Heat is transferred by from one material to another by conduction, convection and/or radiation. Insulators are used to minimise that transfer of heat energy. Convection will be the main heat transfer that will be focused on, as the research is based on insulation that will prevent the roof from heating as well.
Convection occurs when particles with a lot of heat energy in a liquid or gas move and take the place of particles with less heat energy to create thermal equilibrium. This is stated in the first statement of the 2nd law of thermodynamics – heat flows spontaneously from a hot to a cold body.
Now, one may question how exactly this phenomenon occurs. The answer lies in energy and momentum conservation in a collision, where a collision between a faster molecule and slower one at the boundary in elastic collisions will increase the velocity of the slower one and decrease the velocity of the faster ones, transferring energy from the higher temperature to the lower temperature region. After reaching a certain period of time, the molecules in the two separate regions will have the same average kinetic energy, which results in the same temperature. Therefore, it is natural for heat energy is transferred from hot places to cooler places by convection.
Figure 1: Two regions with different temperatures reaching a thermal equilibrium through heat transfer
Liquids and gases expand when they are heated. As mentioned before, this is due to the particles in liquids and gases move faster when they are heated than they do when they are cold. As a result, the particles take up more volume. This is because the gap between particles widens, while the particles themselves stay the same size.
As a result, the liquid or gas in hot areas is less dense than the liquid or gas in cold areas, so it rises into the cold areas. The denser cold liquid or gas falls into the warm areas. In this way, convection currents that transfer heat from place to place are set up. However, due to this convection current, the roof of a house heats up as well. This results in energy waste, as more energy is required to heat up the room.
Therefore, thermal insulation is necessary to save energy. Thermal insulation is the method of inhibiting the transfer of thermal energy from one area to another. Thermal insulation is the most practical and cost-effective way to make a house more energy efficient, as it allows the household to use only the necessary energy to manipulate the temperature.
Due to this, the main focus of this research task is insulation in the attic, as one could lose up to 40% of their heating and cooling energy via the attic. Therefore, an individual would want to insulate their roof, as they’re substantially paying to get their attic heated up, when it’s not necessary.
Overall, according to Your Energy Savings, an Australian Government Website, almost half of the energy we use to heat or cool our homes can simply leak out without insulation.
Insulation helps to:
- Save money on your energy bills
- Reduce your energy use and lower greenhouse gas emissions
- Reduce reliance on heating and cooling systems
- Improve your comfort at home
However, the two main important reasons to install insulation are: Saving money and decreasing environmental impact.
Save money on energy bills: According to houselogic, a website based on saving energy, installing insulation will not only improve the comfort of your home it can save you money on your energy bills too. About $600 a year can be saved by boosting the amount of attic insulation from R-11 to R-49. (R value will be referred later on) Depending on the type of materials used, an average person can pay back their installation fee with the money they save in about 2-3 years. After that, every year $600 is saved on energy bills.
Environmental Impact: All energy sources have some impact on our environment. Fossil fuels—coal, oil, and natural gas—do substantially more harm than renewable energy sources by most measures, including air and water pollution, damage to public health, wildlife and habitat loss, water use, land use, and global warming emissions. Australians are becoming increasingly aware of the impact that the production and use of energy can have on the environment. Energy production and use contributed over two-thirds (69%) of Australia’s greenhouse gas emissions in 2004. Australia’s energy emissions are relatively high on a per capita basis, mainly due to our use of coal as the major source of electricity generation. Therefore, saving energy through insulation will help lessen the environmental impact.
Therefore, it is necessary for homes to insulate their roofs to save energy, save money and save the environment.
The main focus of the research is to determine the relationship between the thickness of the insulator and its ability to insulate an area. In another words, if the thickness of the material helps the material’s insulating ability. To do so, the equation for R-Value will be used. The R-value of a material is its resistance to heat flow and is an indication of its ability to insulate. It is used as a standard way of telling how good a material will insulate. Therefore, there higher the R-value, the better the insulation.
The equation for R-value, according to TheGreenAge, a website based on energy saving is:
R=l/k
Where l is the thickness of the material in metres and k is the thermal conductivity in W/mK.
