Question

In this problem you will estimate the heat lost by a typical house, assuming that the temperature inside is tin=20∘c and the temperature outside is tout=0∘c. the walls and uppermost ceiling of a typical house are supported by 2×6-inch wooden beams (kwood=0.12w/m/k) with fiberglass insulation (kins=0.04w/m/k) in between. the true depth of the beams is actually 558 inches, but we will take the thickness of the walls and ceiling to be lwall=18cm to allow for the interior and exterior covering. assume that the house is a cube of length l=9.0m on a side. assume that the roof has very high conductivity, so that the air in the attic is at the same temperature as the outside air. ignore heat loss through the ground.

Answer 1

Step 1:

Calculate the effective thermal conductivity of the wall or ceiling:

K_eff = [ (13 ÷ 8)(0.12) + (16 - (13 ÷ 8)) × (0.04)] ÷ 16 


K_eff = [ 0.195 + 0.565] ÷ 16


K_eff = 0.76 ÷ 16
 

K_eff = 0.0475 W/ (m K) 


Step 2:

Calculate the interior ceiling area:

Area of each of the interior side walls = 8.82 m x 8.64 m
                                                                = 76.2 m²

Area of the interior ceiling = 8.64 m × 8.64 m
                                             = 74.6 m²

H = - k·A·(Δ - T) ÷ (thickness)

H = - 0.0475 ÷ (379.45 × 20) ÷  45/8

H = - ( - 0.95 × 379.45 ) ÷ 0.1429

H = 2.52 kW