Environmentally Sustainable Buildings - the Calculation of Heating and Cooling Loads - Math Problem Example

Environmentally Sustainable Buildings Assessment Report Date 3542 words Student Name University Environmentally sustainable buildings Introduction In the 21st century, the environment and energy are the two major components that need to be conserved and used in a sustainable manner so that the future generation can also benefit from them. One of the ways in which the conservation of energy as well as the environment can be achieved is by building houses that use less energy as well as ensuring that their impact to the environment is a minimum. This can only be possible if the design parameters of the houses are accurately determined and appropriately adhered to. For any house to sustain life, it has to have a reasonable temperature, sufficient ventilation as well as enough light. These parameters are mostly obtained from the environment. Since the parameters are constant, therefore the design of the house will be important in ensuring the best conditions for life sustainability in the house are attained. It is also important to note that the cost of the house should be minimized as much as possible, this can be possible only by ensuring that the materials used in building the houses are cheap and meet the required standards, therefore, a proper evaluation of the purpose of each material against the cost must be recorded so that the material that meets the required conditions with the minimum cost is selected. Heat transmission Heat in a house must be kept constant all the time. The heat gain and the heat loss must be controlled so that their rates are kept to the standard rates. Heat transferred mainly through conduction, convection and radiation. Heat transfer by conduction is mainly heat transfer through solids such as walls, slabs, ceiling and roofs. Heat transfer by convection involves fluids (air and liquids), this relies on the density changes of the fluids in that heat is transferred from a low density region to a high density region through convectional currents. Radiation is another mode of heat transfer that is mostly transferred through space, mostly sideways and downwards. The common and most applied principle applied in heat transfer is that,’ heat moves from a warm region to a cool region’. This is because, in the warm region, the density of the air is reduced hence as a result the air becomes lighter which makes it easier to move and then replaced by a denser and heavier air. The heat gain in a house is influenced by a number of factors which may include; The available house space; this affects the energy required to heat the house. A smaller house space requires less heat energy to heat the house than a larger house space. The design of the house; this affects the extent to which the heat energy is required as well as the possible obstruction to the heat, if for a example a house has more rooms then the amount of heat energy required to attain a standard temperature in the house is more than a that required by a house with few rooms. Ventilation; this refers to all the possible openings that a house has such as doors, windows and permanent openings that allows heat to escape from the building hence as a result heat is lost and needs to be gained later on. Some materials that can decrease heat loss from the building (insulators) may also affect the rate of heat gain because if insulators are available that means that the rate of heat loss is minimal hence the heat gain is faster. All the mentioned factors have to be accurately determined to ensure that the heat gain is achieved using the minimum energy thus as a result conserving the energy use. The heat exchange occurs between the house and the environment around it. The main goal for determining the most appropriate heat gain is to ensure that the occupants are comfortable most times of the day. Different formulae can be used to calculate the rate of heat exchange for different surfaces. The heat transfer through walls, roof, ceiling and floor is majorly by conduction; the major equations involved in this process are as follows: Where; Quantity of heat flow (W) k thermal conductivity of the material (W/m-K) A area (m2) L thickness of the material (m) temperature of hot surface (K) temperature of cold surface (K) The above formula for determining the quantity of heat flow by conduction can be summarized as below; Where; A surface area (m2) Thermal transmittance (W/m-K) Temperature difference between the inside and the outside air (K)1 The amount of heat transferred through the wall also depends on the position and direction of the wall in relation to other wall and the environment. When two walls are adjacent to one another, then heat transfer through the walls will entirely depend on the heat available on the adjacent wall. When the wall is exposed to the external environment, then it is important to analyse the condition of the environment because the heat to be transferred will depend on the characteristics of the weather at that particular time. If the weather conditions are sunny, which means