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 = 0.17250 mm18 °C10 °Cq″ = ?

A wall of wood is 250 mm thick and has an area of 6 m². Its faces are held at 18 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 250 mmA = 6 m²T1 = 18 °CT2 = 10 °C
q″ = W/m²
2.Easy
Wood, k = 0.1750 mm22 °C4 °Cq″ = ?

A wall of wood is 50 mm thick and has an area of 10 m². Its faces are held at 22 °C and 4 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 50 mmA = 10 m²T1 = 22 °CT2 = 4 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17150 mmBrick, k = 0.7275 mm21 °C-6 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 75 mm of brick, with an area of 8 m². The outer faces are at 21 °C and -6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 8 m²T1 = 21 °CT3 = -6 °C
Ti = °C
4.Medium
Wood, k = 0.17250 mmConcrete, k = 1.450 mm22 °C0 °CTi​ = ?Q̇

A wall is made of 250 mm of wood and 50 mm of concrete, with an area of 15 m². The outer faces are at 22 °C and 0 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 15 m²T1 = 22 °CT3 = 0 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.035150 mmBrick, k = 0.7250 mmroom 20 °Coutside -8 °CQ̇

A wall of 150 mm expanded polystyrene and 50 mm brick separates a room at 20 °C from outside air at -8 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -8 °C
U = W/(m²·K)
6.Hard
Wood, k = 0.1750 mmBrick, k = 0.7225 mmroom 22 °Coutside -4 °CTs​ = ?Q̇

A wall of 50 mm wood and 25 mm brick separates a room at 22 °C from outside air at -4 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -4 °C
Ts = °C

Answer key

  1. 1. q″ = 5.44 W/m²
  2. 2. q″ = 61.2 W/m²
  3. 3. Ti = −3.149 °C
  4. 4. Ti = 0.5216 °C
  5. 5. U = 0.2205 W/(m²·K)
  6. 6. Ts = 15.23 °C

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