Heat Transfer through Building Envelope

Transcription

1 CHAPTER 3 Heat Transfer through Building Envelope Envelope Heat Gain Heat gain or loss in buildings is due to heat transfer through walls, roof, ceiling, floor, and glass etc., i.e., the building fabric or envelope. The load due to such heat transfer is often referred to as the envelope heat gain or loss. In this connection, it is to be considered whether a particular wall or roof is exposed (normal or severe exposure) to the sun or not. In the case of a sunlit wall or roof, the heat gain of the room will be more in comparison to a shaded one, as the outside surface temperature of the wall or roof will increase above the outside air temperature due to the incident solar radiation. The major components of heat load in buildings are due to the direct solar radiation through the west glass, transmission through the building fabric or structure and fresh air for ventilation. In the case of theater and auditoriums the occupancy load is predominant. The maximum temperature may occur outside at 1 or 2 p.m., the maximum heat gain of the room may occur at 3 or 4 p.m. due to the time lag for the heat transfer through the structure. 3.1 Heat transfer: Majority of Heat transfer takes place in buildings through building envelope. Building envelope consists of walls, roof, and fenestrations (openings). Heat transfers through walls and roof is by conduction and is through conduction and radiation in glazing materials. Heat loads are generated through convection which is termed as ventilation load. There are also internal

2 loads inside the building due to occupancy, lighting and heat loads due to air conditioning equipment if any, to maintain indoor comfort. Fig 3.1 shows the heat transfer in buildings. Fig 3.1 Heat transfer in Buildings 31.1 Heat transfer through Conduction: Heat transfer through a material takes place by conduction from warm to cold side. The same process takes place in a building. Generally the thermal conductivity of the building materials will be much lower. In solid bodies including building components, thermal conduction takes place when one part of the component is subjected to higher temperature and the other part to a lower temperature condition. Most cases of thermal conduction are usually analysed and treated in their simplified form as one dimensional heat flow cases, i.e. heat flow in directions other than the main direction is neglected. Similarly, if the changes in atmospheric conditions (inside and I or outside) are

3 assumed to be very slow, neglecting these changes, the process of heat transfer can be assumed to be "Steady State Heat Transfer" in its simplified form Heat transfer through Convection: When heat is transported by a fluid, like air or water, this is called convection. The extent of convective heat transfer depends on a number of things, like the position of the surface (horizontal or vertical), but mainly on the speed of the passing air. The speed in outdoors is determined by wind speed and direction. When the air is driven by an outside wind force, this is called "forced convection". When there is no wind, convection will occur by temperature or density differences. This is called "free convection". The example of the hot air ascending above a radiator is an example of free convection. Room air is heated by the radiator and ascends because the density of the hot air next to the radiator is lower than the density of the cooler air in the rest of the room. This results in the warmer air rising, and being displaced by the cooler air. The heat transfer through forced convection is higher than that due to free convection, because of higher air speed Heat transfer through Radiation: The phenomenon of thermal radiation is described as the transport of energy through electromagnetic waves. Unlike conduction and convection, radiation heat transfer is not bound with material, it can even occur through vacuum. Every body whose temperature is above absolute zero radiates energy in the form of electromagnetic radiation. The spectral distribution of the energy radiated from any body depends on the temperature of its surface. The higher the

4 temperature of the body, the lower is the wavelength of the radiation that makes the major portion of the total emitted radiation. Since the temperature of most building components and their surroundings are much less as compared to heat of the sun, the spectral distribution of their emitted radiation has more share of larger wavelength. It means radiation emitted from such bodies is thermal radiation. In heat transfer due to radiation the rate of heat flow depends on the temperatures of the emitting and receiving surfaces and on certain qualities of these surfaces: the emittance and absorbance. Radiation received by a surface can partly be absorbed and partly be reflected. Heat is transferred into the building through radiation from the glass provided for fenestrations (openings) Sensible heat: Sensible Heat is defined as the heat energy stored in a substance as a result of an increase in its temperature. The heat is absorbed or transmitted by a substance during a change of temperature which is not accompanied by a change of state Latent heat: Latent Heat is defined as the heat which flows to or from a material without a change to temperature. The heat will only change the structure or phase of the material. E.g. melting or boiling of pure materials. The heat is released or absorbed per unit mass by a system in a reversible isobaric-isothermal change of phase. In meteorology, the latent heats of evaporation (or condensation), fusion (melting), and sublimation of water substance are of importance.

