Optimum Insulation Thickness for Walls and Roofs for Reducing Peak Cooling Loads in Residential Buildings in Lahore

Thermal insulation is the most effective energy saving measure for cooling in buildings. Therefore, the main subject of many engineering investigations is the selection and determination of the optimum insulation thickness. In the present study, the optimum insulation thickness on external walls and roofs is determined based on the peak cooling loads for an existing residential building in Lahore, Pakistan. Autodesk® Revit 2013 is used for the analysis of the building and determination of the peak cooling loads. The analysis shows that the optimum insulation thickness to reduce peak cooling loads up to 40.1% is 1 inch for external walls and roof respectively.

E nergy consumption is rapidly increasing due to ever increasing population, urbanization, migration to large cities and improvement in living standards. This is a serious fact that conventional energy sources i.e. fossil fuel are running out and the whole world is facing energy crisis. According to WAPDA (Water and Power Development Authority), it is getting even worse in Pakistan from last decade due to gap between supply and demand [1]. Pakistan needs approximately 20,000MW/day, out of which only 13,500MW is being produced and thus, there is a shortfall of 6500MW [2]. Under this scenario, there is a need to conserve energy.
Lahore is the second largest city in Pakistan with latitude where q è is hourly conductive heat gain, Btu/h (W), for the surface, A is surface area, ft 2 (m 2 ), Y Pj is j th response factor, t e,è-jä is sol-air temperature, o F( o C), j hours ago, and t rc is presumed constant room air temperature, o F( o C).  [13] Where Q è is Cooling load (Q) for the current hour (è), Btu/h (W), q è-nä is the radiant gain at j hours ago, Btu/h (W), and r n is the nth time radiant factor, Btu/h (W).

The Base Case Building
The case study building is located in T-Block, Phase-VIII, DHA Society, Lahore which served as base case.

Modifications in Base Case
The building walls and roof for the base case were modified by applying varying thicknesses of extruded polystyrene as insulation. Extruded polystyrene (XPS Diamond Jumbolon) is closed cell, locally available best insulation to reduce the thermal conductivity. It is more acceptable insulation than the other due to its high insulation performance, long term reliability, stable R-value, moisture resistance, strength and easy installation process without any special skills [14][15].
Only need is to place polythene sheets above the foam (extruded polystyrene) to protect from fresh concrete and water [16]. Its density is 32 kg/m 3 and thermal conductivity is 0.026 W/mK. Seven modifications to the walls and seven to the roof as shown in Table 2 were analyzed.

Wall Modifications
Walls are externally modified by adding the insulation with varying thicknesses ranging from 0.5, 1, 1.5, 2 , 2.5, 3,4. External insulation to wall involves plastering the brick work to provide a smooth surface, attachment of the insulation boards using cement adhesive and mechanical fixings, and inclusion of a fiber mesh in the final surface plastering and additional work to deal with openings and corners is required which needs more cost than roof i.e. 100 Rs/ft 2 for 1 inch thickness.

Roof Modifications
The roof is modified by adding the insulation with varying thicknesses ranging from 0.5, 1, 1.5, 2, 2.5, 3,4 underneath the light weight concrete. The investment cost for roof insulation is 68 Rs/ft 2 for 1 inch thickness.
The mud phuska is retained in roof to prompt the consideration of mixing old and new techniques of insulation instead of totally replace the older techniques which are less expensive.

RESULTS AND DISCUSSION
The base case and all the modifications were analyzed by Autodesk® Revit and their U-value, peak cooling loads, percentage difference with respect to base case and investment cost were calculated shown in Table 2.
It is clearly visible that increasing insulation has its primary effect in the summertime, when the gains through walls and roof are the largest and that the base case has higher peak cooling loads as compare to all other insulation modifications.
The respectively in the peak cooling load compared to the  The percentage difference of the peak cooling loads of roof insulation having different thicknesses from peak cooling load of base case is shown in Fig. 4. Using 4 inches insulation in wall will increase the cost of the building to much extent; however the use of 1 inch insulation in wall is much economical.
The Table 3 shows the simultaneously applied insulation modifications in roof and walls, their percentage difference from base case and investment cost of insulation. Since seven modifications to the walls and roof were formed and total 49 combinations for wall and roof insulation were analyzed.   It is clear that 4 inches insulation thickness in roof and 4

FIG. 5. COMPARISON OF PEAK COOLING LOADS BY MODIFICATIONS IN WALL
inches insulation thickness in wall (R4W4) shows the least peak cooling load. Only 1 inch insulation thickness in roof and 1 inch insulation thickness in wall advocates a significant peak cooling load difference from base case.
The difference among the peak cooling loads of all other combinations with increase in insulation seems nonsignificant as shown in Fig. 7. It is inferred that for economical solution modification with 1 inch insulation thickness in roof and 1 inch insulation thickness in wall (R1W1) should be used.

CONCLUSIONS
The present study has analyzed the thermal performance of a single-family double storey residential building in Lahore to determine the optimum insulation thickness for building roof and walls based on peak cooling loads.
The envelope with 4 inches insulation thickness in roof and 4 inches thickness in walls shows the least peak cooling loads reduction of 47.1% from base case. The construction cost increases with the thickness of insulation and hence, increases the overall cost of the building.
For the cost effective construction, the external wall having 1 inch external layer of extruded polystyrene and the 1 inch insulation layer in roof is considered as optimum insulation thickness for energy efficient and cost effective construction, which show nearly the same results i.e. peak cooling loads reduction of 40.1%, but its construction is cheaper. So this modification can be considered for cost effectiveness.
For cost effective energy efficient envelope construction, it is concluded that the effect of insulation on roof is much significant as compared with the effect of insulation on walls. Therefore in some cases to make cost effective construction the insulation can be applied to roof only which would also give a significant decrease in peak cooling loads.

FUTURE WORK
The whole building life cost and projected energy cost savings data will be incorporated in future study to enhance the assessment of optimum insulation and calculation of payback period.