The Impact of Roof Pitch and Ceiling Insulation on Cooling Load of Naturally-Ventilated Attics

Transcription

1 University of Nebraska - Linoln DigitalCommons@University of Nebraska - Linoln Arhitetural Engineering -- Faulty Publiations Arhitetural Engineering and Constrution, Durham Shool of 2012 The Impat of Roof Pith and Ceiling Insulation on Cooling Load of Naturally-Ventilated Attis Shimin Wang University of Nebraska - Linoln, shiminwang@live.om Zhigang Shen University of Nebraska - Linoln, shen@unl.edu Linxia Gu University of Nebraska-Linoln, lgu2@unl.edu Follow this and additional works at: Part of the Arhitetural Engineering Commons, Constrution Engineering Commons, Environmental Design Commons, and the Other Engineering Commons Wang, Shimin; Shen, Zhigang; and Gu, Linxia, "The Impat of Roof Pith and Ceiling Insulation on Cooling Load of Naturally- Ventilated Attis" (2012). Arhitetural Engineering -- Faulty Publiations This Artile is brought to you for free and open aess by the Arhitetural Engineering and Constrution, Durham Shool of at DigitalCommons@University of Nebraska - Linoln. It has been aepted for inlusion in Arhitetural Engineering -- Faulty Publiations by an authorized administrator of DigitalCommons@University of Nebraska - Linoln.

2 Wang, Shen, & Gu in MDPI Energies (2012) 5. Copyright 2012, the authors. Liensee MDPI, Basel, Switzerland. Open aess, Creative Commons Attribution liense 4.0. Energies 2012, 5, ; doi: /en Artile OPEN ACCESS energies ISSN The Impat of Roof Pith and Ceiling Insulation on Cooling Load of Naturally-Ventilated Attis Shimin Wang 1, Zhigang Shen 1, * and Linxia Gu Durham Shool of Arhitetural Engineering and Constrution, University of Nebraska-Linoln, Linoln, NE 68588, USA; shiminwang@live.om Department of Mehanial and Materials Engineering, University of Nebraska-Linoln, NE 68588, Linoln, USA; lgu@unl.edu * Author to whom orrespondene should be addressed; shen@unl.edu; Tel.: ; Fax: Reeived: 29 May 2012; in revised form: 29 June 2012 / Aepted: 29 June 2012 / Published: 4 July 2012 Abstrat: A 2D unsteady omputational fluid dynamis (CFD) model is employed to simulate buoyany-driven turbulent ventilation in attis with different pith values and eiling insulation levels under summer onditions. The impats of roof pith and eiling insulation on the ooling load of gable-roof residential buildings are investigated based on the simulation of turbulent air flow and natural onvetion heat transfer in atti spaes with roof pithes from 3/12 to 18/12 ombined with eiling insulation levels from R-1.2 to R-40. The modeling results show that the air flows in the attis are steady and exhibit a general streamline pattern that is qualitatively insensitive to the investigated variations of roof pith and eiling insulation. Furthermore, it is predited that the eiling insulation plays a ontrol role on the atti ooling load and that an inrease of roof pith from 3/12 to 8/12 results in a derease in the ooling load by around 9% in the investigated ases. The results suggest that the inrease of roof pith alone, without hanging other design parameters, has limited impat on attis ooling load and airflow pattern. The researh results also suggest both the predited ventilating mass flow rate and atti ooling load an be satisfatorily orrelated by simple relationships in terms of appropriately defined Rayleigh and Nusselt numbers. Keywords: atti; natural ventilation; roof pith; insulation; ooling; turbulene; CFD

