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
Expanded polystyrene, k = 0.035250 mm17 °C-8 °Cq″ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 10 m². Its faces are held at 17 °C and -8 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 10 m²T1 = 17 °CT2 = -8 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.1710 mm22 °C-4 °CQ̇ = ?

A wall of gypsum board is 10 mm thick and has an area of 12 m². Its faces are held at 22 °C and -4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 12 m²T1 = 22 °CT2 = -4 °C
Q̇ = W
3.Medium
Gypsum board, k = 0.17150 mmGlass, k = 0.9625 mm24 °C-14 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 25 mm of glass, with an area of 6 m². The outer faces are at 24 °C and -14 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 6 m²T1 = 24 °CT3 = -14 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035100 mmMineral wool, k = 0.0425 mm20 °C7 °CQ̇ = ?

A wall is made of 100 mm of expanded polystyrene and 25 mm of mineral wool, with an area of 15 m². The outer faces are at 20 °C and 7 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 15 m²T1 = 20 °CT3 = 7 °C
Q̇ = W
5.Hard
Expanded polystyrene, k = 0.035150 mmBrick, k = 0.72100 mmroom 20 °Coutside -11 °CTs​ = ?Q̇

A wall of 150 mm expanded polystyrene and 100 mm brick separates a room at 20 °C from outside air at -11 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -11 °C
Ts = °C
6.Hard
Wood, k = 0.17200 mmConcrete, k = 1.425 mmroom 20 °Coutside 3 °CTs​ = ?Q̇

A wall of 200 mm wood and 25 mm concrete separates a room at 20 °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 20 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 = 1.4 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = 3 °C
Ts = °C

Answer key

  1. 1. q″ = 3.5 W/m²
  2. 2. Q̇ = 5304 W
  3. 3. Ti = −12.91 °C
  4. 4. Q̇ = 56 W
  5. 5. Ts = 19.12 °C
  6. 6. Ts = 18.74 °C

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