Building Heat Loss. How can the most efficient design be determined, taking both building and running costs into account?

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1 Building Heat Loss How can the most efficient design be determined, taking both building and running costs into account? Building Heat Loss page: 1 of 13 Contents Initial Problem Statement 2 Narrative 3-8 Solutions 9-12 Appendix 13

2 Building Heat Loss Initial Problem Statement A building needs to be as energy efficient as possible. One important aspect of the efficiency requires the heat loss through the walls to be minimised. How can the most efficient design be determined, taking both building and running costs into account? Building Heat Loss page: 2 of 13

3 Narrative Introduction Thermal conduction considers the rate of flow of heat through a material with a thickness, d, an area, A, when there is a temperature difference between the two sides. Figure 1 Look at the following two buildings. In which direction do you wish to stop the flow of heat into the building or out of it? Figure 2 Building Heat Loss page: 3 of 13

4 A measure of the thermal efficiency of a wall is the amount of heat lost (or gained) when the inside is at a different temperature to the outside. The lower the value of this heat loss or gain the more energy efficient the design. In your design you have a simple wall made out of a single material which must separate an interior region with an ambient temperature of 20 C from an exterior region with an ambient temperature of 5 C. The wall needs to be 10 m wide and 2.7 m tall. The thickness of the wall needs to be determined and should be designed to meet the heat loss requirements specified for the building. The wall is non-structural so the thickness decision does not need to account of any load-bearing. There are three different materials available. They are characterised by a parameter called the thermal conductivity, k, which is a measure of how efficient they are at transporting heat. The thermal conductivities for the three materials available are given in the table below. k (Wm 1 ) Price per m 3 Material A Material B Material C Insulating materials have a low value of k, while good conductors of heat, such as metals, have high values. For comparison to the above values for the different brick types, copper, which is often used in the base of pans or on heat-exchange fins, has a thermal conductivity of k = 400 Wm -1 K -1. Which of these materials do you expect to have the best insulating properties? Figure 3 Multimedia The animation Building Heat Loss Animation is available to demonstrate thermal conductivity. Building Heat Loss page: 4 of 13

5 For the room described the heat loss per m 2 as a function of wall thickness is shown in the following graph. (Wm -2 ) k = k = 0.3 k = Figure 4 This diagram is available for download: Building Heat Loss Graph PDF. less than (Wm 2 ) Material A Material B Material C Activity 1 Wall thickness (m) You are preparing designs to three possible heat loss specifications. Find the minimum wall thickness (in m to the next largest cm) required for each material to meet the specified target and fill in the following table minimum wall thickness (m) Was your choice of material from the last discussion correct? Building Heat Loss page: 5 of 13

6 2. Choosing the optimal material From the thermal conductivity properties of the wall materials it was concluded that Material C performed the best and required the least amount of material to be used. Is Material C really the best choice? If not, why not? Activity 2 Calculate the volume of material required and the cost to build a wall of width 10 m, height 2.7 m and thickness as determined above for each of the heat loss design criteria. Which material is the most cost effective? < 20 Wm 2 Wall thickness (m) Wall volume (m 3 ) Cost ( ) Material A 0.21 Material B 0.11 Material C 0.04 < 15 Wm 2 Wall thickness (m) Wall volume (m 3 ) Cost ( ) Material A 0.36 Material B 0.18 Material C 0.06 < 10 Wm 2 Wall thickness (m) Wall volume (m 3 ) Cost ( ) Material A 0.66 Material B 0.33 Material C 0.11 Discuss the material costs. Which heat loss specification would you build to? What other factors should you take into account when making your decision? Building Heat Loss page: 6 of 13

7 3. Heating calculations Hint Activity 3 For each of the three possible design specifications heat is lost through the wall. To maintain the temperature inside the building this must be replaced by a heat source in the room. What Wattage rating must this heat source have to provide this? (Assume the other walls are internal and no heat flows through them. Are these power ratings the minimum or maximum required? Activity 4 The heating charges are 0.15 per kilowatt hour (kwhr). If the building is maintained at its temperature for 12 hours each day, what is the total cost to heat this room for one year for the three different specifications? Remember the heating rating calculated above is in Watts not kilowatts. Building Heat Loss page: 7 of 13