3 Energies 2012, Introdution Ventilated atti has been a long-established pratie in residential building onstrution [1], but how different atti designs affeting building energy performane has not been thoroughly investigated. The majority of the existing literature on atti energy performane onerned with sealed attis, as reviewed by Kamiyo et al. [2] and by Saha and Khan [3], while only a few publiations reported studies involving atti ventilation. For example, Medina et al. [4,5] proposed a orrelation-based mathematial model for vented residential attis and ompared model preditions with experimental data, and Moujaes and Alsaiegh [6] employed a finite element model to simulate the thermal effets of plaing a radiant barrier system inside a vented residential atti for a ase study under summer weather onditions. However, very limited literature was found on investigating ventilated attis using turbulene CFD models. Due to relatively large size of attis, turbulene phenomenon in the vented attis is warranted in both summer and winter onditions [7]. Therefore, more aurate results are expeted from using appropriate turbulene flow models. The improved results an provide better sientifi evidene and guidane for building pratitioners to improve energy performane of residential buildings and design ventilation enhanement devies, suh as the wind driven rooftop ventilators [8 11]. Two major parameters are of partiular interest in this paper: Roof pith and eiling insulation. There are many onsiderations behind the roof pith designs, whih range from disharging rainwater and snow to inreasing aestheti appearanes. However, very limited researh investigated its impat on atti energy performane. So, in this paper, the effets of roof pith and eiling insulation on the ooling load are parametrially investigated for gable-roof residential buildings, whih are represented by two-dimensional CFD models. Sine wind effets are not inluded in this study, the air flow and heat transfer in the atti spaes are purely driven by stak effets. Suh buoyany-driven ases are orresponding to a worst-ase senario, beause real atti ventilation is generally enhaned by winds. In order to aount for a wide range of roof pith and eiling insulation, involving several orders of magnitude variation of Rayleigh number, the buoyany-driven air flow and natural onvetion heat transfer are modeled by the k-kl-ω model [12], whih is a physis-based transitional turbulene model apable of modeling turbulent flows from laminar-turbulene transitional regime to fully turbulene regime. An unsteady numerial formulation is adopted in the study, as the steady solutions ould not always onverge, even after arefully adjusting the various under-relaxation fators. Unsteady Reynolds-averaged Navier-Stokes (URANS) modeling has been shown to be an effetive approah to overome numerial stiffness and improve solution onvergene in previous studies for natural onvetion flows in enlosures [13 17]. The URANS approah is also a reommended strategy in ommerial CFD manuals [18] for solving natural onvetion problems. In the following setions, the numerial model will be introdued first, followed by detailed presentation and disussion of the modeling results. 2. Numerial Model A shemati diagram of a ross-setion plan of the physial model is shown in Figure 1. In the diretion perpendiular to the ross-setion shown in Figure 1, it is assumed that the building is long

4 Energies 2012, enough to ignore the effets of the gable-end walls, and thus the problem is simplified to two dimensional. Figure 1. Shemati of the omputational domain and boundary onditions. y p atm symmetry H T rt = K, h r = W/m 2 K air (Boussinesq) 0 0 T b = K, h W p atm, T in = K x The modeled atti spae is in a shape of an isoseles triangle, with a eiling width of 2W and a height of H, resulting in a pith of H/W. Due to the buoyany stableness of the summertime atti ventilation as well as the symmetry in both geometry and boundary onditions, only the right half of the atti is inluded in the omputational domain. In this study, the modeled atti is assumed to have a fixed eiling half-width of W = 4 m and a height varying between 1 m and 6 m, orresponding to a roof pith varying from 3/12 to 18/12. For simpliity, neither roofs nor eiling trusses are inluded in the model, and the omputational domain is only oupied by air, whih is assumed to be a Boussinesq fluid with a referene temperature T 0 speified to the outside ambient air temperature to orretly alulate the buoyany effets. In all the ases reported in this study, T 0 = K is assumed. In order to orretly aount for the thermal resistanes of the eiling and roof, whih are exluded from the omputational domain, onvetion-type boundary onditions are applied to both the eiling and roof boundaries. For example, energy balane aross the eiling thikness gives: T y T T h T y0 y0 b t Tb t where T b and T t are the temperatures at the eiling-bottom and eiling-top, respetively, and the heat transfer oeffiient h is determined by the thermal ondutivity of eiling material divided by eiling thikness t. It should be note that h is the reiproal of the eiling thermal resistane R, whih may be expressed in R-value, i.e., R-1 = 1 h ft 2 F/Btu = Km 2 /W. In this study, a eiling-bottom temperature is speified to T b = K, while a heat transfer oeffiient of h varying between W/m 2 K to W/m 2 K is adopted to approximate a eiling insulation level between R-1.2 (R = Km 2 /W = Km 2 /W) and R-40 (1)

