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
Concrete, k = 1.410 mm23 °C-15 °Cq″ = ?

A wall of concrete is 10 mm thick and has an area of 4 m². Its faces are held at 23 °C and -15 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 10 mmA = 4 m²T1 = 23 °CT2 = -15 °C
q″ = W/m²
2.Easy
Mineral wool, k = 0.0410 mm24 °C-15 °Cq″ = ?

A wall of mineral wool is 10 mm thick and has an area of 12 m². Its faces are held at 24 °C and -15 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 10 mmA = 12 m²T1 = 24 °CT2 = -15 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17200 mmConcrete, k = 1.4150 mm22 °C2 °CQ̇ = ?

A wall is made of 200 mm of gypsum board and 150 mm of concrete, with an area of 4 m². The outer faces are at 22 °C and 2 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 4 m²T1 = 22 °CT3 = 2 °C
Q̇ = W
4.Medium
Wood, k = 0.17100 mmBrick, k = 0.7250 mm19 °C-10 °CQ̇ = ?

A wall is made of 100 mm of wood and 50 mm of brick, with an area of 8 m². The outer faces are at 19 °C and -10 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 8 m²T1 = 19 °CT3 = -10 °C
Q̇ = W
5.Hard
Gypsum board, k = 0.17100 mmMineral wool, k = 0.04150 mmroom 21 °Coutside -5 °CQ̇

A wall of 100 mm gypsum board and 150 mm mineral wool separates a room at 21 °C from outside air at -5 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 20 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -5 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4200 mmWood, k = 0.1725 mmroom 20 °Coutside -14 °CTs​ = ?Q̇

A wall of 200 mm concrete and 25 mm wood separates a room at 20 °C from outside air at -14 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -14 °C
Ts = °C

Answer key

  1. 1. q″ = 5320 W/m²
  2. 2. q″ = 156 W/m²
  3. 3. Q̇ = 62.32 W
  4. 4. Q̇ = 352.8 W
  5. 5. U = 0.2195 W/(m²·K)
  6. 6. Ts = 12.09 °C

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