Propagation of thermal waves for optimum heating and cooling of underground housing Nielsen, Brooke L., Hill, B., Maher, V., Stepaniak, C. Physics Department, University of Minnesota Minneapolis, MN 55455 bln@tc.umn.edu ABSTRACT Traditional means of heating which use nonrenewable energy sources can be very costly during the cold season. In order to reduce costs and conserve consumption of nonrenewable sources, recurring energy sources may be the only option. Earth sheltered housing can provide natural heating and cooling if situated at a depth such that the heat from the sun penetrates with a time delay of six months. Determining the burial depth involves finding the thermal property of the ground soil in addition to the energy output of the sun per unit area of soil. The thermal properties of soil for the great plains region were gathered from other research and the average seasonal temperature was computed from weather data sources. Building 16.31 meters underground proved to be an optimal distance, producing an average year around temperature of 44F. Building at this depth can be done with current construction technologies and can provide enormous economic savings in heating and cooling costs. CONTENTS ------------------------------------------------------------ o 1. INTRODUCTION o 2. MATERIALS AND METHODS o I. THE THERMAL WAVE EQUATION o II. THERMAL PROPERTIES OF SOIL o III. SOLAR ENERGY OUTPUT o 3. RESULTS o 4. DISCUSSION/CONCLUSION o REFERENCES o FIGURES o TABLES ------------------------------------------------------------ 1. INTRODUCTION In regions of extreme climate conditions, such as Minnesota, heating costs in the winter season can be very costly. Traditional means of heating which use nonrenewable energy sources are at a peak during the cold season. The byproducts of consumption of many of these energy sources are harmful to the environment and the sources are on a supply and demand availability, driving the prices higher as resources decrease. In order to reduce costs, conserve consumption of nonrenewable sources and to protect the Earth, recurring energy sources may be the only option. The sun is the most viable recurring energy source available. The use of solar energy is not new. In 1878 it was being used to power a steam-driven printing press at the World's Fair in Paris. This technology is in use today; passive solar buildings are being built that save 50% on heating costs. Even though the use of solar energy is not widespread, the operating solar thermal electric systems in the United States produce enough energy to displace the equivalent of 2.3 million barrels of oil annually. Research is being done today to improve in efficiency and reduce the cost of producing solar panels, the primary technology in producing solar thermal energy. In addition, manufacturers are trying to design a smaller, better looking solar thermal system. Earth sheltered buildings can compliment solar panel gathered energy by reducing the amount of energy needed to heat or cool if situated at a depth such that the heat from the sun penetrates the soil with a time delay of six months. This is a new idea for the use of underground building because current buildings are only a few feet underground and their primary purpose is in using soil as natural insulation to help keep heat in and the elements out. However, this research is focused on building much deeper and using the sun's energy to heat and cool the dwelling in regions having seasonal variance of weather. To further understand solar heating and cooling of underground buildings and to determine an optimal building depth the following elements will need to be evaluated: (1) thermal waves, (2) the thermal properties of ground soil, and (3) energy output from the sun. 2. MATERIALS AND METHODS I. THE THERMAL WAVE EQUATION. This research began by verifying the thermal wave equation: dq/dt = -kA(dT/dx). If the equation was to be valid the results of the data analysis would be within error of the theoretical prediction calculated as follows: Given: Peltier device output: dq/dt = 0.051W thermal properties of Copper: k = density * heat index * diffusity^2 k(Cu) = 0.39 kW/mk area of bar = 0.002565m^2 Calculation: dT/dx = (dq/dt) / (k * a) dT/dx = 0.051W / (-0.39kW/mk * 0.002565m^2) dT/dx = -50.98 k/m The verification was done as an experiment in the lab using 2 copper bars, a Peltier device for a heat source, 2 thermo-couples, an operational amplifier, a volt meter, and a 15V DC power