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
Expanded polystyrene, k = 0.035250 mm19 °C-8 °Cq″ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 20 m². Its faces are held at 19 °C and -8 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 20 m²T1 = 19 °CT2 = -8 °C
q″ = W/m²
2.Easy
Brick, k = 0.72100 mm21 °C-3 °CQ̇ = ?

A wall of brick is 100 mm thick and has an area of 10 m². Its faces are held at 21 °C and -3 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 100 mmA = 10 m²T1 = 21 °CT2 = -3 °C
Q̇ = W
3.Medium
Expanded polystyrene, k = 0.035200 mmWood, k = 0.1725 mm18 °C3 °CTi​ = ?Q̇

A wall is made of 200 mm of expanded polystyrene and 25 mm of wood, with an area of 6 m². The outer faces are at 18 °C and 3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 18 °CT3 = 3 °C
Ti = °C
4.Medium
Wood, k = 0.17200 mmConcrete, k = 1.425 mm17 °C-10 °CQ̇ = ?

A wall is made of 200 mm of wood and 25 mm of concrete, with an area of 15 m². The outer faces are at 17 °C and -10 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 15 m²T1 = 17 °CT3 = -10 °C
Q̇ = W
5.Hard
Brick, k = 0.7250 mmGypsum board, k = 0.17150 mmroom 21 °Coutside -14 °CTs​ = ?Q̇

A wall of 50 mm brick and 150 mm gypsum board separates a room at 21 °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 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -14 °C
Ts = °C
6.Hard
Gypsum board, k = 0.17250 mmMineral wool, k = 0.0425 mmroom 20 °Coutside 1 °CTs​ = ?Q̇

A wall of 250 mm gypsum board and 25 mm mineral wool separates a room at 20 °C from outside air at 1 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 1 °C
Ts = °C

Answer key

  1. 1. q″ = 3.78 W/m²
  2. 2. Q̇ = 1728 W
  3. 3. Ti = 3.376 °C
  4. 4. Q̇ = 339.1 W
  5. 5. Ts = 16.92 °C
  6. 6. Ts = 18.62 °C

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