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Investigation of wall's optimum insulation position from maximum time lag and minimum decrement factor point of view
Energy and Buildings 32 Ž2000. 197–203 www.elsevier.comrlocaterenbuild
Investigation of wall’s optimum insulation position from maximum time lag and minimum decrement factor point of view H. Asan Department of Mechanical Engineering, Karadeniz Technical UniÕersity, 61080 Trabzon, Turkey Received 6 December 1999; received in revised form 19 December 1999; accepted 28 December 1999
Abstract In this study, optimum insulation position from maximum time lag and minimum decrement factor point of view has been investigated numerically. For this purpose, one-dimensional transient heat conduction equation was solved for a composite wall using Crank–Nicolson’s scheme under periodic convection boundary conditions. Four-centimeter thick insulation was placed in different positions of 20-cm thick wall as a whole Ž1 piece, 4 cm. or as two slices Ž2 q 2 cm.. Total six different configurations were selected as initial state, and these configurations were swept across the wall cross-section where time lags and decrement factors were calculated. Placing half of the insulation in the inner surface and the other half in the outer surface of the wall gives minimum decrement factor. On the other hand, maximum time lag was obtained in the case of placing two slices of insulation in a certain distance apart inside the wall. Placing half of the insulation in the mid-center plane of the wall and the half of it in the outer surface of the wall gives very high time lags and low decrement factors Žclose to optimum values.. This configuration is very practical and can be done without any difficulty during construction. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Optimum insulation position; Time lag; Decrement factor
1. Introduction At the cross-section of the outer wall of a building, there are different temperature profiles during any instant of a 1-day period. These profiles are functions of inside temperature, outside temperature and thermophysical properties of the wall. Since the outside temperature changes periodically during a 1-day period, there will be new temperature profiles at any instant of time of the day. During this transient process, a heat wave flows through the wall from outside to inside, and the amplitude of these waves shows the temperature magnitudes, and wavelength of the waves shows the time. The amplitude of the heat wave on the outer surface of the wall is based on solar radiation and convection in-between the outer surface of the wall and ambient air. During the propagation of this heat wave through the wall, its amplitude will decrease depending on the thermophysical properties of wall materials. When this wave reaches the inner surface, it will have an amplitude that is considerably smaller than the value it had at the outer surface. The times it takes for heat wave to propagate from outer surface to the inner surface named as ‘time lag’ and the decreasing ratio of its amplitude during
this process is named as ‘decrement factor’ w1x. Time lag and decrement factors are very important characteristics to determine the heat storage capabilities of any materials. Depending on the thermophysical properties and thickness of the wall materials, different time lags and decrement factors can be obtained. In recently conducted studies by the present author, effects of wall’s thermophysical properties, insulation thickness and position on time lag and decrement factor were investigated. It was shown that thermophysical properties, thickness and position of wall materials have a very profound effect on the time lag and decrement factor w2,3x. These studies were parametric in nature and most of the results came out from these work are not practical. If we look at the insulation industry, we see that most of the manufactured heat insulation materials are being sold as sheets that have different thickness. During the wall construction, practically these insulation sheets can be placed in the inner surface, in the outer surface or in the mid-center plane of the wall. If we need to increase the heat insulation capabilities of already constructed walls or old buildings, then the only places we can put these insulation sheets are the inner surface and outer surface of the wall.
0378-7788r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 8 - 7 7 8 8 Ž 0 0 . 0 0 0 4 4 - X
H. Asan r Energy and Buildings 32 (2000) 197–203
198
In this study, optimum insulation position from maximum time lag and minimum decrement factor point of view has been investigated numerically. Four-centimeter thick insulation was placed in different positions of 20-cm thick wall as a whole Ž1 piece, 4 cm. or as two slices Ž2 q 2 cm.. After detailed investigation, some practical solutions are suggested.