5 Energies 2012, (R = Km 2 /W). Similarly, a roof-top temperature of T rt = K and a heat transfer oeffiient of h r = W/m 2 K (equivalent to an insulation level of R-1.2) are speified to the roof boundary to simulate a ondition of a 3 m plywood roof. For all the ases investigated in this study, balaned vent areas are assumed. Both the soffit and ridge vents are assumed to be 1 m wide, resulting in a ventilation ratio of 1/200, whih is a representative atti ventilation rate in onstrution pratie. Typially, the net free vent area (unobstruted area where air an freely flow from outside to inside to outside) is required by the building odes to be 1/150 of the floor area of the atti spae being ventilated, and a redution of the ventilation ratio from 1/150 to 1/300 is allowed if at least 50% of the ventilating area is in the upper portion of the spae and a ontinuous vapor retarder is installed on the warm side of the eiling. In this study, pressures at the soffit and ridge vents are both speified to be zero gauge pressure. Therefore, the obtained air flow is purely driven by the thermally indued buoyany fores, i.e., the stak effet. At the soffit vent, the inlet air is assumed to enter at an ambient temperature of K and a turbulent intensity of 1%. Following the URANS approah to turbulene, the time-averaged air veloity ( u i ), pressure (p), and temperature (T) distributions in the atti spae shown in Figure 1 are governed by the following ontinuity, momentum, and energy equations: ui x i 0 (2) Du Dt i 1 p x i x j u x i j v v k g T T T j u xi 2 3 ij i 0 (3) DT Dt x T (4) i x i where density ρ, kineti visosity, thermal expansion oeffiient β, and thermal diffusivity α are air properties, while flutuation kineti energy k, eddy visosity T, and eddy thermal diffusivity are determined by the employed turbulene model. In Equations (3) and (4), the substantial derivative terms inlude unsteady terms (partial derivative with respetive to time) that aount for all unsteadiness that does not belong to the turbulene, i.e., the unsteadiness that is not represented by the turbulene model [14]. The turbulene model employed in this study is the k-kl-ω transition model [12], whih is an eddy-visosity turbulene model based on the k-ω framework and inludes laminar kineti energy to represent the pretransitional flutuations in boundary layers. Additional information about the k-kl-ω transition model an be found in [12]. The governing equations formulated above are solved by the ommerial CFD software Ansys Fluent 13.0 [18], with the spae variables being disretized by the finite volume method and time domain disretized by the fully impliit sheme. The oupled algorithm is employed for solving the pressure and veloity oupling. The disretization of pressure is based on the seond order sheme, while the third-order MUSCL sheme is adopted for all the other variables. Non-uniform triangular grids are employed, and the boundaries are inflated with nodes tightly lustered near the walls to ensure that the y + value for the first grid lose to the walls is everywhere less than 1.

