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 = 0.03550 mm16 °C-11 °CQ̇ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 12 m². Its faces are held at 16 °C and -11 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 12 m²T1 = 16 °CT2 = -11 °C
Q̇ = W
2.Easy
Brick, k = 0.7220 mm16 °C2 °Cq″ = ?

A wall of brick is 20 mm thick and has an area of 10 m². Its faces are held at 16 °C and 2 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 20 mmA = 10 m²T1 = 16 °CT2 = 2 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17100 mmBrick, k = 0.7225 mm25 °C5 °CQ̇ = ?

A wall is made of 100 mm of gypsum board and 25 mm of brick, with an area of 6 m². The outer faces are at 25 °C and 5 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 6 m²T1 = 25 °CT3 = 5 °C
Q̇ = W
4.Medium
Glass, k = 0.96250 mmExpanded polystyrene, k = 0.03525 mm24 °C3 °CTi​ = ?Q̇

A wall is made of 250 mm of glass and 25 mm of expanded polystyrene, with an area of 12 m². The outer faces are at 24 °C and 3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 12 m²T1 = 24 °CT3 = 3 °C
Ti = °C
5.Hard
Wood, k = 0.17150 mmMineral wool, k = 0.0475 mmroom 20 °Coutside -2 °CTs​ = ?Q̇

A wall of 150 mm wood and 75 mm mineral wool separates a room at 20 °C from outside air at -2 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -2 °C
Ts = °C
6.Hard
Brick, k = 0.72150 mmGlass, k = 0.9675 mmroom 22 °Coutside -7 °CQ̇

A wall of 150 mm brick and 75 mm glass separates a room at 22 °C from outside air at -7 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 8 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -7 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 226.8 W
  2. 2. q″ = 504 W/m²
  3. 3. Q̇ = 192.6 W
  4. 4. Ti = 18.39 °C
  5. 5. Ts = 18.76 °C
  6. 6. U = 1.988 W/(m²·K)

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