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 = 1.4150 mm23 °C-5 °Cq″ = ?

A wall of concrete is 150 mm thick and has an area of 8 m². Its faces are held at 23 °C and -5 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 150 mmA = 8 m²T1 = 23 °CT2 = -5 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.17200 mm25 °C-3 °CQ̇ = ?

A wall of gypsum board is 200 mm thick and has an area of 6 m². Its faces are held at 25 °C and -3 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 6 m²T1 = 25 °CT2 = -3 °C
Q̇ = W
3.Medium
Glass, k = 0.96200 mmWood, k = 0.1750 mm18 °C-9 °CQ̇ = ?

A wall is made of 200 mm of glass and 50 mm of wood, with an area of 8 m². The outer faces are at 18 °C and -9 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 18 °CT3 = -9 °C
Q̇ = W
4.Medium
Wood, k = 0.17200 mmMineral wool, k = 0.0450 mm15 °C7 °CQ̇ = ?

A wall is made of 200 mm of wood and 50 mm of mineral wool, with an area of 8 m². The outer faces are at 15 °C and 7 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 8 m²T1 = 15 °CT3 = 7 °C
Q̇ = W
5.Hard
Concrete, k = 1.4100 mmGlass, k = 0.9625 mmroom 22 °Coutside 3 °CTs​ = ?Q̇

A wall of 100 mm concrete and 25 mm glass separates a room at 22 °C from outside air at 3 °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 temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 4 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = 3 °C
Ts = °C
6.Hard
Mineral wool, k = 0.0450 mmBrick, k = 0.7275 mmroom 21 °Coutside 1 °CTs​ = ?Q̇

A wall of 50 mm mineral wool and 75 mm brick separates a room at 21 °C from outside air at 1 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = 1 °C
Ts = °C

Answer key

  1. 1. q″ = 261.3 W/m²
  2. 2. Q̇ = 142.8 W
  3. 3. Q̇ = 429.9 W
  4. 4. Q̇ = 26.38 W
  5. 5. Ts = 12.77 °C
  6. 6. Ts = 18.86 °C

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