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 = 0.17150 mm18 °C-9 °Cq″ = ?

A wall of gypsum board is 150 mm thick and has an area of 8 m². Its faces are held at 18 °C and -9 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 150 mmA = 8 m²T1 = 18 °CT2 = -9 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.1720 mm24 °C8 °CQ̇ = ?

A wall of gypsum board is 20 mm thick and has an area of 20 m². Its faces are held at 24 °C and 8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 20 mmA = 20 m²T1 = 24 °CT2 = 8 °C
Q̇ = W
3.Medium
Glass, k = 0.96200 mmExpanded polystyrene, k = 0.035100 mm24 °C-2 °CQ̇ = ?

A wall is made of 200 mm of glass and 100 mm of expanded polystyrene, with an area of 4 m². The outer faces are at 24 °C and -2 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 4 m²T1 = 24 °CT3 = -2 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035150 mmGypsum board, k = 0.1725 mm20 °C-15 °CTi​ = ?Q̇

A wall is made of 150 mm of expanded polystyrene and 25 mm of gypsum board, with an area of 15 m². The outer faces are at 20 °C and -15 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 20 °CT3 = -15 °C
Ti = °C
5.Hard
Brick, k = 0.72250 mmWood, k = 0.17150 mmroom 21 °Coutside -3 °CTs​ = ?Q̇

A wall of 250 mm brick and 150 mm wood separates a room at 21 °C from outside air at -3 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 15 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -3 °C
Ts = °C
6.Hard
Mineral wool, k = 0.04250 mmGlass, k = 0.9625 mmroom 20 °Coutside 0 °CQ̇ = ?

A wall of 250 mm mineral wool and 25 mm glass separates a room at 20 °C from outside air at 0 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = 0 °C
Q̇ = W

Answer key

  1. 1. q″ = 30.6 W/m²
  2. 2. Q̇ = 2720 W
  3. 3. Q̇ = 33.93 W
  4. 4. Ti = −13.84 °C
  5. 5. Ts = 18.21 °C
  6. 6. Q̇ = 18.7 W

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