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 = 1.4100 mm16 °C-5 °Cq″ = ?

A wall of concrete is 100 mm thick and has an area of 4 m². Its faces are held at 16 °C and -5 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 100 mmA = 4 m²T1 = 16 °CT2 = -5 °C
q″ = W/m²
2.Easy
Glass, k = 0.96150 mm18 °C-10 °Cq″ = ?

A wall of glass is 150 mm thick and has an area of 8 m². Its faces are held at 18 °C and -10 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 150 mmA = 8 m²T1 = 18 °CT2 = -10 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035150 mmGypsum board, k = 0.1725 mm24 °C3 °CQ̇ = ?

A wall is made of 150 mm of expanded polystyrene and 25 mm of gypsum board, with an area of 10 m². The outer faces are at 24 °C and 3 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 10 m²T1 = 24 °CT3 = 3 °C
Q̇ = W
4.Medium
Gypsum board, k = 0.17150 mmExpanded polystyrene, k = 0.03575 mm19 °C-13 °CQ̇ = ?

A wall is made of 150 mm of gypsum board and 75 mm of expanded polystyrene, with an area of 20 m². The outer faces are at 19 °C and -13 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.035 W/(m·K)A = 20 m²T1 = 19 °CT3 = -13 °C
Q̇ = W
5.Hard
Wood, k = 0.17100 mmGypsum board, k = 0.17150 mmroom 21 °Coutside -10 °CQ̇ = ?

A wall of 100 mm wood and 150 mm gypsum board separates a room at 21 °C from outside air at -10 °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 heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -10 °C
Q̇ = W
6.Hard
Mineral wool, k = 0.0450 mmWood, k = 0.1775 mmroom 21 °Coutside -3 °CTs​ = ?Q̇

A wall of 50 mm mineral wool and 75 mm wood 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 12 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 = 0.17 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -3 °C
Ts = °C

Answer key

  1. 1. q″ = 294 W/m²
  2. 2. q″ = 179.2 W/m²
  3. 3. Q̇ = 47.37 W
  4. 4. Q̇ = 211.6 W
  5. 5. Q̇ = 76.99 W
  6. 6. Ts = 19.7 °C

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