supply. The copper bars were each 18" long with a radius of 1.25". Each bar had 3 drilled holes 1.25" deep placed at 12", 14" and 16" along the bar. Each bar had 4 copper heat syncs placed evenly between 16.25" and 18" on the bar; fans blew across these heat syncs to prevent reflected thermal waves from flowing back up the bar which could cause false data. Both bars were wrapped in insulating tape to keep the heat from dissipating into the room. The bars were situated end to end, with the holes farthest from the adjacent ends. A Peltier device, covered in thermal grease, was placed in between the connecting ends of the bars and held in place by a clamp. The Peltier device was wired to a DC power supply with an output set to 13 volts. The output from the setup [Fig. 1] was to be measured by two thermo-couples placed in one of the holes in each bar. An operational amplifier [Fig. 2] was built to amplify the signal from the thermo-couples. A volt meter read the amplified signal. The data was gathered by sending current through the Peltier device and recording the reading on the voltmeter every minute for 10 minutes with the thermo-couples placed in the hole at 12" on each bar. The direction of current through the Peltier device was then reversed, causing the bar that was heating to cool and vice versa. The readings were then again recorded every minute. Every 10 minutes this was repeated, for 30 minutes. After 30 minutes the thermo-couples were moved into the next farther hole in each bar. Data was then gathered in the same way, recording every minute for 10 minutes and then switching the current and repeating. After 60 minutes the thermo- couples were moved into the farthest holes and the same process continued. This resulted in 90 minutes total of data at 3 distances from the heat source [table 1]. A plot of voltage versus time [fig. 3] shows we collected data for 4 complete thermal waves. After gathering the data it was necessary to convert the voltage readings into temperature. To do this, the thermo-couples were calibrated using two beakers, one filled with ice water and one filled with boiling water. Both thermo-couples were placed into the ice water beaker for 45 seconds and then one was moved into the boiling water beaker [fig. 4]. The output from the thermo-couples was sent through the same operational amplifier as in the above setup and the readings were taken from the same volt meter. The ice water beaker was wrapped in insulating material and covered so it would not heat over the duration of the calibration. A Bunsen burner was left running under the boiling water beaker. Prior to placing the thermo-couples in the ice water, the reading on the volt meter was recorded at 0.4 - 0.5 volts. After placing both thermo-couples in the ice water the reading was 0.5 - 0.6 volts. This potential difference was due both to slight variation in the water temperature in the beaker and the accuracy of the thermo-couples. The voltage difference between boiling and ice water was recorded to be 14.7 volts [table 2]. Therefore, a temperature difference of 100 degrees C will result in a voltage reading of 14.7 +/- 0.5 volts. Knowing the temperature to voltage conversion, the thermal wave equation could be verified. The data collected above was converted from voltage to temperature in degrees Kelvin [table 3]. To calculate dT/dx, the change in temperature for each of the distances needed to calculated from the data. This was done by taking the peak temperature value for a wave at each distance and comparing the values. The difference in distance was the distance between the holes, 2" or 0.0508m. The error for each reading is 0.5 volts as found by calibrating the thermal couples. Error in Kelvin: 0.5 volts / 0.147 volts/c = 3c + 273 = 276k For the 2nd wave between the first and second holes the following calculation of the change in temperature over distance (dT/dx) was made: dT/dx = (357.9k +/- 41.55k) - (360.6k +/- 41.55k) / 0.0503m = -2.7k -(2.7 +/- 83.1 k) / 0.0503m = -53.14 +/- 83.1 k/m Calculation of dT/dx for 2nd and 3rd hole peaks: dT/dx = (355.2 +/- 41.55k) - (359.1 +/- 41.55k) / 0.0505 = -3.9k -(3.9 +/- 83.1 k) / 0.0503 = -76.77 +/- 83.1 k/m The findings for dT/dx is well within error parameters of the theoretical calculation, therefore the thermal wave equation is valid and can be used in the subsequent research. II. THERMAL PROPERTIES OF SOIL. After the thermal wave equation was verified, the thermal properties of soil