ISAT 413 - Module III: Building Energy Efficiency

1. ISAT 413 - Module III:Building Energy Efficiency Topic 5: Insulation Economics • Heat Transfer Fundamentals of Insulation • Case Example on Optimum Insulation • Case Example on Long Steam Pipes • Case Example on Water Tanks

2. Economic Thickness of Insulation • Insulation is one of the most obvious and basic ways of recovering energy. The annual fuel cost is reduced as the thickness of the insulation is increased but the capital cost of the insulation increases with the thickness and hence the financial saving must be off-set against the capital cost. • For a typical write-off period there will normally be an economic thickness of insulation for a particular case.

3. r T o o dr ò ò & = - p Q 2 kL dT cond r r T i i æ ö r ( ) & ç ÷ Þ = p - o Q ln 2 kL T T ç ÷ cond i o r è ø i - T T & Þ = i o Q cond æ ö r æ ö r ç ÷ o ln ç ÷ ç ÷ o ln ç ÷ r è ø r i è ø i = R p 2 kL p 2 kL Thermal Resistance of Cylinder Wall

4. Optimum Radius of Insulation The refrigerant of a heat pump is circulating through a thin walled copper tube of radius ri = 6 mm as shown in the Figure at left. The refrigerant temperature is Ti, ambient temperature is To, and Ti<To. The outside convection heat transfer coefficient is ho = 7 W/m2.K. What would the optimum thickness of the insulation, assuming the thermal conductivity of the insulation material is k = 0.06 W/m.K.

5. Optimum Radius of Insulation (continued) • In the thermal analysis of radius systems, we must keep in mind that there are competing effects associated with changing the thickness of insulation. Increasing the insulation thickness increases the conduction resistance; however, the area available for convection heat transfer increases as well, resulting in reduced convection resistance. • To find the optimum radius for insulation, we first identify the major resistance in the path of heat flow. Our assumptions are that (1) the tube wall thickness is small enough that conduction resistance can be ignored, (2) heat transfer occurs at steady state, (3) insulation has uniform properties, and (4) radial heat transfer is one-dimension.

6. Optimum Radius of Insulation (continued) • The resistances per unit length are where r , the outer radius of insulation, is unknown. The total resistance is • The optimum thickness of the insulation is obtained when the total resistance is maximized. By differentiating Rt with respect to r, we have

7. Optimum Radius of Insulation (continued)

8. Example 1. Insulation on Long Steam Pipes A steel pipe carries wet steam from a gas-fired boiler through a small workshop to a process plant. It is proposed to insulate the pipe using a glass fiber insulation with an aluminum alloy casing. Using the data below making suitable assumptions, determine: (i) the most economic thickness of insulation; (ii) the simple pay-back period for this thickness. Data:

9. Example 1 (continued)

10. Example 1 (continued)

11. Example 1 (continued)

12. Example 1 (conclusion) The economic thickness of insulation is about 50 mm.

13. Example 2. Insulation on Water Tanks A factory has five steel tanks used for dip cleaning a product; each tank is 2 m long by 1 m high by 1.5 m wide. The detergent solution in the tanks is heated to a temperature of 65oC by steam in tubes immersed in the liquid; the steam is provided by a boiler with an efficiency, including steam distribution losses, of 60%. Using the additional data below, assuming that the heat loss through the floor of the tanks is negligible and neglecting the thermal resistance of the steel tank walls, calculate: (i) the annual cash saving if the tank walls are insulated using a 25 mm thick slab of insulating material; (ii) the annual cash saving if a double layer of Allplas balls is applied to the liquid surfaces; (iii) the simple pay-back period if the measure in (i) and (ii) are both implemented.

14. Example 2 (continued) Data:

15. Example 2 (continued)

16. Example 2 (continued)

17. Example 2 (continued)

18. Example 2 (conclusion)