Architect Post: Thermal Bridge Heat Loss for Dodgy Wall

We are rebuilding the new extension against the neighbours party wall, and insulating with a small amount of insulation.

Site discovered a section of brickwork approx. 1.2 x 1.2m square that sticks out 70mm from the wall, as it looks like a section of the old garden wall was simply built into next doors extension.

Mish-mash of brickwork to neighbouring rear extension party wall

We intend to insulate the party wall slightly in this area with 70mm insulation to minimise heat loss to next door, so this protruding brickwork cuts into our insulation, and we don't have any tolerance in the extension to insulate around, as a narrow site!

The clerk of works for the housing association does not want to cut back this brick, as next doors wall build-up is unknown, so I've done two calculations on this section of wall to consider the effect of forgoing party wall insulation to the square of wall:

Difference in Heat Loss for Party Wall to next door: 
 A x  U1 x ft x Gt
 = 1.08 x 1.769 x 0.25 x 68
=  32.5 kWh/yr
=  0.5 kWh/sqm.yr

Difference in Heat Loss for Party Wall to below ground: 

 A x  U1 x ft x Gt 

 = 0.36 x 1.769 x 0.59 x 68

=  25.6   kWh/yr

=  0.40 kWh/sqm.yr

TOTAL HEAT LOSS = 0.9 kWh/sqm.yr

Would increase heat demand from 23 to 23.9 kWh/sqm.yr

A = Area (m2)
U1 = Difference in U-Value between insulated & non-insulated party wall (W/m2K)
ft =  Temperature correction factor for party wall assuming 15oC low next door & 21oC interior temp & -3oC external temp
Gt = Heating degree hours per year (kKh/a) - used manchester weather data

Internal Wall Surface Temperature of section of wall below neighbours floor level

(Bottom corner):

= Room Temp x (U x Rsi x (Room Temp - Outside Temp)

= 21 x (2.205 x 0.13 x (21 - 10)

= 21 - 3.15

= 17.85 oC (So no mould growth risk)

U = U-Value of non-insulated party wall (W/m2K)

Rsi = Internal Surface Resistance for wall

Outside temp = 10oC as below ground