that high solar radiations are experienced at that time, then more heat is to be transferred through the walls to the interior positions. On the other hand, if the weather is cloudy then it means that heat will be lost from the building through the walls to the outer environment because the outside temperature will be less than the inside temperature. In regions which are situated outside the tropics such as Australia, different seasons that dictate the rate of heat transfer through the walls , ceiling and floors exist. These seasons are, spring, summer, autumn and winter. The summer and winter seasons represent the extreme conditions of the environment. In summer, more heat transfer through the walls from the exterior parts to the interior parts is experienced while in winter, the highest level of heat loss from the buildings is expected because of extreme low temperatures in the outside environment is experienced. Since the ultimate goal of having environmentally sustainable buildings it to ensure that the occupants are comfortable, the process by which the heat that has been transferred from the external environment through the wall to the building reaches the occupants must be considered. The house contains free air molecules that fill the free space in the house. The heat from the surface of the wall has to be transferred to the occupants as well as to the surface of the other walls, ceiling or floors. The air near the heated surface such the wall is heated hence as a result, the density of the air reduces due the increased volume and then moves to a place of lower temperature as it is being replaced by a denser air. As this process continues through free convection currents, the whole room is heated and achieves a higher temperature. Depending on the level of comfort required, the temperature will then be adjusted accordingly using any appropriate mechanical or natural means. The most applicable formula for determining heat transfer by convection is; Where; quantity of heat flow (W) h heat transfer coefficient (W/m-K) Ts temperature of surface (K) Tf temperature of fluid (air or liquid) (K) A area of surface (m2) After considering the effect of conduction and convection processes on the comfort of the occupants, it is necessary to consider the radiation process. As mentioned earlier, radiation does not require any medium for heat to be transferred. It is enabled by the temperature difference between two surfaces. Therefore, in this case the distance between the two surfaces and the sizes of the surfaces involved is very critical. The closer the surfaces, the more effective the process of radiation is and vice versa. Also the larger the surface the more effective and the faster the rate of radiation is and vice versa. As objects in the house gain heat, they tend to distribute the heat gained to other surfaces nearby sideways and downwards by the process of radiation. Several equations have been developed to account for this process of radiation which may include; With; Where; net radiative exchange between surfaces (W) Stefan-Boltzmann constant (5.67 qx10-8 W/m2-K4) A area of surface (m2) T1 temperature of surface 1 (K) T2 temperature of surface 2 (K) emissivities of surfaces 1 and 2 respectively If the building is exposed in any way to the external atmosphere, then the radiations between the surfaces have to be considered; Where; A area of the building exposed surface (m2) emissivity of the building exposed surface Ts temperature of the building exposed surface (K) Tsky sky temperature (K) To understand the above equations, it is important have an example based on the data below of a town in Australia. The most appropriate geographical location to be considered in Australia is Darwin, Northern Territory. This is because this the region receiving the highest amount of solar insolation the area. The month to be considered is October. The surface temperatures can be measured using various techniques such as sun charts, radiation papers etc. once the temperatures have been determined, the building temperature is also determined, the temperature difference obtained can then be used to calculate the heat load required. Conduction Considering the building material being burnt brick then Considering a house of and height of then The thickness of the burnt brick Thermal transmittance Therefore, Then, Applying the formula; Then, Convection Heat transfer coefficient Therefore, Convection Using the equation; Given; Then Therefore; Elements of solar geometry The solar system is very diverse and consists of very many objects. It consist of the sun as the main object, the eight planets, meteors, comets, then moon and so many other objects. The planet earth which is of our interest because it is our home is the third planet in the solar system and it is the only planet that supports life. Geographically, the earth is spherical and it is held in position by the sun’s immense gravitational force. Therefore, the earth revolves around the sun once in every 365 days. The earth’s axis of rotation is slightly tilted from the normal plane of the earth at an angle of approximately 