C from outside air at -15 °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 heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -15 °C
Q̇ = W
6.Hard
Gypsum board, k = 0.17150 mmBrick, k = 0.72150 mmroom 21 °Coutside -3 °CTs​ = ?Q̇

A wall of 150 mm gypsum board and 150 mm brick separates a room at 21 °C from outside air at -3 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -3 °C
Ts = °C

Answer key

  1. 1. Q̇ = 7680 W
  2. 2. Q̇ = 1210 W
  3. 3. Q̇ = 333.6 W
  4. 4. Ti = 9.59 °C
  5. 5. Q̇ = 309 W
  6. 6. Ts = 18.53 °C

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