2. Time lag f, decrement factor f and sol–air temperature Tsa Time lag and decrement factor are very important characteristics to determine the heat storage capabilities of any material. As mentioned before, the time it takes for heat wave to propagate from outer surface to the inner surface named as ‘time lag’ and the decreasing ratio of its amplitude during this process is named as ‘decrement factor’. The schematics of time lag and decrement factor are shown in Fig. 1. In this study, the time lag and decrement factor are computed as follows. The time lag is defined as:
°t f s~t ¢t
Toma x Toma x Toma x
)
t Tema x
-
t Temax
s
t Temax
´ ´ ´
t Toma x y t Tema x t Tomax y t Temax q P
Ž 1.
P
where t T oma x and t T omin Žh. represents the time in hours when inside and outside surface temperatures are at their maxi-
Fig. 2. Comparison of sol–air temperatures.
mum, respectively, and P Ž24 h. is the period of the wave. The decrement factor is defined as:
fs
Ao Ae
s
Tomax y Tomin Temax y Temin
Ž 2.
where A o and A e are the amplitudes of the wave in the inner and outer surfaces of the wall, respectively. The sol–air temperature, Tsa , includes the effects of the solar radiation combined with outside air temperature and changes periodically. This temperature is assumed to show sinusoidal variations during a 24-h period. Since time lag and decrement factor are dependent on only wall material
Fig. 1. The schematic representation of time lag f and decrement factor f.
H. Asan r Energy and Buildings 32 (2000) 197–203
not the climatological data w4x, very general equation for sol–air temperature is taken as follows: Tsa Ž t . s
< Tmax y Tmin < 2 q Tmin
sin
ž
2p t
p y
P
2
/
q
ET k
2
Ž 3.
3. Methods In this study, the wall under investigation is assumed to be only in x direction and time-dependent. The problem geometry is shown in Fig. 3. The one-dimensional, transient heat conduction equation for this problem is as follows: E2 T Ex
2
ET s r Cp
Et
conditions are present. At the inner surface, the boundary condition is
< Tmax y Tmin <
The profile of this sol–air temperature and the one which was obtained from a real climatological data by Threlkeld w5x is presented in Fig. 2. As seen from Fig. 2, Eq. Ž3. is a very reasonable choice for sol–air temperature.
k
199
Ž 4.
where k is the thermal conductivity, r is the density and Cp is the heat capacity of the wall material. To solve this problem, two boundary conditions and one initial condition are needed. On both sides of wall, convection boundary
ž / Ex
s h i Txs0 Ž t . y Ti
Ž 5.
xs 0
whereas on the outer surface of the wall, the boundary condition can be written as ET k
ž / Ex
s h o Tsa Ž t . y TxsLŽ t .
Ž 6.
xs L
Here, h i is the wall inner surface heat transfer coefficient, h o the wall outer surface heat transfer coefficient, Txs0 is the wall inner surface temperature, Txs L is the wall outer surface temperature, Ti is the room air temperature and TsaŽ t . is the ‘sol–air temperature’. As an initial condition, the steady-state solution of the problem at t s 0 is taken. In the computations, inside temperature of a room, Ti , is taken to be constant. As seen in Eq. Ž3., TsaŽ t . changes in between Tmax and Tmin during the 24-h period. The problem now is reduced to one-dimensional heat conduction, which has a periodic boundary condition on the outer surface, the sol–air temperature boundary condition, and normal convection boundary condition on the inner surface. The analytical solution of this problem for one layer is given in Ref. w5x. Here, the algorithm is developed to take care of n layers. For this
Fig. 3. The schematic of the problem geometry.