5 3.2 Heat loads in the interior of the building: Steady state conditions do not occur in nature. The equation and calculation methods given below are valid if and only if, both out-door and indoor temperatures are constant. The basis of the below mentioned methods is the assumption of steady state conditions. This is an obvious simplification of the actual situation but the results can be taken as reliable if the fluctuations of temperature do not exceed f 3 deg. C. Such a situation may prevail in the winter of moderdte climates when the interior is heated and kept at a given temperature or in a warm-humid climate where the indoor temperature is kept constant by air conditioning. Calculations based on steady state assumptions are useful to determine the rate of heat loss or heat gain, also for the purpose of establishing the size and capacity of heating and cooling installations. The steady state calculation methods can also be considered as preliminary studies, to lead up to the understanding of the more complex non-steady-state heat transfer problems Conduction of heat: Qc: Conduction heat flow rate through a wall of given area can be calculated using Qc A U = condition heat flow rate in W = surface area in m2 = transmittance value in w/m2 OC A~E = temperature difference (effective temperature)

6 Effective temperatures are calculated based on tables provided in appendix A5 For a building, enclosed by various elements and a possible temperature difference varying from side to side, the above equation is solved for each element and the results are added. U value (transmittance coefficient) is air to air transmittance and its unit of measurement is wlm2. This is the quantity most often used in building in heat loss and heat gain problems as its use greatly simplifies the calculations. Some of the values are listed in Appendix A.1. If the construction is different from the type of construction given in A.1, then the U value (refer 3.4) is computed for that specific case Convection: Qv: Convention heat flow between the interior of a building and the open air, depends on the rate of ventilation i.e. air exchange. This may be unintentional air infiltration or may be deliberate ventilation. The rate of ventilation is expressed in m3/sec. There are two methods of estimating the infiltration into buildings. They are Crack method Air change method In the crack method the estimate is based on measured leakage characteristics and the width and length of the crack around the windows and doors. The air change method assumes a certain number of air changes per hour for each space depending on its usage, 'I'he crack method is generally regarded as more accurate method and is used in case of windows. The air change method is more convenient to use in case of doors. The leakage of air in this case is a

7 hction of the wind pressure Ap which can be determined by knowing the wind velocity C using the equation Where Ap is in cm HzO and C is in Kmh. It is a common practice to take 0.64 Ap only as the pressure difference between the outside and inside air to evaluate the infiltration rate. The ASHRAE (American society of Heating Refrigeration Air-conditioning Engineers) guide publishes data that indicates that wind pressure causes a leakage of air even through brick and concrete walls. Its numerical value is, however, very small. For example, for a 21.5cm plastered brick wall at 24kmph wind velocity, it is only cmm.sqm of the wall area which can be ignored. The ventilation air requirements, depending on individual applications are given in Table3,l The minimum requirement is taken as 0.2 cmm (cubic meter per minute per person). This is based on population density of 5 to 7.5 sqm per person and a ceiling height of 2.4m. When people are smoking, the minimum ventilation requirement is 0.4 to 0.7 cmm per person. Infiltration occurs due to: (1) windowslopenings (2) Infiltration through gaps in the building fabric (3) Porous materials

8 90 Table 3.1 Ventilation air requirements (Arora C.P) In air conditioned buildings as pressure inside the building is more when compared to out doors, infiltration doesn't take place and hence this load is neglected. Instead of this the heat loads due to bypass air is considered Radiation through glazing surfaces: QS : Direct Gain: Qs = A I 0 A = area of window in m2 1 = solar radiation heat flow density in w/m2 8 = Solar gain factor of window glass The values of I (solar radiation) are computed from tables A3 provided in appendix. '0' is the solar gain factor which varies from material to material and is detined as the heat flow rate through the construction due to solar radiation expressed as a fraction of the incident solar radiation.

