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
Brick, k = 0.7220 mm17 °C-12 °Cq″ = ?

A wall of brick is 20 mm thick and has an area of 15 m². Its faces are held at 17 °C and -12 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 20 mmA = 15 m²T1 = 17 °CT2 = -12 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03550 mm18 °C-9 °CQ̇ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 12 m². Its faces are held at 18 °C and -9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 12 m²T1 = 18 °CT2 = -9 °C
Q̇ = W
3.Medium
Wood, k = 0.17200 mmConcrete, k = 1.425 mm23 °C-1 °CQ̇ = ?

A wall is made of 200 mm of wood and 25 mm of concrete, with an area of 10 m². The outer faces are at 23 °C and -1 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 10 m²T1 = 23 °CT3 = -1 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035250 mmGypsum board, k = 0.17100 mm24 °C-3 °CTi​ = ?Q̇

A wall is made of 250 mm of expanded polystyrene and 100 mm of gypsum board, with an area of 8 m². The outer faces are at 24 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 24 °CT3 = -3 °C
Ti = °C
5.Hard
Brick, k = 0.72250 mmGlass, k = 0.9675 mmroom 22 °Coutside 5 °CQ̇ = ?

A wall of 250 mm brick and 75 mm glass separates a room at 22 °C from outside air at 5 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = 5 °C
Q̇ = W
6.Hard
Wood, k = 0.17250 mmBrick, k = 0.7250 mmroom 20 °Coutside -13 °CQ̇

A wall of 250 mm wood and 50 mm brick separates a room at 20 °C from outside air at -13 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -13 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 1044 W/m²
  2. 2. Q̇ = 226.8 W
  3. 3. Q̇ = 200.9 W
  4. 4. Ti = −0.9457 °C
  5. 5. Q̇ = 269 W
  6. 6. U = 0.5747 W/(m²·K)

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