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
Glass, k = 0.9620 mm21 °C-14 °Cq″ = ?

A wall of glass is 20 mm thick and has an area of 15 m². Its faces are held at 21 °C and -14 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 20 mmA = 15 m²T1 = 21 °CT2 = -14 °C
q″ = W/m²
2.Easy
Glass, k = 0.9620 mm19 °C8 °Cq″ = ?

A wall of glass is 20 mm thick and has an area of 10 m². Its faces are held at 19 °C and 8 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 20 mmA = 10 m²T1 = 19 °CT2 = 8 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035250 mmBrick, k = 0.72150 mm22 °C5 °CTi​ = ?Q̇

A wall is made of 250 mm of expanded polystyrene and 150 mm of brick, with an area of 8 m². The outer faces are at 22 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 8 m²T1 = 22 °CT3 = 5 °C
Ti = °C
4.Medium
Glass, k = 0.96150 mmMineral wool, k = 0.0450 mm17 °C-13 °CQ̇ = ?

A wall is made of 150 mm of glass and 50 mm of mineral wool, with an area of 20 m². The outer faces are at 17 °C and -13 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 20 m²T1 = 17 °CT3 = -13 °C
Q̇ = W
5.Hard
Gypsum board, k = 0.17200 mmExpanded polystyrene, k = 0.03550 mmroom 20 °Coutside -12 °CQ̇ = ?

A wall of 200 mm gypsum board and 50 mm expanded polystyrene separates a room at 20 °C from outside air at -12 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -12 °C
Q̇ = W
6.Hard
Mineral wool, k = 0.04250 mmGypsum board, k = 0.1725 mmroom 20 °Coutside -15 °CTs​ = ?Q̇

A wall of 250 mm mineral wool and 25 mm gypsum board separates a room at 20 °C from outside air at -15 °C. The convection coefficients are 10 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 = 250 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -15 °C
Ts = °C

Answer key

  1. 1. q″ = 1680 W/m²
  2. 2. q″ = 528 W/m²
  3. 3. Ti = 5.482 °C
  4. 4. Q̇ = 426.7 W
  5. 5. Q̇ = 138.1 W
  6. 6. Ts = 19.46 °C

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