9 3.2.4 lnternal Heat Gains: The sensible and latent heat gains due to occupants, lights, appliances, machines, piping, etc., within the conditional space, form the components of the internal heat gains. Occupancy Load The occupants in a conditional space give out heat at a metabolic rate that more or less depends on their rate of working. The relative proportion of the sensible and latent heats given out, however, depends on the ambient dry bulb temperature. The lower the dry bulb temperature, the greater is the heat given out as sensible heat. Typical values of heat given out are given in Table 3.2.The values for restaurants include the heat given out by food as well. It will be seen that the sensible heat (SH) gain does not vary much with activity, more and more heat being liberated as latent heat (LH), thus making up for total heat. Table 3.2 Heat Liberated due to Occupancy (Arora C.P)

10 Light Load: Electric lights generate sensible heat equal to the amount of the electric power consumed. Most of the energy is liberated as heat, and the rest as light which also eventually becomes heat after multiple reflections. Lighting manufacturers give some guidance as to the requirement of power for different fittings to produce varying standards of illumination. In connection with fluorescent tubes, it may be stated that the electric power absorbed at the fitting is about 25 percent more than necessary to produce the required lighting. Thus, a 60 W tube will need 75 W at the fitting. The excess of 15 W is liberated at the control gear of the fitting. As a rough calculation, one may use the lighting load equal to 33.5 w/m2 to produce a lighting standard of 540 lurnens/m2 in an ofice space; minimum wattage required is 20 wlm2. After the wattage is known, the calculation of the heat gain is done as follows. Fluorescent Q = Total watts x 1.25 Incandescent Q = Total watts Appliances Load Most appliances contribute both sensible and latent heats. The latent heat produced depends on the function the appliances perform, such as drying, cooking, etc. Gas appliances produce additional moisture as product of combustion. Some of the heat loads generated by appliances are listed in table 3.3

11 93 Table 3.3 Appliance Load in Watts (Arora C.P) Bypass factor: The effect of the bypass factor is such as to add some arnount(x) of the outside air directly to the room and remaining air (I-X) to pass through the apparatus. Thus we can say that a part of the ventilation load forms a component of the room load. This bypassed outside air load is proportional to the bypass factor. It has both sensible and latent heat components. The other part which is proportional to (1- X) has both sensible and latent, which is bypassed around the apparatus and is added to the equipment load. Thus the bypassed outside air loads on the room are: SH LH SH = (OASH) (BPF) = (OALH) (BPF) = sensible heat OASH = out door air sensible heat OALH = out door air latent heat

12 LH BPF = latent heat = bypass factor These loads are imposed on the room in exactly the same manner as the infiltration load. Total Heat Load: The components of the heat loads can be summarized as follows. Effective Room Sensible Heat (ERSH): Solar and transmission heat gain through walls, roof, etc. Solar and transmission heat gain through glass. Transmission gain through partition walls, ceiling, floor, etc. Infiltration a Internal heat gain from people, power, lights, appliances, etc. Additional heat gain not accounted above, safety factor, etc. Supply duct heat gain, supply duct leakage loss and fan horsepower. Bypassed outside air load. The sum of items above gives the effective room sensible heat (ERSH). Effective Room Latent Heat (RLH): Infiltration Internal heat gain hm people, steam, appliances, etc. a r Vapour transmission. Additional heat gain not accounted above, safety factor, etc.

13 e Supply duct leakage loss. The sum of above items gives the effective room latent heat (ERLH) The sum of effective room sensible heat and effective room latent heat gives the total heat load inside the building. 3.3 Procedure to calculate overall Heat Transmission Coeficient - U value: The conduction heat transfer through the wall or roof will depend on the thickness and the thermal conductivity of the material used. In addition, there will be convection and radiation from both the outside and inside surfaces. Hence, the steady-state heat transfer is expressed in terms of as overall heat transfer coefficient U and the overall temperature difference between the outside and inside AtE = (fo - ti) as given by Eq.(3.1). Also, the wall may consist of composite layers of different materials including insulation. In that case, U will incorporate the effect of all the materials. In the first instance, therefore, it is necessary to evaluate the value of the overall heattransfer coefficient U. Further, since the outside air temperature and solar radiation vary almost periodically over the 24 hours, it is required to establish a method to evaluate the transient heat transfer instead of using Eq.3.1 which is only applicable to steady-state heat transfer. A wall may be composite, consisting of many sections of different construction and insulating materials. Also, the outside and inside wall surfaces may exchange heat by convection and radiation with the surrounding atmosphere. Thus, there will be more than one thermal resistance to heat transfer. Taking into account the number of layers of different