needed to be found. Because the thermal properties k = pch^2 and h, the diffusivity is dependent on temperature two value for k needed to be found for each season. According to research completed by Gosnold and Todhunter for the Great Plains Regional Center Director's Report the thermal property of soil in the summer is 0.0012 kW/mk. In further research they completed they found soil thermal properties are much less in the winter, 0.0003 kW/mk. III. SOLAR ENERGY OUTPUT. There has already been extensive research completed in the study of solar radiation in various regions. In the midwestern United States the radiation from the sun varies to a 6% distance fluctuation causing the seasons. According to Tipler in "Physics" this radiation is equal to 30MJ/m^2 or 8.33KWh/m^2 on a sunny summer day. In December the output is equal to 2.78KWh/m^2 on a sunny day. The output is a few watts less for overcast. 3. RESULTS Taking the findings of the soil thermal properties and solar radiation output, the optimal distance at which to build can be determined. The first calculation that needs to be made is to find the average seasonal temperature for both summer and winter. According to Weather of Us Cities the mean temperature in June is 67.9F or 292.9k and in December is equal to 19.2F or 265.9k. The change in temperature between summer and winter is 27k. In order to solve for dx/dt, which would result in depth/time, the following calculation was made: Summer: dx = - k(Soil) * a * dT / (dq/dt) dx = - 0.0012 kW/k * 1 m * 27k * (1/8.333kW hour) * 4380 hours dx = - 17.03 meters Winter: dx = - k(Soil) * a * dT / (dq/dt) dx = - 0.0003 kW/k * 1 m * 27k * (1/2.78kW hour) * 4380 hours dx = - 15.60 meters The optimal burial depth would be the average of the two depths, 16.31 meters. To determine the average year around temperature at this depth, take the average summer temperature, 292.9k and subtract dT divided by 2 for the two seasons, as follows: Tavg(-16.31m) = T(summer) - dT/2 Tavg(-16.31m) = 292.9k - 27k/2 Tavg(-16.31m) = 279.4k = 44F The average year around temperature at 16.31m below ground would be 44F. 4. DISCUSSION/CONCLUSION In doing this research we have tried to thoroughly examine the propagation of thermal waves through ground soil. In doing so, we have discovered that underground housing at 16.31m can provide huge savings in heating and cooling costs due to an average underground temperature of 44F. These findings will have a significant impact on future building development, in addition to those generally concerned with conservation of nonrenewable resources. This research has been a successful introduction to the use of underground buildings for conservation of energy usage. By building at an optimal depth, solar thermal energy can be exploited to naturally heat and cool. These findings open the door to a plethora of further studies that need to be completed. One such area of further study is to determine how different ground properties, such as other soils, rock, snow, ice or sand will affect the propagation of solar energy. In addition to different ground types, surface coverings such as snow, ice, crops, and buildings can alter the amount of solar energy penetrating the soil. Further studies on how both these aspects will vary ground temperature and wave depth need to be completed. Currently, research is being done by the Great Plains Regional Center that will help understand how soil temperature varies with natural conditions. These studies are focused on the affects of wind and latent heat released during freezing of soil moisture. Once completed, results from the Center will play a significant role in this topic as well. Applications of this research apply not only to building underground housing, offices and malls but beyond the Earth, to building energy saving solar powered space stations and underground moon stations. Such uses of solar thermal energy will not only be an advancement of technology, but will be a harbinger of future technologies. REFERENCES o Blair, Frank E. 1993, Weather of Us Cities: A Guide to the Weather Histories of 270 Key Cities and Weather Observation Stations in the United States and Its Island Territories, 4th Ed. (Gale Research) o Department of Energy 1993, The Climate Change Action Plan. o Gosnold, William D. & Todhunter, Paul E. 1995, Climate Change in the Midcontinent of North America. o Levine, Ira N. 1995, Physical Chemistry 4th Ed. o Tipler, Paul A. 1982, Physics 2nd Ed. (New York: Worth)