200
H. Asan r Energy and Buildings 32 (2000) 197–203
Fig. 4. Comparison of present computations with analytical solution of Threlkeld w5x.
purpose, finite-difference formulation of Eq. Ž4. is obtained and the Crank–Nicolson’s method is applied. The input values of code are: number of layers, the thickness of each layer, density of each layer, specific heat and conductivity of each layer and heat generation of each layer, if any. To interpret the graphics and the results better, Tmin s 08C and Tmax s 18C were selected in Eq. Ž3., and indoor temperature 0.58C is selected, accordingly. The outputs of the code were time lag, decrement factor, wall inner surface temperature and the temperature of any location at any time of the day. To test the correctness of the code developed, computed time-dependent heat fluxes across the wall were compared with harmonic analysis results of Threlkeld w5x in Fig. 4. As seen in Fig. 4, computed results of present study match pretty well with harmonic analysis results of Threlkeld. The detailed of the analytical solution for one layer with real climatological data can be found in the work of Threlkeld w5x.
Here, initially, half of the insulation Ž2 cm. is placed in the inner surface of the wall and the other half Ž2 cm. is placed in the outer surface of the wall. Then these two pieces of insulation were being moved to each other, sweeping every point in the wall and finally they ended up as a one-piece insulation Ž4 cm. in the center mid-plane of the wall Ž2-C.. The third configuration is 3-A. Here, initially, half of the insulation is placed in the inner surface, half of it placed in the mid-center plane of the wall. The distance between these two insulation boards was 10 cm at the beginning Ž3-A.. Then, keeping this 10-cm distance constant, two pieces were swept from inner
4. Thermal mass-insulation configurations Fig. 5 shows different configurations of insulation inside the wall. For healthy interpretation of present results, good understanding of thermal mass-insulation configuration is very important. In Fig. 5, A, B and C show the beginning, middle and end points, respectively, of the sweeping of insulation geometry inside the wall. A total of six initial thermal mass-insulation configurations are selected. These are 1-A, 2-A, 3-A, 4-A, 5-A and 6-A. In 1-A, insulation is placed as one piece Ž4 cm. in the inner surface of the 20-cm wall. Then it was swept as a whole from inner to outer surfaces of the wall and ended in 1-C. 2-A is the second initial wall-insulation configuration.
Fig. 5. Thermal mass–insulation configurations.
H. Asan r Energy and Buildings 32 (2000) 197–203
surface to outer surface as seen in Fig. 5 Ž3-A, 3-B, 3-C.. In Fig. 5, 4-A is the fourth initial thermal mass-insulation configuration. As seen in Fig. 2, 4-A is exactly the same with 2-A initial configuration. But here sweeping is different. As seen in 4-B and 4-C in Fig. 5, the insulation in the outer surface stays in place and the inner surface insulation board moves towards to outer surface finally ending up as a 4-cm insulation in the outer surface Ž4-C.. 5-A is the fifth initial wall-insulation configuration and, as seen, it is exactly the same with 2-A and 4-A at the beginning. Here, after the initial state Ž5-A., the inner insulation stays in place and the outer insulation moves towards to the inner surface insulation finally ending up as a one-piece Ž4 cm. insulation in the inner surface Ž5-C.. The last configuration is presented in 6-A of Fig. 5 where half of the insulation is placed in the mid-center plane of the wall and the other half placed in the outer surface of the wall. Then, the outer surface insulation stays in place and the insulation in the mid-center plane of the wall moves toward to outer surface of the wall ending up with 4 cm insulation in the outer surface of the wall Ž6-C..
201
5. Results and discussion Two different thermal masses Ž20-cm thick brick and granite blocks. and two different insulation boards Ž2 q 2 cm two polyurethane sheets and 2 q 2 cm two cork sheets. are selected in this study Ž k granite f 5k brick , Cgranite f 1.6C brick , k cork f 1.3k polyurethane , Ccork f 12Cpolyurethane .. Figs. 6 and 7 show time lag and decrement factor variation vs. thermal mass-insulation configuration as discussed in Section 3. In Fig. 6a and b, time lags and decrement factors are presented for brick as a thermal mass and polyurethane board as an insulation material. In Fig. 6c and d, time lags and decrement factors are presented for brick as thermal mass and cork board as an insulation material. In Fig. 7a and b, time lags and decrement factors are presented for granite as a thermal mass and polyurethane board as an insulation material. In Fig. 7c and d, time lags and decrement factors are presented for granite as a thermal mass and cork board as an insulation material. The following conclusions can be drawn from these results.