8 Activity 5 The wall is built using material B at the cost shown in the table below for each of the specifications. < 20 Wm 2 < 15 Wm 2 <10 Wm Denoting the year in which the building is built as year 0 and counting heating costs for the year at the beginning of the following year work out the total material plus cumulative heating costs for the first 6 years of operation by completing in the following table. Plot the results on a graph. Total cost 3, , , , , Total build plus heating cost year < 20 Wm 2 < 15 Wm 2 < 10 Wm Year Figure 5 Discuss the results. In which year does the lower heating cost of the lowest heat loss specification offset the increased building cost when compared with the other two specifications? Building Heat Loss page: 8 of 13

9 Solutions Introduction solution The answer could be both! The image on the left is in a hot location so the temperature outside is probably higher than the temperature inside. In this case you want to stop heat entering the building. The image on the right is an igloo. In this case you want to keep the inside warmer than the outside so you want to stop heat from leaving the building. These are extreme examples. In temperate regions (such as the UK) you find that in winter the outside temperature is usually lower than the temperature which would be comfortable inside the building so you wish to prevent heat loss from the building to the outside. In summer however, the outside temperature might be higher than would be comfortable inside the building and to minimise the use of air-conditioning you wish to prevent heat gain into the building. solution The lower the thermal conductivity, the poorer at heat transfer in the material. The table shows that material C has the lowest thermal conductivity and so should be the best insulator. Activity 1 solution less than (Wm 2 ) minimum wall thickness (m) Material A Material B Material C A simple comparison of thickness values shows that Material C requires the thinnest wall to be built. Building Heat Loss page: 9 of 13

10 2. Choosing the optimal material solution The simple analysis so far has only looked at the wall thickness. It hasn t looked at the material costs the thinnest wall may not be the most cost effective! Activity 2 solution < 20 Wm 2 Wall thickness (m) Wall volume (m 3 ) Cost ( ) Material A Material B Material C < 15 Wm 2 Wall thickness (m) Wall volume (m 3 ) Cost ( ) Material A Material B Material C < 10 Wm 2 Wall thickness (m) Wall volume (m 3 ) Cost ( ) Material A Material B Material C solution In terms of cost effectiveness, Material B is the best for all design considerations. It is seen that when the heat loss is halved from < 20 Wm 2 to < 10 Wm 2 the cost increases by a factor 3 for material B ( compared with ) so based on the cost of building alone you design to the higher heat loss specification. However, a building with a higher heat loss will cost more to heat! To consider this you need to perform some heating cost calculations. Building Heat Loss page: 10 of 13

11 3. Heating solutions Activity 3 solution Each of the design criteria has a heat loss in Wm 2 of wall. To work out the total loss through the wall you multiply this by the total area of the wall. < 20 Wm 2 : Rating 2.7 x 10 x 20 = 540 (W) < 15 Wm 2 Rating 2.7 x 10 x 15 = 405 (W) < 10 Wm 2 Rating 2.7 x 10 x 10 = 270 (W) These ratings are the maximum heating powers required because they are calculated using the maximum possible heat loss values. Activity 4 solution total hours = 12 x 365 = 4380 Price is 0.15 per kwhr To calculate the number of kwhr used you multiply the number of kilowatts by the number of hours. < 20 Wm 2 Heating cost 4380 x x 0.15 = < 15 Wm 2 Heating cost 4380 x x 0.15 = < 10 Wm 2 Heating cost 4380 x x 0.15 = Building Heat Loss page: 11 of 13

12 Total cost 3, , , , , Activity 5 solution <10 Wm -2 <15 Wm -2 <20 Wm -2 year Total build plus heating cost < 20 Wm 2 < 15 Wm 2 < 10 Wm , , , , , , , , , , , , , , , , solution Year Figure 6 The total cost for the < 10 Wm 2 specification becomes the lowest in year 5 when compared with either of the other two specifications. You can see that the < 15 Wm 2 specification is cheaper than the < 20 Wm 2 specification in year 3. The results show that the lower heat loss specifications have a higher initial cost but over time they are a cheaper option. Building Heat Loss page: 12 of 13

13 Appendix mathematical coverage Use algebra to solve engineering problems Solve problems involving area, perimeter and volume Use scale drawings Work with formula, including those for the areas and perimeters of plane shapes, and the surface area and volume of regular solids Be able to draw graphs by constructing a table of values Be able to extract information from a graph Building Heat Loss page: 13 of 13