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 = 0.17200 mm25 °C-10 °Cq″ = ?

A wall of gypsum board is 200 mm thick and has an area of 20 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 = 200 mmA = 20 m²T1 = 25 °CT2 = -10 °C
q″ = W/m²
2.Easy
Glass, k = 0.9650 mm19 °C-2 °CQ̇ = ?

A wall of glass is 50 mm thick and has an area of 20 m². Its faces are held at 19 °C and -2 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 50 mmA = 20 m²T1 = 19 °CT2 = -2 °C
Q̇ = W
3.Medium
Mineral wool, k = 0.04150 mmGypsum board, k = 0.1775 mm25 °C-10 °CTi​ = ?Q̇

A wall is made of 150 mm of mineral wool and 75 mm of gypsum board, with an area of 8 m². The outer faces are at 25 °C and -10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 25 °CT3 = -10 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035200 mmBrick, k = 0.72100 mm23 °C9 °CTi​ = ?Q̇

A wall is made of 200 mm of expanded polystyrene and 100 mm of brick, with an area of 20 m². The outer faces are at 23 °C and 9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 20 m²T1 = 23 °CT3 = 9 °C
Ti = °C
5.Hard
Wood, k = 0.1750 mmBrick, k = 0.7250 mmroom 21 °Coutside 3 °CTs​ = ?Q̇

A wall of 50 mm wood and 50 mm brick separates a room at 21 °C from outside air at 3 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = 3 °C
Ts = °C
6.Hard
Concrete, k = 1.450 mmGypsum board, k = 0.17150 mmroom 22 °Coutside -14 °CTs​ = ?Q̇

A wall of 50 mm concrete and 150 mm gypsum board separates a room at 22 °C from outside air at -14 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -14 °C
Ts = °C

Answer key

  1. 1. q″ = 29.75 W/m²
  2. 2. Q̇ = 8064 W
  3. 3. Ti = −6.316 °C
  4. 4. Ti = 9.332 °C
  5. 5. Ts = 17.43 °C
  6. 6. Ts = 16.67 °C

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