Question

An exterior wall of a house may be approximated by a 0.1 m layer of common brick (k = 0.7 W/m°C) followed by a 0.04 m layer of gypsum plaster (k = 0.48 W/m°C). What thickness of loosely packed rock wool insulation (k = 0.065 W/m°C) should be added to reduce the heat loss or (gain) through the wall by 80 per cent ?

Answer 1

Thickness of common brick, L_A = 0.1 m 

Thickness of gypsum plaster,L_B = 0.04 m 

Thickness of rock wool, L_C = x (in m) = ? 

Thermal conductivities : Common brick, k_A = 0.7 W/m°C 

Gypsum plaster, k_B = 0.48 W/m°C 

Rock wool, k_C = 0.065 W/m°C 

Case I. Rock wool insulation not used

Case II. Rock wool insulation used :

0.1428 + 0.0833 = 0.2 [0.1428 + 0.0833 + 15.385 x] 

or 0.2261 = 0.2 (0.2261 + 15.385 x) 

or x = 0.0588 m or 58.8 mm 

Thus, the thickness of rock wool insulation should be 58.8 mm.