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 = 0.17100 mm18 °C3 °CQ̇ = ?

A wall of gypsum board is 100 mm thick and has an area of 20 m². Its faces are held at 18 °C and 3 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 20 m²T1 = 18 °CT2 = 3 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.1750 mm16 °C-14 °Cq″ = ?

A wall of gypsum board is 50 mm thick and has an area of 8 m². Its faces are held at 16 °C and -14 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 8 m²T1 = 16 °CT2 = -14 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035200 mmGypsum board, k = 0.1750 mm24 °C-5 °CQ̇ = ?

A wall is made of 200 mm of expanded polystyrene and 50 mm of gypsum board, with an area of 6 m². The outer faces are at 24 °C and -5 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 24 °CT3 = -5 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035150 mmGlass, k = 0.9675 mm22 °C0 °CTi​ = ?Q̇

A wall is made of 150 mm of expanded polystyrene and 75 mm of glass, with an area of 12 m². The outer faces are at 22 °C and 0 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 12 m²T1 = 22 °CT3 = 0 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17100 mmGlass, k = 0.96150 mmroom 22 °Coutside -14 °CTs​ = ?Q̇

A wall of 100 mm gypsum board and 150 mm glass separates a room at 22 °C from outside air at -14 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -14 °C
Ts = °C
6.Hard
Mineral wool, k = 0.04250 mmGypsum board, k = 0.17150 mmroom 22 °Coutside 5 °CQ̇

A wall of 250 mm mineral wool and 150 mm gypsum board separates a room at 22 °C from outside air at 5 °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 overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = 5 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 510 W
  2. 2. q″ = 102 W/m²
  3. 3. Q̇ = 28.96 W
  4. 4. Ti = 0.3939 °C
  5. 5. Ts = 16.85 °C
  6. 6. U = 0.1373 W/(m²·K)

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