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
Wood, k = 0.1720 mm21 °C-5 °Cq″ = ?

A wall of wood is 20 mm thick and has an area of 20 m². Its faces are held at 21 °C and -5 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 20 mmA = 20 m²T1 = 21 °CT2 = -5 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.1710 mm19 °C-7 °CQ̇ = ?

A wall of gypsum board is 10 mm thick and has an area of 20 m². Its faces are held at 19 °C and -7 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 20 m²T1 = 19 °CT2 = -7 °C
Q̇ = W
3.Medium
Expanded polystyrene, k = 0.035200 mmMineral wool, k = 0.0450 mm22 °C-5 °CQ̇ = ?

A wall is made of 200 mm of expanded polystyrene and 50 mm of mineral wool, with an area of 15 m². The outer faces are at 22 °C and -5 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 15 m²T1 = 22 °CT3 = -5 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035200 mmGlass, k = 0.9650 mm25 °C-12 °CTi​ = ?Q̇

A wall is made of 200 mm of expanded polystyrene and 50 mm of glass, with an area of 4 m². The outer faces are at 25 °C and -12 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 4 m²T1 = 25 °CT3 = -12 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17250 mmExpanded polystyrene, k = 0.03550 mmroom 22 °Coutside -14 °CQ̇ = ?

A wall of 250 mm gypsum board and 50 mm expanded polystyrene separates a room at 22 °C from outside air at -14 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -14 °C
Q̇ = W
6.Hard
Concrete, k = 1.4250 mmBrick, k = 0.7225 mmroom 21 °Coutside -12 °CTs​ = ?Q̇

A wall of 250 mm concrete and 25 mm brick separates a room at 21 °C from outside air at -12 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 15 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -12 °C
Ts = °C

Answer key

  1. 1. q″ = 221 W/m²
  2. 2. Q̇ = 8840 W
  3. 3. Q̇ = 58.15 W
  4. 4. Ti = −11.67 °C
  5. 5. Q̇ = 69.55 W
  6. 6. Ts = 11.66 °C

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