The R-value is measured in metres squared Kelvin per Watt (m2K/W)
The R-value is therefore a relatively simple way to see the impact of adding thicker layers of the same insulating material.
If the material does not significantly affect the insulator’s ability to insulate, the R-value will remain relatively the same. However, through research, it is highly likely that the thickness of a material will affect the insulator’s insulating material. This claim is supported by both Green Building Advisor and Energy Saver. Green Building Advisors states, “The thicker the insulation, the better it works to reduce heat flow”. Energy Saver states, “In general, increased insulation thickness will proportionally increase the R-value.”
The R-value, furthermore, is the only known value to compare whether the experiment is valid or not, as it also subsequently measures whether the heat loss has decreased or not. This can be explained through the heat loss equation:
Q=(At(T_1-T_2))/R
Where Q stands for Heat loss
A stands for Area
T stands for time
T1 stands for inside temperature
T2 stands for outside temperature
As shown, Q is proportional to A, t, change in temperature, and the inverse of R, which is 1/l, since the equation for the R-value is just flipped upside down. Since the Area and Time will be the same throughout the experiment, this means that Q will be directly affected by the R value, as everything else is constant. Therefore, even if the inside temperature, the temperature inside the light box is not measured, there will be a sense of knowing that there has been a decrease in heat loss, due to the R value increasing, which also means the heat loss decreases due to the increase in thickness. Therefore, it is justified that the use of R-value is a very effective way of validating whether the results from the experiment are true or not, as it shows that the thicker the material, the better insulator it is.
The logarithmic equation will also be used for the experiment, as heat increases in a logarithmic trend. This is because the natural log equation shows the temperature increase and the time it takes to increase to that temperature. At 0 minutes, the temperature will already be at a certain temperature and will not gradually increase, but will rapidly increase until it starts to equal in temperature with the heat source or when it reaches its specific heat capacity. This was explained previously through molecules in pg 1. Therefore, instead of an exponential equation, where the temperature rises slowly and then fast, the inverse of it will be used, where the temperature rises quickly and then slow.
y=〖a ln〗(x)+z
The focus of this equation lies on a. Since the value of ln(x), the measure in temperature increase and the time it takes to increase to that temperature, will stay the same for all line equations as they’re plotted against the same graph, the coefficient of ln(x) will be important, as that’s the factor that multiplies the heat flow rate, and therefore shows in an equation which layer increases in heat the fastest. z is not as important, as it will not differ between the equations for the layers as much. The logarithmic equations will be derived from the layer’s trendline’s equation. Throughout the report, the coefficient of ln(x) will be referred as the m-value, for a quick way of referring to it. In conclusion, the m-value will show which whether the layers, (the additional thickness), will decrease the heat flow rate or not.
Three insulators were chosen for this experiment; Pressed Cardboard, Corrugated Cardboard and Expanded Polystyrene Board (Figures 1, 2, 3 respectively), despite the main focus of the experiment (thickness), to make sure that the theory did not only apply to one specific insulator, and to see which insulator was most affected by its thickness. The thickness of the insulator was kept thin, as the lightbox had to withstand the weight of the insulators. Furthermore, since all the insulators had different thickness, some insulators had to be doubled to match the other insulator’s thickness. If the starting thickness of the insulators had different thicknesses, it would be hard to maintain the same thickness between insulators, while determining the results of the experiment.
For the thermal conductivity of the insulators, the website, School Physics, was used.
Table 1: The thermal conductivity of different insulators
Insulator Thermal Conductivity (k- value; W/mK)
Cardboard 0.22
Corrugated Cardboard 0.047
Expanded Polystyrene 0.034
It was assumed that the website used to obtain the values of thermal conductivity used the same insulator as the ones used in the experiment. The thermal conductivity of each insulator was obtained from the same website, therefore, the same method would have been used to calculate the thermal conductivity of all three insulators. (This makes the values fair).
Figure 2: Pressed Cardboard Figure 3: Corrugated Cardboard
Figure 4: Polystyrene Foam