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 = 0.96250 mm16 °C-13 °CQ̇ = ?

A wall of glass is 250 mm thick and has an area of 10 m². Its faces are held at 16 °C and -13 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 250 mmA = 10 m²T1 = 16 °CT2 = -13 °C
Q̇ = W
2.Easy
Wood, k = 0.17200 mm22 °C-15 °Cq″ = ?

A wall of wood is 200 mm thick and has an area of 15 m². Its faces are held at 22 °C and -15 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 15 m²T1 = 22 °CT2 = -15 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17250 mmBrick, k = 0.7225 mm22 °C2 °CTi​ = ?Q̇

A wall is made of 250 mm of gypsum board and 25 mm of brick, with an area of 20 m². The outer faces are at 22 °C and 2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 20 m²T1 = 22 °CT3 = 2 °C
Ti = °C
4.Medium
Glass, k = 0.9650 mmMineral wool, k = 0.0475 mm23 °C6 °CQ̇ = ?

A wall is made of 50 mm of glass and 75 mm of mineral wool, with an area of 8 m². The outer faces are at 23 °C and 6 °C. Find the heat flow Q̇ through the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.04 W/(m·K)A = 8 m²T1 = 23 °CT3 = 6 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.0450 mmBrick, k = 0.72100 mmroom 20 °Coutside -1 °CQ̇ = ?

A wall of 50 mm mineral wool and 100 mm brick separates a room at 20 °C from outside air at -1 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 4 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -1 °C
Q̇ = W
6.Hard
Expanded polystyrene, k = 0.03550 mmMineral wool, k = 0.0425 mmroom 22 °Coutside -6 °CTs​ = ?Q̇

A wall of 50 mm expanded polystyrene and 25 mm mineral wool separates a room at 22 °C from outside air at -6 °C. The convection coefficients are 7.7 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 = 50 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -6 °C
Ts = °C

Answer key

  1. 1. Q̇ = 1114 W
  2. 2. q″ = 31.45 W/m²
  3. 3. Ti = 2.461 °C
  4. 4. Q̇ = 70.57 W
  5. 5. Q̇ = 53.89 W
  6. 6. Ts = 20.36 °C

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