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
Mineral wool, k = 0.0420 mm17 °C-7 °Cq″ = ?

A wall of mineral wool is 20 mm thick and has an area of 6 m². Its faces are held at 17 °C and -7 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 20 mmA = 6 m²T1 = 17 °CT2 = -7 °C
q″ = W/m²
2.Easy
Glass, k = 0.9610 mm22 °C-9 °Cq″ = ?

A wall of glass is 10 mm thick and has an area of 6 m². Its faces are held at 22 °C and -9 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 10 mmA = 6 m²T1 = 22 °CT2 = -9 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17200 mmBrick, k = 0.7275 mm25 °C5 °CTi​ = ?Q̇

A wall is made of 200 mm of gypsum board and 75 mm of brick, with an area of 10 m². The outer faces are at 25 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 10 m²T1 = 25 °CT3 = 5 °C
Ti = °C
4.Medium
Mineral wool, k = 0.0450 mmGypsum board, k = 0.17100 mm23 °C-3 °CQ̇ = ?

A wall is made of 50 mm of mineral wool and 100 mm of gypsum board, with an area of 10 m². The outer faces are at 23 °C and -3 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 10 m²T1 = 23 °CT3 = -3 °C
Q̇ = W
5.Hard
Glass, k = 0.96200 mmGypsum board, k = 0.1750 mmroom 22 °Coutside -4 °CQ̇ = ?

A wall of 200 mm glass and 50 mm gypsum board separates a room at 22 °C from outside air at -4 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -4 °C
Q̇ = W
6.Hard
Glass, k = 0.96150 mmConcrete, k = 1.4100 mmroom 22 °Coutside -14 °CQ̇

A wall of 150 mm glass and 100 mm concrete separates a room at 22 °C from outside air at -14 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 10 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -14 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 48 W/m²
  2. 2. q″ = 2976 W/m²
  3. 3. Ti = 6.627 °C
  4. 4. Q̇ = 141.4 W
  5. 5. Q̇ = 159.4 W
  6. 6. U = 2.454 W/(m²·K)

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