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 = 0.7250 mm18 °C-3 °Cq″ = ?

A wall of brick is 50 mm thick and has an area of 6 m². Its faces are held at 18 °C and -3 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 50 mmA = 6 m²T1 = 18 °CT2 = -3 °C
q″ = W/m²
2.Easy
Wood, k = 0.1710 mm17 °C10 °Cq″ = ?

A wall of wood is 10 mm thick and has an area of 20 m². Its faces are held at 17 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 20 m²T1 = 17 °CT2 = 10 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04200 mmBrick, k = 0.7250 mm21 °C-9 °CQ̇ = ?

A wall is made of 200 mm of mineral wool and 50 mm of brick, with an area of 10 m². The outer faces are at 21 °C and -9 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 10 m²T1 = 21 °CT3 = -9 °C
Q̇ = W
4.Medium
Brick, k = 0.72100 mmWood, k = 0.1725 mm17 °C-13 °CQ̇ = ?

A wall is made of 100 mm of brick and 25 mm of wood, with an area of 12 m². The outer faces are at 17 °C and -13 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 12 m²T1 = 17 °CT3 = -13 °C
Q̇ = W
5.Hard
Brick, k = 0.72200 mmConcrete, k = 1.4150 mmroom 20 °Coutside -6 °CQ̇

A wall of 200 mm brick and 150 mm concrete separates a room at 20 °C from outside air at -6 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 12 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -6 °C
U = W/(m²·K)
6.Hard
Concrete, k = 1.4150 mmGlass, k = 0.96100 mmroom 20 °Coutside -15 °CTs​ = ?Q̇

A wall of 150 mm concrete and 100 mm glass separates a room at 20 °C from outside air at -15 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.96 W/(m·K)A = 4 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -15 °C
Ts = °C

Answer key

  1. 1. q″ = 302.4 W/m²
  2. 2. q″ = 119 W/m²
  3. 3. Q̇ = 59.18 W
  4. 4. Q̇ = 1259 W
  5. 5. U = 1.69 W/(m²·K)
  6. 6. Ts = 8.075 °C

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