14 materials with varying thickness Ax and thermal conductivity k, we have for the overall heat transfer coefficient and overall thermal resistance R. At q = UAt = - R So that the overall heat-transfer coefficient may be calculated from the relation In Eq.3.9, conductance C has been included which are equivalent to the value of k I Ax for a material. For some materials such as plaster, hollow tiles, etc., data is available in the form of conductance C instead of the thermal conductivity k. These values of C are only applicable to the prescribed thickness Ax. Also, j~ and f; in the equation represent the heat-transfer coefficients for combined convection and radiation for the outside and inside wall surfaces respectively. These terms are also referred to as surface conductance and available in appendix A.4 The properties of thermal conductivity, conductance, specific heat, density, etc., are referred to as thermo physical properties. The same for the common building and insulating materials are given in Table 3.4

15 Table 3.4: Tbermo physical Properties of Selected Building and Insulating Materials (Koeings Berger, et al, 2004) Following example is worked out to understand how to calculate U value for any composite construction. Some of the standard constructions are listed in appendix A.1

16 Example to calculate U -value for the following construction: Plaster on inside wall 12.5mm Outside wall construction : 200 mm concrete block I00 mm brick veneer Partition wall construction : 330 mm brick Roof construction Floor construction Densities, brick 200 mm RCC slab with 4 cm asbestos cement board 200 mm concrete 20000~/m~ Concrete ~ / m ~ Plaster ~ / m ~ Asbestos board 5200 ~ / m ~ Fenestration (Weather - stripped, 2 rn x I K m glass Loose fit) : U = 5.9 W m'2 K-' Doors 1 % m x 2 m wood panels U = 0.63 W ms K' Outdoor-design conditions : 43 C DBT( dry bulb temperature), 27 C WBT( wet bulb temperature), Indoor-design conditions : 25 C DB'T, 50% RH( relative humidity)

17 Daily range : 31"Ct043~C=12~C Occupancy : 100No Lights : 15,000 W fluorescent (Thermal conductivities from Table 3.4) kgss = 0.78 W m-i K' kconcrcte = 1.73 W m-i K" kbriek = 1.32 W K" kplsier = 8.65 W m-i R' kmbestos = W m-' K-I Assumed film coefficients fo = 23 w m" K-I fi = 7 ~ r n - ~ ~ ' Outside wall

18 Partition wall Roof Floor 3.4 Solar radiation: The position of the sun is described by its altitude and azimuth angles. These angles can be easily determined with the help of a solar chart. The solar chart is a graphical representation of the paths of the sun in the sky for various days in the year. Fourteen such charts, one for each of the 14 latitudes, viz. 9", 1 lo, 13", 15", 17", 19O, 21, 23", 2S0, 27O, 2g0, 31, 33" and 35" N covering India are presented in the Climatic hand book published by CBRI, Roorkee. Figure 3.2 shows the sun path diagram for Bangalore which is on12'58' latitude.

19 Fig 3.2 Sun path Diagram The radial lines depict the solar azimuth and the concentric circles indicate the solar altitudes. The center of the chart represents the zenith and the outermost circle, the horizon. The radial graduations marked on the circumference denote the azimuth angles measurcd from north. Series of curved lines running from east to west depict the sun's path for selected days of each month, including the days of solstices and equinox. These lines are crossed by another series of curved lines which represent the hour lines. The hours are integral values by the local solar time. The point of intersection of the sun's path line and the hour line shows the position of the sun at that hour of that particular day. The figure marked on the concentric circle passing

