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
Gypsum board, k = 0.1720 mm23 °C1 °Cq″ = ?

A wall of gypsum board is 20 mm thick and has an area of 12 m². Its faces are held at 23 °C and 1 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 20 mmA = 12 m²T1 = 23 °CT2 = 1 °C
q″ = W/m²
2.Easy
Concrete, k = 1.410 mm23 °C5 °CQ̇ = ?

A wall of concrete is 10 mm thick and has an area of 6 m². Its faces are held at 23 °C and 5 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 10 mmA = 6 m²T1 = 23 °CT2 = 5 °C
Q̇ = W
3.Medium
Wood, k = 0.17200 mmGypsum board, k = 0.17100 mm22 °C-1 °CQ̇ = ?

A wall is made of 200 mm of wood and 100 mm of gypsum board, with an area of 20 m². The outer faces are at 22 °C and -1 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 20 m²T1 = 22 °CT3 = -1 °C
Q̇ = W
4.Medium
Gypsum board, k = 0.17100 mmWood, k = 0.17100 mm19 °C4 °CTi​ = ?Q̇

A wall is made of 100 mm of gypsum board and 100 mm of wood, with an area of 6 m². The outer faces are at 19 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 19 °CT3 = 4 °C
Ti = °C
5.Hard
Mineral wool, k = 0.04200 mmConcrete, k = 1.425 mmroom 22 °Coutside -9 °CTs​ = ?Q̇

A wall of 200 mm mineral wool and 25 mm concrete separates a room at 22 °C from outside air at -9 °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 = 200 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -9 °C
Ts = °C
6.Hard
Brick, k = 0.72250 mmGlass, k = 0.9675 mmroom 21 °Coutside 2 °CQ̇

A wall of 250 mm brick and 75 mm glass separates a room at 21 °C from outside air at 2 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 8 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 8 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 2 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 187 W/m²
  2. 2. Q̇ = 15120 W
  3. 3. Q̇ = 260.7 W
  4. 4. Ti = 11.5 °C
  5. 5. Ts = 21.01 °C
  6. 6. U = 1.652 W/(m²·K)

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