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
Concrete, k = 1.4200 mm21 °C3 °Cq″ = ?

A wall of concrete is 200 mm thick and has an area of 4 m². Its faces are held at 21 °C and 3 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 200 mmA = 4 m²T1 = 21 °CT2 = 3 °C
q″ = W/m²
2.Easy
Glass, k = 0.9610 mm17 °C-1 °Cq″ = ?

A wall of glass is 10 mm thick and has an area of 4 m². Its faces are held at 17 °C and -1 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 10 mmA = 4 m²T1 = 17 °CT2 = -1 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04150 mmExpanded polystyrene, k = 0.035150 mm25 °C7 °CQ̇ = ?

A wall is made of 150 mm of mineral wool and 150 mm of expanded polystyrene, with an area of 15 m². The outer faces are at 25 °C and 7 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 15 m²T1 = 25 °CT3 = 7 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.03550 mmConcrete, k = 1.4150 mm25 °C10 °CQ̇ = ?

A wall is made of 50 mm of expanded polystyrene and 150 mm of concrete, with an area of 6 m². The outer faces are at 25 °C and 10 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 6 m²T1 = 25 °CT3 = 10 °C
Q̇ = W
5.Hard
Brick, k = 0.72150 mmWood, k = 0.1775 mmroom 22 °Coutside -12 °CQ̇ = ?

A wall of 150 mm brick and 75 mm wood separates a room at 22 °C from outside air at -12 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 150 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -12 °C
Q̇ = W
6.Hard
Brick, k = 0.72100 mmExpanded polystyrene, k = 0.035100 mmroom 22 °Coutside -4 °CTs​ = ?Q̇

A wall of 100 mm brick and 100 mm expanded polystyrene separates a room at 22 °C from outside air at -4 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 15 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -4 °C
Ts = °C

Answer key

  1. 1. q″ = 126 W/m²
  2. 2. q″ = 1728 W/m²
  3. 3. Q̇ = 33.6 W
  4. 4. Q̇ = 58.6 W
  5. 5. Q̇ = 252.5 W
  6. 6. Ts = 20.65 °C

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