Question

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?

Answer 1

Answer:

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