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 = 1.4200 mm21 °C-1 °Cq″ = ?

A wall of concrete is 200 mm thick and has an area of 10 m². Its faces are held at 21 °C and -1 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 200 mmA = 10 m²T1 = 21 °CT2 = -1 °C
q″ = W/m²
2.Easy
Wood, k = 0.17100 mm24 °C-15 °CQ̇ = ?

A wall of wood is 100 mm thick and has an area of 4 m². Its faces are held at 24 °C and -15 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 4 m²T1 = 24 °CT2 = -15 °C
Q̇ = W
3.Medium
Glass, k = 0.96250 mmExpanded polystyrene, k = 0.03550 mm23 °C1 °CTi​ = ?Q̇

A wall is made of 250 mm of glass and 50 mm of expanded polystyrene, with an area of 4 m². The outer faces are at 23 °C and 1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 4 m²T1 = 23 °CT3 = 1 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17200 mmWood, k = 0.1725 mm25 °C2 °CQ̇ = ?

A wall is made of 200 mm of gypsum board and 25 mm of wood, with an area of 15 m². The outer faces are at 25 °C and 2 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 15 m²T1 = 25 °CT3 = 2 °C
Q̇ = W
5.Hard
Wood, k = 0.17100 mmExpanded polystyrene, k = 0.03525 mmroom 21 °Coutside 4 °CQ̇

A wall of 100 mm wood and 25 mm expanded polystyrene separates a room at 21 °C from outside air at 4 °C. The convection coefficients are 6 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 = 100 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 8 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 4 °C
U = W/(m²·K)
6.Hard
Wood, k = 0.17100 mmGlass, k = 0.9675 mmroom 21 °Coutside -15 °CQ̇

A wall of 100 mm wood and 75 mm glass separates a room at 21 °C from outside air at -15 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -15 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 154 W/m²
  2. 2. Q̇ = 265.2 W
  3. 3. Ti = 19.61 °C
  4. 4. Q̇ = 260.7 W
  5. 5. U = 0.6582 W/(m²·K)
  6. 6. U = 1.205 W/(m²·K)

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