Answer:
16 W
Explanation:
The sum of convective and conductive heat transfer through layers of walls can be modeled as:
Q = (T₂ − T₁) A / R
where Q is the rate of heat transfer,
T₂ − T₁ is the temperature difference,
and A is the cross sectional area.
R, the thermal resistance, is defined as:
R = ∑1/h + ∑L/k
where h is the convective heat transfer coefficient of the fluid,
L is the thickness of the wall,
and k is the thermal conductivity of the wall.
Given:
T₂ − T₁ = 35 K
A = 21 m²
h₁ = 11 W/m²/K
h₂ = 23 W/m²/K
For the polystyrene:
L₁ = 0.05 m
k₁ = 0.0011 W/m/K
For the cement:
L₂ = 0.02 m or 0.21 m
k₂ = 0.33 W/m/K
For the brick:
L₃ = 0.17 m
k₃ = 0.77 W/m/K
For the layer above and below the brick:
R = (1/11 + 1/23 + 0.05/0.0011 + 0.21/0.33)
R = 46.2 m²K/W
For the layer containing the brick:
R = (1/11 + 1/23 + 0.05/0.0011 + 0.02/0.33 + 0.17/0.77 + 0.02/0.33)
R = 45.9 m²K/W
So the average thermal resistance is:
R = (6/30) (46.2) + (24/30) (45.9)
R = 46.0 m²K/W
Therefore, the heat transfer through the wall is:
Q = (35 K) (21 m²) / (46.0 m²K/W)
Q = 16.0 W
Rounding to two significant figures, the rate of heat transfer through the wall is 16 W.