23.50. The radiation from the sun keeps the earth’s temperature controlled in most parts of the year. Due to the tilted rotation axis of the earth, the altitude of the sun varies from time to time. The orbit of the earth is elliptical in shape, therefore, the distance of the earth from the sun varies at it revolves around the sun from season to season. From the solar geometry, the sun is nearer the earth’s surface in the months of March and September and furthest in the months of June and December. In most cases, as the earth revolves around the sun, the position of the sun changes which results in having different seasons on the earth’s surface. The main seasons experienced in regions far away from the tropics include, spring, summer, winter and autumn. When the sun is nearest to the earth’s surface, summer season is experienced, on the other hand when the sun is far away from the earth, winter season is experienced. It is therefore important to try to determine the position of the sun at any time of the day as well as at any location on the earth’s surface so that proper preparation can be done in respect to the seasons to be experienced. In the design of buildings, the knowledge on the position of the sun is very important so that the amount of natural lighting to be expected to the building is determined to safe on the costs of acquiring artificial lighting. Also the external temperatures expected will be determined to decide on the ventilation as well as the type of roof, walls and floor to be used in constructing the building. Since different methods do exist to determine the position of the sun at different times of the day as well as different times of the year, the method that is most commonly used is the method of Spherical Geometry. This approach enables someone to accurately determine the radiation intensity, the azimuth as well as the altitude of the sun above the earth’s surface. This approach is also applied together with the vector analysis approach to accurately determine the various positions of the sun. In the determination of the position of the sun, the elliptical, horizon and equatorial parameters have to be considered. The determination of the sun’s position is base mainly on determining the altitude as well as the azimuth of the sun. before determining these two components, its important to firstly understand key terms such as the latitude, longitude and declination. Latitude and longitude To locate any position on the earth’s surface, the latitude and longitude of the place have to be determined. These components are expressed in degrees, minutes and seconds depending on the precision of the data required. Basically, latitude is an elliptical horizontal plane running across the earth’s surface while a longitude is a vertical plane running perpendicularly to the horizontal plane (latitudes) The main latitude in which all the other latitudes make reference to is the equator at 0 degrees. The main longitude is the prime meridian that runs from the earth’s north pole to the south pole. Declination Is the angular vertical displacement to an object on the celestial sphere from perpendicularly north or south from the celestial equator. The declination angle varies from +23.5 degrees to -23.5 degrees from summer solstice to winter solstice respectively. The value of the declination angle is always zero during the spring and autumn equinoxes. Altitude of the sun Altitude is the vertical distance of the sun from the earth’s surface. The altitude of the sun can be calculated using the formula; Azimuth of the sun This is the direction or the bearing of the sun. It is the angle that the sun makes to the true south. This can be determined using the sun chart or any other most appropriate method. Solar time calculation The equation for calculating the solar time is as shown below: Where; E equation of time Lst standard longitude (in degrees) Lloc longitude of the observer in the local time zone (in degrees) Direct beam intensity It is important to determine the incident radiation on any surface on the building or on the earth’s surface so that proper design materials and adjustments can be put in place. The most applicable equation to be used is as below; Where; Incident beam intensity direct beam intensity on a plane normal to the direct solar radiation angle of incidence of the direct beam radiation onto the surface The sun’s angle of incidence which is the angle at which the sun’s rays strikes the earth’s surface will also form a basis to determine the position of the sun at any time. The angle of incidence in this regard affects the intensity of the sun; this is because when the sun is perpendicular to the earth’s surface. The sun rays strikes the earth’s surface at right angles which mean that the sun rays concentrate over a small area resulting to a very high intensity than when the sun’s angle of incidence is less than 90 degrees. This can be illustrated using the sketch below; A SURFACE Fig. effect of the angle of incidence on the insolation intensity Let the angle of incidence be A Therefore, Using the above equation, the intensity of the solar radiation