Fig. 6. Ža. Variation of time lag vs. different configurations of brick as a thermal mass and polyurethane board as an insulation. Žb. Variation of decrement factor vs. different configurations of brick as a thermal mass and polyurethane board as an insulation. Žc. Variation of time lag vs. different configurations of brick as a thermal mass and cork board as an insulation. Žd. Variation of decrement factor vs. different configurations of brick as a thermal mass and cork board as an insulation.
202
H. Asan r Energy and Buildings 32 (2000) 197–203
Fig. 7. Ža. Variation of time lag vs. different configurations of granite as a thermal mass and polyurethane board as an insulation. Žb. Variation of decrement factor vs. different configurations of granite as a thermal mass and polyurethane board as an insulation. Žc. Variation of time lag vs. different configurations of granite as a thermal mass and cork board as an insulation. Žd. Variation of decrement factor vs. different configurations of granite as a thermal mass and cork board as an insulation.
Ž1. A-2, A-4 and A-5 configurations Žplacing half of the insulation in the inner wall surface, half of the insulation in the outer wall surface. result the best decrement factors Žminimum decrement factors. among the all configurations considered ŽFigs. 6b,d and 7b,d.. Ž2. The best result for time lag Žmaximum time lag. is for the case where two pieces of insulation are placed in a certain distance apart from each other in the wall Žthey are equally located from the inner and outer surfaces of the wall.. This is somewhere between 2-B and 2-C in Figs. 6a,c and 7a,c. This distance is 5 cm for polyurethane and 4 cm for cork. So as the heat capacity of the insulation increases, the distance gets smaller Ž k cork f 1.3k polyurethane , Ccork f 12Cpolyurethane .. Ž3. The worst situation is for the case of placing insulation as a whole Žwithout slicing it. in any position of the wall except in the outer surface ŽA-1 C-1, C-2, C-5. where minimum time lags and maximum decrement factors occur. As explained above, the optimum positions of insulation do not coincide from maximum time lag and minimum decrement factor point of view. Also, the optimum position of insulation from maximum time lag point of view is not practical Žwhere two pieces of insulation are
™
placed in a certain distance apart from each other in the wall.. During the wall construction, practically, these insulation sheets can be placed in the inner surface, in the outer surface or in the mid-center plane of the wall. If we need to increase the heat insulation capabilities of already constructed walls or old buildings, then the only places we can put these insulation sheets are the inner surface and outer surface of the wall. So looking at Figs. 6 and 7, the following practical recommendations can be suggested. Ž1. Never use the insulation as a whole in any location of the wall except in the outer surface wall. This gives the worst results for maximum time lag and minimum decrement factor point of view. Ž2. Placing half of the insulation in the mid-center plane of the wall and the half of it in the outer surface of the wall ŽA-6. gives very high time lags and low decrement factors Žclose to optimum values.. This configuration is very practical and can be done without any difficulty during construction. References w1x R.J. Duffin, A passive wall design to minimize building temperature swings, Sol. Energy 33 Ž3–4. Ž1984. 337–342.
H. Asan r Energy and Buildings 32 (2000) 197–203 w2x H. Asan, Y.S. Sancaktar, Effects of Wall’s thermophysical properties on time lag and decrement factor, Energy and Building 28 Ž1998. 159–166. w3x H. Asan, Effects of wall’s insulation thickness and position on time lag and decrement factor, Energy and Building 28 Ž1998. 299–305.
203
w4x P.J. Burns, K. Han, C.B. Winn, Dynamic effects of bang-bang control on the thermal performance of walls of various constructions, Sol. Energy 46 Ž3. Ž1991. 129–138. w5x J.L. Threlkeld, Thermal Environmental Engineering, Prentice-Hall, Englewood Cliffs, NJ, 1970.