20 through this point gives the altitude of the sun and the reading of the point where the radial line through the aforesaid point meets the scale marked on the perimeter will be the azimuth of the sun. The position of the sun for dates other than those given in these diagrams can be determined by interpolation. Solar radiation values for different latitudes are given in table A.3. The values are listed for latitudes OOto 50 1atitude. The places lying in the intermediate latitudes can be interpolated to get the solar radiation at that place. Table A3(Appendix) also shows the values for different surfaces like north,east, west and south walls as well as north east, south east, south west and north west walls too. The radiations on roof (horizontal surface) are also listed. 3.5 Periodic Heat Transfer through Walls and Roofs: Meat transmission through the walls and roofs of building structures is not steady and is therefore, difficult to evaluate. The two principal factors causing this are: The variation of the outside air temperature over a period of 24 hours. r The variation of the solar radiation intensity that is incident upon the surface over a period of 24 hours. The phenomenon is Mher complicated by the fact that a wall has a thermal capacity due to which a certain amount of heat passing through it is stored and is transmitted to the outside andlor inside at some later time. In nature the variation of climatic conditions produces a non-steady state. Diurnal variations produce an approximately repetitive 24-hour cycle of increasing and decreasing temperatures. The effect of this on a building is that in a hot period, heat flows from the environment into the

21 building where some of it is stored, and at night during the cool period, heat flow is reversed fiom the building to the environment. As the cycle is repetitive, it can be described as periodic heat flow. The diurnal variations of external and internal temperatures during the day occur in a periodically changing thennal regime. In the morning, as the out-door temperature increases, heat starts entering the outer surface of the wall. Each particle in the wall will absorb a certain amount of heat for every degree of rise in temperature; depending on the specific heat of the wall material. Heat to the next particle will only be transmitted after the temperature of the first particle has increased. The out-door temperature will have reached its peak and started decreasing, before the inner surface temperature has reached the same level. From this moment the heat stored in the wall will be dissipated partly to the outside and only partly to the inside. As the out-door air cools, an increasing proportion of this stored heat tlows outwards, and when the wall temperature falls below the indoor temperature the direction of the heat flow is completely reversed. The two quantities characterizing this periodic change are the tie-lag (or phase shift,+) and the decrement factor (or amplitude attenuation,^). The latter is the ratio of the maximum outer and inner surface temperature amplitude taken from the daily mean. The maximum temperature usually occurs just 2-3 hours after solar noon while the minimum temperatures occur just before sunrise. The outside air temperature to follows nearly a harmonic variation. The combined effect of the solar radiation and outside air temperature

22 can be incorporated into a single effective temperatwe. The problem requires a solution of the governing equation for unsteady - state, onedimensional heat transfer, viz. Where t is the temperature at any section of the wall at a distance x from the surface at time (z) and thermal diffusivity (a) given by Where k is the thermal conductivity and pc is the capacity of the wall, in which p and C are density and specific heat respectively. Equation 3.10 is to be solved with the boundary condition of periodic variation of the outside air temperature and solar radiation. The analytical solution of the problem requires many assumptions and is extremely cumbersome. 3.6 Sol-Air Temperature For calculation of heat transfer through structures, it has been found convenient to combine the effect of the outside air temperature and incident solar radiation intensity into a single quantity as was introduced by Mackey and Wright (1943). For the purpose, an expression for the rate of heat transfer (qd from the environment to the outside surface of the wall may be written as 90 = f~ (to -!So )+ a1 3.12

23 Where fo is the outside filmcoefficient of heat transfer, tso is the temperature of the outside surface, a absorptivity of the surface and I the total radiation intensity, as shown in fig.3.3. Introducing an equivalent temperature t, the heat transfer rate equation may be re-written as 40 = fdtc - tso) 3.13 Then, from Eqs. (3.12) and (3.13) This temperature t, is called the sol-air temperature which is also equivalent temperature and can be considered as an equivalent outside air temperature such that the total heat transferred is the same as due to the combined effect of the incident solar radiation and outside air and the wall temperature difference. Fig 3.3 Heat transfer to Outer surface ofa building wall

24 3.7 Empirical methods to evaluate heat transfer through walls and roofs: There are two approaches to empirical calculations of heat transfer through walls and roofs. The decrement factor and time lag method. The equivalent temperature differential method. Both these methods use analytical and experimental results for their formulations. The equivalent temperature differential method is more commonly used, by the air-conditioning engineers as it is also applicable to sunlit walls and roofs and is also less cumbersome Decrement factor and Time lag method: If the thermal capacity of the wall is ignored, then the instantaneous rate of heat transfer through the wall at any time 7 is given by And on an average basis, the mean heat flow is given by But most building materials have a finite capacity which is expressed as m C = pcv = pc (AAx) Where m = Mass of wall p, C = Density and specific heat of wall material A = Cross-sectional area of wall

