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 = 0.72100 mm25 °C3 °CQ̇ = ?

A wall of brick is 100 mm thick and has an area of 8 m². Its faces are held at 25 °C and 3 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 100 mmA = 8 m²T1 = 25 °CT2 = 3 °C
Q̇ = W
2.Easy
Glass, k = 0.9620 mm18 °C-8 °Cq″ = ?

A wall of glass is 20 mm thick and has an area of 4 m². Its faces are held at 18 °C and -8 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 20 mmA = 4 m²T1 = 18 °CT2 = -8 °C
q″ = W/m²
3.Medium
Brick, k = 0.72100 mmExpanded polystyrene, k = 0.035100 mm19 °C7 °CTi​ = ?Q̇

A wall is made of 100 mm of brick and 100 mm of expanded polystyrene, with an area of 10 m². The outer faces are at 19 °C and 7 °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 = 0.035 W/(m·K)A = 10 m²T1 = 19 °CT3 = 7 °C
Ti = °C
4.Medium
Concrete, k = 1.4250 mmExpanded polystyrene, k = 0.03575 mm24 °C-12 °CQ̇ = ?

A wall is made of 250 mm of concrete and 75 mm of expanded polystyrene, with an area of 12 m². The outer faces are at 24 °C and -12 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 12 m²T1 = 24 °CT3 = -12 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.0450 mmConcrete, k = 1.4150 mmroom 21 °Coutside -10 °CTs​ = ?Q̇

A wall of 50 mm mineral wool and 150 mm concrete separates a room at 21 °C from outside air at -10 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 8 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -10 °C
Ts = °C
6.Hard
Glass, k = 0.96250 mmMineral wool, k = 0.04100 mmroom 21 °Coutside 3 °CQ̇

A wall of 250 mm glass and 100 mm mineral wool separates a room at 21 °C from outside air at 3 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = 3 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 1267 W
  2. 2. q″ = 1248 W/m²
  3. 3. Ti = 18.44 °C
  4. 4. Q̇ = 186.1 W
  5. 5. Ts = 18.45 °C
  6. 6. U = 0.342 W/(m²·K)

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