Investigation of wall’s optimum insulation position from maximum time lag and minimum decrement factor point of view H. Asan Department of Mechanical Engineering, Karadeniz Technical UniÕersity, 61080 Trabzon, Turkey Received 6 December 1999; received in revised form 19 December 1999; accepted 28 December 1999
Abstract In this study, optimum insulation position from maximum time lag and minimum decrement factor point of view has been investigated numerically. For this purpose, one-dimensional transient heat conduction equation was solved for a composite wall using Crank–Nicolson’s scheme under periodic convection boundary conditions. Four-centimeter thick insulation was placed in different positions of 20-cm thick wall as a whole Ž1 piece, 4 cm. or as two slices Ž2 q 2 cm.. Total six different configurations were selected as initial state, and these configurations were swept across the wall cross-section where time lags and decrement factors were calculated. Placing half of the insulation in the inner surface and the other half in the outer surface of the wall gives minimum decrement factor. On the other hand, maximum time lag was obtained in the case of placing two slices of insulation in a certain distance apart inside the wall. Placing half of the insulation in the mid-center plane of the wall and the half of it in the outer surface of the wall gives very high time lags and low decrement factors Žclose to optimum values.. This configuration is very practical and can be done without any difficulty during construction. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Optimum insulation position; Time lag; Decrement factor
1. Introduction At the cross-section of the outer wall of a building, there are different temperature profiles during any instant of a 1-day period. These profiles are functions of inside temperature, outside temperature and thermophysical properties of the wall. Since the outside temperature changes periodically during a 1-day period, there will be new temperature profiles at any instant of time of the day. During this transient process, a heat wave flows through the wall from outside to inside, and the amplitude of these waves shows the temperature magnitudes, and wavelength of the waves shows the time. The amplitude of the heat wave on the outer surface of the wall is based on solar radiation and convection in-between the outer surface of the wall and ambient air. During the propagation of this heat wave through the wall, its amplitude will decrease depending on the thermophysical properties of wall materials. When this wave reaches the inner surface, it will have an amplitude that is considerably smaller than the value it had at the outer surface. The times it takes for heat wave to propagate from outer surface to the inner surface named as ‘time lag’ and the decreasing ratio of its amplitude during
this process is named as ‘decrement factor’ w1x. Time lag and decrement factors are very important characteristics to determine the heat storage capabilities of any materials. Depending on the thermophysical properties and thickness of the wall materials, different time lags and decrement factors can be obtained. In recently conducted studies by the present author, effects of wall’s thermophysical properties, insulation thickness and position on time lag and decrement factor were investigated. It was shown that thermophysical properties, thickness and position of wall materials have a very profound effect on the time lag and decrement factor w2,3x. These studies were parametric in nature and most of the results came out from these work are not practical. If we look at the insulation industry, we see that most of the manufactured heat insulation materials are being sold as sheets that have different thickness. During the wall construction, practically these insulation sheets can be placed in the inner surface, in the outer surface or in the mid-center plane of the wall. If we need to increase the heat insulation capabilities of already constructed walls or old buildings, then the only places we can put these insulation sheets are the inner surface and outer surface of the wall.
0378-7788r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 8 - 7 7 8 8 Ž 0 0 . 0 0 0 4 4 - X
H. Asan r Energy and Buildings 32 (2000) 197–203
198
In this study, optimum insulation position from maximum time lag and minimum decrement factor point of view has been investigated numerically. Four-centimeter thick insulation was placed in different positions of 20-cm thick wall as a whole Ž1 piece, 4 cm. or as two slices Ž2 q 2 cm.. After detailed investigation, some practical solutions are suggested.