25 Ax = Wall thickness. & = mean temperature ti = indoor temperature It has been seen that there is a two-fold effect of thermal capacity on heat transfer: There is a time lag between the heat transfer at the outside surface q, and the heat transfer at the inside surface qi, There is a decrement in the heat transfer due to the absorption of heat by the wall and subsequent transfer of a part of this heat back to the outside air when its temperature is lower. The use of the rigorous analytical method to determine the time lag 4 and decrement factor h is quite complicated. The use of finite difference approximation for each wall, roof, etc., for each building is also time-consuming from the point of view of a practicing engineer. Hence an empirical approach based on the determination of 4 and h for standard wall construction, and their use for calculations can be employed. It is observed that the specific heat of most construction materials is about 0.84 kji kg. K. The thermal capacity of most materials, therefore, essentially depends on their density and thickness. Fig.3.4 gives values of time lag for three different densities, while in Fig.3.5 the effect of thickness on the decrement factor has been considered insignificant. In addition to these figures, Tables 3.5 and 3.6gives values for h and 4 for certain constructions taken from the ASHRAE Handbook.

26 - Thickness AK, cm Fig3.4 Time Lag of walls Considering the effect of thermal capacity, the actual heat transfer at any time t is when te,is the sol -air temperature at timer - 4 i.e. 4 hours before the heat transfer is'to be calculated. Fig 3.5 Decrement factor of walls

27 A comparison of Eq (3.18) with Eq. (3.16) shows that Qt can be greater or less than Q, depending on whether &+ is greater or less than t, I$ hours before. The second term in Eq(3.18) therefore, represents the periodic component which is equal to the sum of all such component harmonics. It is evident that if the wall is thick, the decrement factor will be small as is also seen from Tables 3.5 and 3.6. For example, from Table 3.5 the decrement factor for a 150mm concrete roof is 0.48 whereas for a 50mm concrete roof, it is Thus in the case of a very thick wall, the second term on the right hand side in Eq. (3.18) can be ignored so that Eq. (3.16) holds. This implies that the heat transfer across the wall remains uniform at its mean value throughout the day. It is, therefore, advantageous to provide thicker walls in buildings that are not air conditioned. Such buildings will not become excessively hot in summer or extremely cold in winter. Opposite conditions prevail when the wall is too thin. In the limiting case, when the wall thickness approaches zero, the decrement factor h tends to unity and the time lag 9 tends to zero. Eq. (3.15) is applicable. i.e., the heat transfer through the wall is equal to its instantaneous value. Accordingly, for thick wall, the heat gain does not vary much, whereas for thin walls, it varies considerably over 24 hours, The effect of the type of construction on heat gain is shown

28 in fig.3.6. It is seen that a light wall with a low thermal capacity having a time lag of about 3 hours has a maximum heat gain at 3 pm., and great variation in heat transfer over a 24 hour period. A heavier wall with high thermal capacity has a reduced and more uniform heat gain. The peak value occur much later, say at 12 midnight, with a corresponding tie lag of 12 hours. A still heavier construction may result in very small and uniform heat-transfer rate. 'nermal Capacity tieavy Wall High x ----/ I N Solar rime, M - Fig 3.6 Heat Gain-Solar Time Thus in a locality where the daily range of variation of the outside air temperature is small, it is immaterial what thickness of wall is provided. But in a locality where the daily range of temperature is large, it is desirable to have thick walls so as to cut the cooling load in summer and the heating load in winter. Moreover, such walls will not allow the inside temperature to rise very much during the day and drop at night, and thus maintains a reasonably uniform and moderate inside temperature even without air conditioning. Also, in buildings that are not conditioned, night ventilation helps to maintain them cooler during the day.

