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 = 1.4250 mm25 °C4 °Cq″ = ?

A wall of concrete is 250 mm thick and has an area of 8 m². Its faces are held at 25 °C and 4 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 250 mmA = 8 m²T1 = 25 °CT2 = 4 °C
q″ = W/m²
2.Easy
Brick, k = 0.7220 mm16 °C4 °Cq″ = ?

A wall of brick is 20 mm thick and has an area of 4 m². Its faces are held at 16 °C and 4 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 20 mmA = 4 m²T1 = 16 °CT2 = 4 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.17250 mmConcrete, k = 1.450 mm24 °C10 °CQ̇ = ?

A wall is made of 250 mm of gypsum board and 50 mm of concrete, with an area of 4 m². The outer faces are at 24 °C and 10 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 4 m²T1 = 24 °CT3 = 10 °C
Q̇ = W
4.Medium
Concrete, k = 1.4100 mmBrick, k = 0.72100 mm23 °C-4 °CQ̇ = ?

A wall is made of 100 mm of concrete and 100 mm of brick, with an area of 12 m². The outer faces are at 23 °C and -4 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 12 m²T1 = 23 °CT3 = -4 °C
Q̇ = W
5.Hard
Concrete, k = 1.4250 mmMineral wool, k = 0.0425 mmroom 20 °Coutside -7 °CQ̇

A wall of 250 mm concrete and 25 mm mineral wool separates a room at 20 °C from outside air at -7 °C. The convection coefficients are 8 W/(m²·K) inside and 25 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 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -7 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.96150 mmConcrete, k = 1.4150 mmroom 22 °Coutside -8 °CTs​ = ?Q̇

A wall of 150 mm glass and 150 mm concrete separates a room at 22 °C from outside air at -8 °C. The convection coefficients are 7.7 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 = 150 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -8 °C
Ts = °C

Answer key

  1. 1. q″ = 117.6 W/m²
  2. 2. q″ = 432 W/m²
  3. 3. Q̇ = 37.18 W
  4. 4. Q̇ = 1541 W
  5. 5. U = 1.032 W/(m²·K)
  6. 6. Ts = 13.21 °C

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