6 Energies 2012, The modeling results presented in this paper are based on grids onsisting of about 25,000 50,000 nodes and a time step size of 1 s. All the alulations start from initial onditions of zero veloity and uniform temperature. Within eah time step, 20 iterations are exeuted. Three ases for grid and time-step dependene tests are ompared in Table 1 and Figure 2. All the three ases are orresponding to 5/12 atti and R-20 eiling insulation. It is lear that dereasing the time step to 0.5 s and requiring 40 iterations in eah time step generate negligible differene in solutions. In addition, refinement of the grid by doubling the node numbers results in notieable differenes in veloity and temperature profiles, as shown in Figure 2, but the overall differenes in the total mass flow rate ( m ) as well as eiling ooling load (Q ) and roof heat gain (Q r ) results are less than 2% (Table 1). Sine there is no omparable experimental data found in the literature for this kind of atti ventilation, the present numerial model is validated through a benhmark problem of mixed turbulent onvetion in a square avity, whih has been studied both experimentally [19] and numerially [19 21]. The mixed turbulent onvetive air flow within a 1.04 m 1.04 m avity is reated by a horizontal plane wall jet entering from an inlet slot at the eiling level together with a heated floor. Table 1. Summary of grid and time-step dependene tests for a 5/12 atti with R-20 eiling insulation. Case A B C Total nodes 26,508 26,508 53,430 Total elements 46,835 46,835 88,715 Time step (s) Iterations per time step Q (W/m) Q r (W/m) m (kg/s m) Figure 2. Predited profiles of (a) horizontal veloity along the vertial line x = 2 m and (b) temperature along the symmetri line x = 0 for gird and time-step dependene test ases defined in Table 1. (a)

7 Energies 2012, Figure 2. Cont. (b) Subjet to the experimentally measured boundary onditions [19], the preditions of the present model are shown in Figures 3 and 4. The predited mean veloity pattern shown in Figure 3 is very similar to that measured from the experiment (Figure 3a) [19] and that averaged from large eddy simulation (Figure 3b) [20], while the predited profiles of veloity and temperature agree well with the experimental data, as shown in Figure 4. Figure 3. Comparison of veloity distribution between (a) experimental measurement [19]; (b) large-eddy predition [20]; and () present study (streamlines in kg/m s), together with (d) the isotherms (in K) predited by the present study, for the validation ase of turbulent mixed onvetion in a square avity. (a) (b)

8 Energies 2012, Figure 3. Cont. () (d) Figure 4. Comparison of modeling preditions with experimental data for the validation ase: (a) vertial veloity along the setion of y = m; (b) horizontal veloity along the setion of x = m; () temperature along the setion of y = m; (d) temperature along the setion of x = m. (a) (b) () (d)

9 Energies 2012, Results and Disussion In order to failitate a parametri study of the effets of roof pith and eiling insulation on the ooling load, a total of 20 ases are alulated with five typial pith values (3/12, 5/12, 8/12, 12/12, and 18/12), ombined with four eiling insulation levels (R-40, R-20, R-10, and R-1.2). The seleted pith values are typial in residential onstrution pratie. Therefore, the results an be used to provide pratial referene in atti and roof designs. For eah ase, the simulation onverges to a steady solution after about 3500 time steps. The predited veloity and temperature distributions for the R-40, R-20, and R-10 ases exhibit quite similar patterns, thus only the results of the R-20 ases are presented in Figures 5 and 6. The streamlines in Figure 5 show that the general patterns of the flow and temperature fields are essentially independent of the roof pith variation. For all the roof pith ases, the outside air enters from the soffit vent, travels along the roof bottom for a distane about 1/5 of the roof length, then follows two different paths. The mainstream of the ventilating air ontinues traveling along the roof bottom and leaves the atti from the ridge vent, while a portion of the ventilating air travels a detoured zigzag path bounded by three onvetion ells: A ounterlokwise swirling ell near the soffit, a lokwise one oupying more than half of the atti spae, and another ounterlokwise one under the top portion of the roof. The temperature distributions shown in Figure 5 indiate that for all the pith value ases, the thermal boundary layers develop along the roof and eiling walls, and the atti spae is dominated by thermal stratifiation, exept for the soffit region. Figure 5. Predited (left) streamlines (in kg/m s) and (right) isotherms (in K) for attis with R-20 eiling insulation. 3/12 5/12