2. Time lag f, decrement factor f and sol–air temperature Tsa Time lag and decrement factor are very important characteristics to determine the heat storage capabilities of any material. As mentioned before, the time it takes for heat wave to propagate from outer surface to the inner surface named as ‘time lag’ and the decreasing ratio of its amplitude during this process is named as ‘decrement factor’. The schematics of time lag and decrement factor are shown in Fig. 1. In this study, the time lag and decrement factor are computed as follows. The time lag is defined as:
°t f s~t ¢t
Toma x Toma x Toma x
)
t Tema x
-
t Temax
s
t Temax
´ ´ ´
t Toma x y t Tema x t Tomax y t Temax q P
Ž 1.
P
where t T oma x and t T omin Žh. represents the time in hours when inside and outside surface temperatures are at their maxi-
Fig. 2. Comparison of sol–air temperatures.
mum, respectively, and P Ž24 h. is the period of the wave. The decrement factor is defined as:
fs
Ao Ae
s
Tomax y Tomin Temax y Temin
Ž 2.
where A o and A e are the amplitudes of the wave in the inner and outer surfaces of the wall, respectively. The sol–air temperature, Tsa , includes the effects of the solar radiation combined with outside air temperature and changes periodically. This temperature is assumed to show sinusoidal variations during a 24-h period. Since time lag and decrement factor are dependent on only wall material
Fig. 1. The schematic representation of time lag f and decrement factor f.
H. Asan r Energy and Buildings 32 (2000) 197–203
not the climatological data w4x, very general equation for sol–air temperature is taken as follows: Tsa Ž t . s
< Tmax y Tmin < 2 q Tmin
sin
ž
2p t
p y
P
2
/
q
ET k
2
Ž 3.
3. Methods In this study, the wall under investigation is assumed to be only in x direction and time-dependent. The problem geometry is shown in Fig. 3. The one-dimensional, transient heat conduction equation for this problem is as follows: E2 T Ex
2
ET s r Cp
Et
conditions are present. At the inner surface, the boundary condition is
< Tmax y Tmin <
The profile of this sol–air temperature and the one which was obtained from a real climatological data by Threlkeld w5x is presented in Fig. 2. As seen from Fig. 2, Eq. Ž3. is a very reasonable choice for sol–air temperature.
k
199
Ž 4.
where k is the thermal conductivity, r is the density and Cp is the heat capacity of the wall material. To solve this problem, two boundary conditions and one initial condition are needed. On both sides of wall, convection boundary
ž / Ex
s h i Txs0 Ž t . y Ti
Ž 5.
xs 0
whereas on the outer surface of the wall, the boundary condition can be written as ET k
ž / Ex
s h o Tsa Ž t . y TxsLŽ t .
Ž 6.
xs L
Here, h i is the wall inner surface heat transfer coefficient, h o the wall outer surface heat transfer coefficient, Txs0 is the wall inner surface temperature, Txs L is the wall outer surface temperature, Ti is the room air temperature and TsaŽ t . is the ‘sol–air temperature’. As an initial condition, the steady-state solution of the problem at t s 0 is taken. In the computations, inside temperature of a room, Ti , is taken to be constant. As seen in Eq. Ž3., TsaŽ t . changes in between Tmax and Tmin during the 24-h period. The problem now is reduced to one-dimensional heat conduction, which has a periodic boundary condition on the outer surface, the sol–air temperature boundary condition, and normal convection boundary condition on the inner surface. The analytical solution of this problem for one layer is given in Ref. w5x. Here, the algorithm is developed to take care of n layers. For this
Fig. 3. The schematic of the problem geometry.
