2.) A plane wall is made of brick with a thermal conductivity of 1.5 W/(m⸳K). The wall is 20 cm thick and has a surface area of 10 m2 . One side of the wall is exposed to outside air blowing against the wall resulting in a heat transfer coefficient of 20 W/(m2 ⸳K). The other side is exposed to an air-conditioned room with a convective heat transfer coefficient of 5 W/(m2 ⸳K). a. What are the thermal resistances corresponding to conduction through the wall and convection at each wall surface? b. For every 1 o C of temperature difference between the outside and inside air, how much additional cooling power is required from the air conditioner?

The answers to the question are

a. The thermal resistances corresponding to conduction through the wall and convection at each wall surface is 2.167×10^(-2)

b. 46.15 W. That is for every 1 °C of temperature difference between the outside and inside air, 46.15 W additional cooling power is required from the air conditioner.

Explanation:

For a wall with convective heat transfer on either side, the total thermal resistance is given by

R = (1/(h1×A) + L/(A×k) + 1/(h2×A))

Where R = Total thermal resistance

h1 = 20 W/(m2×K)

h2 = 5 W/(m2×K)

A = Wall surface area = 10 m^2

L = Wall thickness = 20 cm = 0.2 m

Therefore, R = 2.167×10^(-2)

(b) The heat transferred for every 1 °C difference between the inside and outside temperatures is given by

Q = (T2 - T1)/R where T2 and T1 are the inside and outside temperatures respectively. Hence for (T2 - T1) = 1 °C we have

Q = (1 °C/2.167×10^(-2)) = 46.15 W

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