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
Glass, k = 0.9620 mm20 °C4 °Cq″ = ?

A wall of glass is 20 mm thick and has an area of 12 m². Its faces are held at 20 °C and 4 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 20 mmA = 12 m²T1 = 20 °CT2 = 4 °C
q″ = W/m²
2.Easy
Wood, k = 0.17100 mm19 °C-1 °CQ̇ = ?

A wall of wood is 100 mm thick and has an area of 10 m². Its faces are held at 19 °C and -1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 10 m²T1 = 19 °CT2 = -1 °C
Q̇ = W
3.Medium
Glass, k = 0.96250 mmExpanded polystyrene, k = 0.03575 mm22 °C-11 °CTi​ = ?Q̇

A wall is made of 250 mm of glass and 75 mm of expanded polystyrene, with an area of 8 m². The outer faces are at 22 °C and -11 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 8 m²T1 = 22 °CT3 = -11 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035100 mmMineral wool, k = 0.04150 mm18 °C4 °CTi​ = ?Q̇

A wall is made of 100 mm of expanded polystyrene and 150 mm of mineral wool, with an area of 10 m². The outer faces are at 18 °C and 4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 10 m²T1 = 18 °CT3 = 4 °C
Ti = °C
5.Hard
Mineral wool, k = 0.04100 mmBrick, k = 0.72100 mmroom 21 °Coutside -4 °CQ̇ = ?

A wall of 100 mm mineral wool and 100 mm brick separates a room at 21 °C from outside air at -4 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -4 °C
Q̇ = W
6.Hard
Glass, k = 0.96100 mmMineral wool, k = 0.04150 mmroom 21 °Coutside 5 °CQ̇

A wall of 100 mm glass and 150 mm mineral wool separates a room at 21 °C from outside air at 5 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 15 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 5 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 768 W/m²
  2. 2. Q̇ = 340 W
  3. 3. Ti = 18.42 °C
  4. 4. Ti = 11.95 °C
  5. 5. Q̇ = 35.86 W
  6. 6. U = 0.2497 W/(m²·K)

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