200
H. Asan r Energy and Buildings 32 (2000) 197–203
Fig. 4. Comparison of present computations with analytical solution of Threlkeld w5x.
purpose, finite-difference formulation of Eq. Ž4. is obtained and the Crank–Nicolson’s method is applied. The input values of code are: number of layers, the thickness of each layer, density of each layer, specific heat and conductivity of each layer and heat generation of each layer, if any. To interpret the graphics and the results better, Tmin s 08C and Tmax s 18C were selected in Eq. Ž3., and indoor temperature 0.58C is selected, accordingly. The outputs of the code were time lag, decrement factor, wall inner surface temperature and the temperature of any location at any time of the day. To test the correctness of the code developed, computed time-dependent heat fluxes across the wall were compared with harmonic analysis results of Threlkeld w5x in Fig. 4. As seen in Fig. 4, computed results of present study match pretty well with harmonic analysis results of Threlkeld. The detailed of the analytical solution for one layer with real climatological data can be found in the work of Threlkeld w5x.
Here, initially, half of the insulation Ž2 cm. is placed in the inner surface of the wall and the other half Ž2 cm. is placed in the outer surface of the wall. Then these two pieces of insulation were being moved to each other, sweeping every point in the wall and finally they ended up as a one-piece insulation Ž4 cm. in the center mid-plane of the wall Ž2-C.. The third configuration is 3-A. Here, initially, half of the insulation is placed in the inner surface, half of it placed in the mid-center plane of the wall. The distance between these two insulation boards was 10 cm at the beginning Ž3-A.. Then, keeping this 10-cm distance constant, two pieces were swept from inner
4. Thermal mass-insulation configurations Fig. 5 shows different configurations of insulation inside the wall. For healthy interpretation of present results, good understanding of thermal mass-insulation configuration is very important. In Fig. 5, A, B and C show the beginning, middle and end points, respectively, of the sweeping of insulation geometry inside the wall. A total of six initial thermal mass-insulation configurations are selected. These are 1-A, 2-A, 3-A, 4-A, 5-A and 6-A. In 1-A, insulation is placed as one piece Ž4 cm. in the inner surface of the 20-cm wall. Then it was swept as a whole from inner to outer surfaces of the wall and ended in 1-C. 2-A is the second initial wall-insulation configuration.
Fig. 5. Thermal mass–insulation configurations.
H. Asan r Energy and Buildings 32 (2000) 197–203
surface to outer surface as seen in Fig. 5 Ž3-A, 3-B, 3-C.. In Fig. 5, 4-A is the fourth initial thermal mass-insulation configuration. As seen in Fig. 2, 4-A is exactly the same with 2-A initial configuration. But here sweeping is different. As seen in 4-B and 4-C in Fig. 5, the insulation in the outer surface stays in place and the inner surface insulation board moves towards to outer surface finally ending up as a 4-cm insulation in the outer surface Ž4-C.. 5-A is the fifth initial wall-insulation configuration and, as seen, it is exactly the same with 2-A and 4-A at the beginning. Here, after the initial state Ž5-A., the inner insulation stays in place and the outer insulation moves towards to the inner surface insulation finally ending up as a one-piece Ž4 cm. insulation in the inner surface Ž5-C.. The last configuration is presented in 6-A of Fig. 5 where half of the insulation is placed in the mid-center plane of the wall and the other half placed in the outer surface of the wall. Then, the outer surface insulation stays in place and the insulation in the mid-center plane of the wall moves toward to outer surface of the wall ending up with 4 cm insulation in the outer surface of the wall Ž6-C..
201
5. Results and discussion Two different thermal masses Ž20-cm thick brick and granite blocks. and two different insulation boards Ž2 q 2 cm two polyurethane sheets and 2 q 2 cm two cork sheets. are selected in this study Ž k granite f 5k brick , Cgranite f 1.6C brick , k cork f 1.3k polyurethane , Ccork f 12Cpolyurethane .. Figs. 6 and 7 show time lag and decrement factor variation vs. thermal mass-insulation configuration as discussed in Section 3. In Fig. 6a and b, time lags and decrement factors are presented for brick as a thermal mass and polyurethane board as an insulation material. In Fig. 6c and d, time lags and decrement factors are presented for brick as thermal mass and cork board as an insulation material. In Fig. 7a and b, time lags and decrement factors are presented for granite as a thermal mass and polyurethane board as an insulation material. In Fig. 7c and d, time lags and decrement factors are presented for granite as a thermal mass and cork board as an insulation material. The following conclusions can be drawn from these results.
