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 mm21 °C-9 °Cq″ = ?

A wall of gypsum board is 200 mm thick and has an area of 10 m². Its faces are held at 21 °C and -9 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 10 m²T1 = 21 °CT2 = -9 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.1720 mm15 °C0 °CQ̇ = ?

A wall of gypsum board is 20 mm thick and has an area of 8 m². Its faces are held at 15 °C and 0 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 20 mmA = 8 m²T1 = 15 °CT2 = 0 °C
Q̇ = W
3.Medium
Glass, k = 0.96250 mmConcrete, k = 1.475 mm23 °C-11 °CQ̇ = ?

A wall is made of 250 mm of glass and 75 mm of concrete, with an area of 12 m². The outer faces are at 23 °C and -11 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 12 m²T1 = 23 °CT3 = -11 °C
Q̇ = W
4.Medium
Glass, k = 0.96100 mmBrick, k = 0.72100 mm23 °C-2 °CTi​ = ?Q̇

A wall is made of 100 mm of glass and 100 mm of brick, with an area of 12 m². The outer faces are at 23 °C and -2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 12 m²T1 = 23 °CT3 = -2 °C
Ti = °C
5.Hard
Mineral wool, k = 0.04150 mmGypsum board, k = 0.1750 mmroom 20 °Coutside -7 °CTs​ = ?Q̇

A wall of 150 mm mineral wool and 50 mm gypsum board separates a room at 20 °C from outside air at -7 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -7 °C
Ts = °C
6.Hard
Wood, k = 0.17100 mmGypsum board, k = 0.17150 mmroom 21 °Coutside -12 °CQ̇

A wall of 100 mm wood and 150 mm gypsum board separates a room at 21 °C from outside air at -12 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -12 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 25.5 W/m²
  2. 2. Q̇ = 1020 W
  3. 3. Q̇ = 1299 W
  4. 4. Ti = 12.29 °C
  5. 5. Ts = 19.2 °C
  6. 6. U = 0.5962 W/(m²·K)

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