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
Mineral wool, k = 0.0420 mm18 °C-11 °CQ̇ = ?

A wall of mineral wool is 20 mm thick and has an area of 6 m². Its faces are held at 18 °C and -11 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.04 W/(m·K)L = 20 mmA = 6 m²T1 = 18 °CT2 = -11 °C
Q̇ = W
2.Easy
Gypsum board, k = 0.17200 mm17 °C0 °Cq″ = ?

A wall of gypsum board is 200 mm thick and has an area of 6 m². Its faces are held at 17 °C and 0 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 6 m²T1 = 17 °CT2 = 0 °C
q″ = W/m²
3.Medium
Wood, k = 0.17200 mmBrick, k = 0.7225 mm25 °C-2 °CTi​ = ?Q̇

A wall is made of 200 mm of wood and 25 mm of brick, with an area of 10 m². The outer faces are at 25 °C and -2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 10 m²T1 = 25 °CT3 = -2 °C
Ti = °C
4.Medium
Mineral wool, k = 0.04200 mmBrick, k = 0.7225 mm19 °C4 °CQ̇ = ?

A wall is made of 200 mm of mineral wool and 25 mm of brick, with an area of 15 m². The outer faces are at 19 °C and 4 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 15 m²T1 = 19 °CT3 = 4 °C
Q̇ = W
5.Hard
Wood, k = 0.17200 mmGlass, k = 0.9625 mmroom 21 °Coutside 5 °CTs​ = ?Q̇

A wall of 200 mm wood and 25 mm glass separates a room at 21 °C from outside air at 5 °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 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = 5 °C
Ts = °C
6.Hard
Concrete, k = 1.4150 mmBrick, k = 0.72150 mmroom 21 °Coutside 3 °CQ̇

A wall of 150 mm concrete and 150 mm brick separates a room at 21 °C from outside air at 3 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 3 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 348 W
  2. 2. q″ = 14.45 W/m²
  3. 3. Ti = −1.226 °C
  4. 4. Q̇ = 44.69 W
  5. 5. Ts = 19.81 °C
  6. 6. U = 2.148 W/(m²·K)

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