can be determined at any point if the angle of incidence is known. Solar radiation The earth obtains its energy from the sun, as mentioned earlier, the shape of the earth is spherical and at the same time, the earth’s orbit is elliptical. Therefore, this means that the distance of the earth from the sun varies from time to time as it revolves around the sun. as the distance changes, the insolation intensity also changes and the effect of the solar radiation on the earth’s surface also changes. In determining the intensity of extraterrestrial radiation on a plane normal to sun's rays on any day, the formula below is used. Where; solar constant n day of the year () The solar radiation moves through the atmosphere before reaching the earth’s surface. The atmosphere contains so many particles, moisture, gases and other small objects that absorb, diffuse,reflect as well as scatter the solar radiation from the sun. As a result, there are two main solar radiations, the beam radiation on which no reflection or scattering has taken place and the diffuse radiation on which a large extent of reflection and scattering is evident. Therefore, to obtain the total radiation; The amount of solar radiation (insolation) received on the earth’s surface has to be calculated so as to determine the energy received at that particular point. To be able to calculate the insolation of a place, the zenith angle ,solar declination angle, hour angle and cloud cover of the place has to be determined. After determining all the parameters mentioned, the following steps have to be followed. The hour angle (H) is calculated; Time is in 24-hour clock system in this case The zenith angle (Z) is calculated; Where; X latitude Y solar declination angle H hour angle The solar insolation is calculated; Where; S solar constant (approx 1000W/m2) The amount of insolation received on the earth’s surface will depend entirely on the position of the sun. when the sun is 90 degrees above the earh’s surface, maximum insulation is obtained at that time, especially at 12 noon, the amount of insolation then starts diminishing as the angle of incidence reduces until a minimum at around 6pm. This is because when the sun rays are at an angle, the rays travel over a large distance to reach the earth’s surface hence most of the solar radiation is reflected and scattered in the atmosphere. 2 When the sun is very close (perihelion) to the earth in the month of June, the day length is longer than the night length, therefore the amount of solar insolation is very high at this time of the year. On the other hand, when the sun is very far away (aphelion) from the earth in the month of July, the day length is shorter than the night length hence the insolation is very low at this time of the year. Solar loads variation with the diurnal cycle The diurnal cycle takes exactly 24 hours, during this time, the solar load vary with time. The sun rises in the morning at around 6am, thereafter, the solar loads increase with increase in time to around 12noon when the maximum solar loads are experienced. At this time the sun is directly perpendicular to the earth’s surface. Considering the temperature change, the maximum temperature is experienced at around 3pm; this is a lag from the time the maximum solar loads are experienced. This occurs because, at this time, the incoming solar radiation is more than the cooling rate by radiation. The solar loads then decrease with time to a minimum at around12am. When the sun sets and the radiative cooling then begin until the minimum solar load is attained at 12am when the temperatures are at the lowest point. Heat transmission through windows Windows form the main ventilation routes as well as the main source of solar lighting to a building. In the past, various modifications have been applied to the glasses of the windows to reduce the amount of solar heat that could be gained through the windows. Some of the methods that were applied include using tinted glass that could reflect the highest amount if solar radiations. Therefore, it is evident that windows control the heat flow that gets into and out of any building and also the amount of the natural lighting obatianed in the house which if enough could save a on the light needed by the artificial lighting thus saving on costof lighting the house. A clear single-pane glass can reflect as much as 24% of the sun’s UV radiation while an insulating can reflect up to 40% of the sun’s UV radiation. Shading the window effectively modifies the radiation incident on it. The best way to shade the window is to provide a simple rectangular overhang over the window. In this case different formulas can be used. Let, H be the height of the window W be the width of the window D be the depth of the overhang Therefore, the hourly radiation in the window is got by; Where; fi fraction of the unshaded region Given by; Standard tables are available to provide the window radiation view factor. Reference list Koenigsberger O.H., Ingersoll T.G., Mayhew A. and Szokolay S.V., Manual of tropical housing and building, part 1- climatic design, Orient Longman, Madras, 1975. Read More