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
Brick, k = 0.7220 mm16 °C-1 °Cq″ = ?

A wall of brick is 20 mm thick and has an area of 10 m². Its faces are held at 16 °C and -1 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 20 mmA = 10 m²T1 = 16 °CT2 = -1 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.035250 mm16 °C-15 °CQ̇ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 6 m². Its faces are held at 16 °C and -15 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 6 m²T1 = 16 °CT2 = -15 °C
Q̇ = W
3.Medium
Brick, k = 0.72100 mmWood, k = 0.17100 mm23 °C-1 °CTi​ = ?Q̇

A wall is made of 100 mm of brick and 100 mm of wood, with an area of 10 m². The outer faces are at 23 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 10 m²T1 = 23 °CT3 = -1 °C
Ti = °C
4.Medium
Concrete, k = 1.4100 mmExpanded polystyrene, k = 0.03575 mm16 °C3 °CQ̇ = ?

A wall is made of 100 mm of concrete and 75 mm of expanded polystyrene, with an area of 12 m². The outer faces are at 16 °C and 3 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 12 m²T1 = 16 °CT3 = 3 °C
Q̇ = W
5.Hard
Brick, k = 0.72250 mmGypsum board, k = 0.1775 mmroom 22 °Coutside -5 °CTs​ = ?Q̇

A wall of 250 mm brick and 75 mm gypsum board separates a room at 22 °C from outside air at -5 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 8 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -5 °C
Ts = °C
6.Hard
Concrete, k = 1.4150 mmExpanded polystyrene, k = 0.035150 mmroom 21 °Coutside -15 °CTs​ = ?Q̇

A wall of 150 mm concrete and 150 mm expanded polystyrene separates a room at 21 °C from outside air at -15 °C. The convection coefficients are 10 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 = 150 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 15 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -15 °C
Ts = °C

Answer key

  1. 1. q″ = 612 W/m²
  2. 2. Q̇ = 26.04 W
  3. 3. Ti = 18.42 °C
  4. 4. Q̇ = 70.45 W
  5. 5. Ts = 18.44 °C
  6. 6. Ts = 20.21 °C

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