29 Table 3.5 Amplitude Decrement Factor and Time Lag of Shaded Walls Construction 10 cm brick or stone veneer + frame 20 cm hollow tile or 30 cm cinder block 10 cm brick or concrete 20 cm brick or concrete, or Decrement Factor Time Lag 4 hours 30 cm hollow tile or cinder block 0.39 I I I I Table 3.6 Amplitude Decrement Factor and Time Lag of Roofs Exposed to Sun h Construction 5 cm concrete 5 cm concrete + 5 cm insulating board 10 cm concrete 15 cm concrete 15 cm hollow tile or cinder block 5 cm insulating board Decrement Factor li Time Lag 4 hours Equivalent Temperature Differential Method. Equation (3.18) for heat transfer through walls and roofs can also be expressed in terms of an equivalent temperature differential AtE defined Qt = UA(t em - ti) f UAa (ter., - tern = UA At,

30 So that Thus AtE when multiplied by AU gives the heat transfer rate. It can be seen that A~E depends on: r Decrement factor h and time la&, which in turn depend on the thermo physical properties of the construction. The outside air temperature t, and solar radiation intensity I Room temperature ti. Thus, the equivalent temperature differential approach takes care of the exposure of the wall or roof to the sun. Tables for AtE are prepared for fixed values oft, and ti, for different types of constructions, and as a hction of latitude and tie for roofs, and latitude, time and orientation for walls. It will be noticed from these tables A.5 in Appendix, that the effect of density and wall thickness is incorporated by specifying the mass of the wall per unit area of its crosssection. Further, it must be pointed out here that these tables have been established from calculations made on an analogue computer using Schmidt's method( Arora C.P,2000) based on the conditions given below. Latitude 40' N, but normally suitable for latitudes 0 to 50 N, for the hottest summer period. An outdoor daily range of a dry bulb temperature of 11. lo C (20" F). An outside and inside design temperature difference of 8.3OC (1 5" F)

31 0 Dark colour walls and roofs with absorptivity of 0.9 A specific heat of the construction material of kj/kg.k. When there is a departure from these conditions, the following corrections may be applied. The values of b and ti are additive to A~E. Hence add or subtract the difference of t, - ti and 8.3" C. If the daily range is different from 1 1.lo C, then apply effective corrections as follows: a) For each 1" C difference Add 0.25O for medium construction Less than 11.1" C Add 0.5" for heavy construction b) For each 1" C difference Subtract 0.25" for medium construction Greater than " C c) Maximum correction d) Light construction Subtract 0.5" for heavy construction. 2" for medium and 3" for heavy Construction. No correction. Example to calculate effective temperature (At,): Thickness and density of wall Ax = 0.25 m p = N lm2 Mass of wall: m = p (Ax) A = (2400)(0.25) (1) = 6000 ~ / area m ~

32 Overall heat - transfer coefficient U value Outdoor daily range Outside and inside temperature difference Correction for equivalent temperature difference The following table gives the values of equivalent temperature differentials from Table A.5 (Appendix) and those obtained after correction by adding to the values from the table. The table also gives the calculated values of the heat flux from the relation.

33 115 Table 3.7 Corrected Effective Temperatures 3.8 Present study: In the present study heat loads due to conduction, radiation, transmission gain, and internal heat gain in the form of both latent heat and sensible heat are accounted for. The out door air bypassed is also accounted for. The method followed to calculate heat loads is Equivalent Temperature Differential (ETD) method. Heat loads due to infiltration, transmission gain through partition walls, ceiling, floor, etc, are ignored. a Infiltration is ignored as pressure inside the building is more and the leakage due to outdoor air entering the conditioned building does not happen. There is actually no infiltration as the room is under positive pressure. There is however exfiltration which is equivalent to exhaust of room air. When the doors are operated it is the indoor conditioned air which goes out.

34 a Supply duct heat gain and losses in the duct, fan horse power are also ignored as this heat load remains constant for all the simulations. A factor of safety of 5% of the total heat load is added to the final heat load. r To calculate internal heat gain, human occupancy is calculated based on the assumption that 5.5sqm area (as recommended by Time Savers Standard) is required per person, and one light fixture is required for this area. As the plan area increases the occupancy and number of light fixtures also increases. This is considered while calculating heat loads for different plan areas. r loow per person is assumed as heat load generated by the appliance the person uses. 75 W per person is the sensible heat and 65W per person is the latent heat assumed in calculating heat loads. In the present study heat loads are calculated for different volumes, ranging from l5ocwn to 180,000cum and two different combinations of materials, north-south and east-west orientations, and percentage fenestrations on each of the walls and varying Length to Breadth ratios for the same orientation and plan area. Approximately 850 combinations of the above parameters are considered and heat loads are computed.