Fig. 6. Ža. Variation of time lag vs. different configurations of brick as a thermal mass and polyurethane board as an insulation. Žb. Variation of decrement factor vs. different configurations of brick as a thermal mass and polyurethane board as an insulation. Žc. Variation of time lag vs. different configurations of brick as a thermal mass and cork board as an insulation. Žd. Variation of decrement factor vs. different configurations of brick as a thermal mass and cork board as an insulation.
202
H. Asan r Energy and Buildings 32 (2000) 197–203
Fig. 7. Ža. Variation of time lag vs. different configurations of granite as a thermal mass and polyurethane board as an insulation. Žb. Variation of decrement factor vs. different configurations of granite as a thermal mass and polyurethane board as an insulation. Žc. Variation of time lag vs. different configurations of granite as a thermal mass and cork board as an insulation. Žd. Variation of decrement factor vs. different configurations of granite as a thermal mass and cork board as an insulation.
Ž1. A-2, A-4 and A-5 configurations Žplacing half of the insulation in the inner wall surface, half of the insulation in the outer wall surface. result the best decrement factors Žminimum decrement factors. among the all configurations considered ŽFigs. 6b,d and 7b,d.. Ž2. The best result for time lag Žmaximum time lag. is for the case where two pieces of insulation are placed in a certain distance apart from each other in the wall Žthey are equally located from the inner and outer surfaces of the wall.. This is somewhere between 2-B and 2-C in Figs. 6a,c and 7a,c. This distance is 5 cm for polyurethane and 4 cm for cork. So as the heat capacity of the insulation increases, the distance gets smaller Ž k cork f 1.3k polyurethane , Ccork f 12Cpolyurethane .. Ž3. The worst situation is for the case of placing insulation as a whole Žwithout slicing it. in any position of the wall except in the outer surface ŽA-1 C-1, C-2, C-5. where minimum time lags and maximum decrement factors occur. As explained above, the optimum positions of insulation do not coincide from maximum time lag and minimum decrement factor point of view. Also, the optimum position of insulation from maximum time lag point of view is not practical Žwhere two pieces of insulation are
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placed in a certain distance apart from each other in the wall.. During the wall construction, practically, these insulation sheets can be placed in the inner surface, in the outer surface or in the mid-center plane of the wall. If we need to increase the heat insulation capabilities of already constructed walls or old buildings, then the only places we can put these insulation sheets are the inner surface and outer surface of the wall. So looking at Figs. 6 and 7, the following practical recommendations can be suggested. Ž1. Never use the insulation as a whole in any location of the wall except in the outer surface wall. This gives the worst results for maximum time lag and minimum decrement factor point of view. Ž2. Placing half of the insulation in the mid-center plane of the wall and the half of it in the outer surface of the wall ŽA-6. gives very high time lags and low decrement factors Žclose to optimum values.. This configuration is very practical and can be done without any difficulty during construction. References w1x R.J. Duffin, A passive wall design to minimize building temperature swings, Sol. Energy 33 Ž3–4. Ž1984. 337–342.
H. Asan r Energy and Buildings 32 (2000) 197–203 w2x H. Asan, Y.S. Sancaktar, Effects of Wall’s thermophysical properties on time lag and decrement factor, Energy and Building 28 Ž1998. 159–166. w3x H. Asan, Effects of wall’s insulation thickness and position on time lag and decrement factor, Energy and Building 28 Ž1998. 299–305.
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w4x P.J. Burns, K. Han, C.B. Winn, Dynamic effects of bang-bang control on the thermal performance of walls of various constructions, Sol. Energy 46 Ž3. Ž1991. 129–138. w5x J.L. Threlkeld, Thermal Environmental Engineering, Prentice-Hall, Englewood Cliffs, NJ, 1970.