10 Energies 2012, Figure 5. Cont. 8/12 12/12 18/12 The predited horizontal veloity profiles along the vertial line x = 2 m for the R-20 ases are shown in Figure 6(a). For eah roof pith ase, sine the vertial line uts through two onvetion ells, the horizontal veloity hanges diretions at orresponding heights aordingly. The veloity

11 Energies 2012, peak under the roof is assoiated with the mainstream ventilating air flow, whih has a muh higher veloity than the air irulating within the two onvetion ells. Figure 6. Predited profiles of (a) horizontal veloity along the vertial line x = 2 m and (b) temperature along the symmetri line x = 0 for attis with R-20 eiling insulation. (a) (b) The predited temperature profiles along the symmetri line x = 0 for the R-20 ases are shown in Figure 6(b). For all the roof pith ases, the temperature inreases almost linearly with y/h, exept in the regions near the soffit vent and ridge vent, where muh greater temperature gradients indiate the effets of the eiling and roof thermal boundary layers. It is also lear from the figure that the average atti temperature dereases with the inrease of roof pith from 3/12 to 8/12, but keeps essentially unhanged with roof pith further inreasing from 8/12 to 18/12. This result suggests that the overall ooling effet of the ventilating air (entering at K) an be enhaned by inreasing the roof pith

12 Energies 2012, as long as it is less than 8/12. For pithes higher than 8/12, the atti ventilation seems reahed a saturated state that further inreasing the atti height gains very marginal ooling benefits. This finding is very useful in terms of providing quantitative guidane for roof and atti design and onstrution pratitioner. The predited veloity and temperature distributions for R-1.2 ases are presented in Figures 7 and 8. Although the basi patterns of the streamlines and isotherms shown in Figure 7 appear similar to those shown in Figure 5, some important differenes exist. First, the eiling-top temperatures are below the ambient temperature for all the R-1.2 ases but above the ambient temperature for all the R-20 ases, showing a diret onsequene of the differene in eiling insulation. At the R-1.2 insulation level, the ventilating air above the eiling is ooled from below to a temperature lower than the ambient, as a result of the poor eiling insulation. Seond, the flow and temperature distributions in the soffit onvetion ell shown in Figure 7 are signifiant different from those in Figure 5. This may be explained by the most profound effet of the eiling temperature and heat flux in the soffit region, as ompared to other regions. Finally, from the streamline results of the 12/12 and 18/12 ases in Figure 7, an additional ounterlokwise onvetion ell an be observed right above the eiling wall. The horizontal veloity profiles along x = 2 m shown in Figure 8(a) indiate that suh a ell also exists for the 8/12 ase, although it is not aptured by any streamlines in Figure 7. The temperature profiles along x = 0 in Figure 8(b) exhibit similar trends, as ompared to Figure 6(b), exept that the urves in Figure 8(b) all start from eiling top temperatures lower than the ambient temperature. Figure 7. Predited (left) streamlines (in kg/m s) and (right) isotherms (in K) for attis with R-1.2 eiling insulation. 3/12 5/12

13 Energies 2012, Figure 7. Cont. 8/12 12/12 18/12

14 Energies 2012, Figure 8. Predited profiles of (a) horizontal veloity along the vertial line x = 2 m and (b) temperature along the symmetri line x = 0 for attis with R-1.2 eiling insulation. (a) (b) The numerial results are summarized in Tables 2 5 for the ases orresponding to R-40, R-20, R-10, and R-1.2, respetively. In these tables, the values for the heat loss to the eiling (Q ), the heat gain from roof (Q r ), and the ventilating mass flow rate ( m ) are diret modeling outputs. The eiling heat loss measures the atti ooling load and is diretly related to the building energy performane. As evident in eah of the tables, regardless of the eiling insulation, the dependene of the roof heat gain and the ventilating flow rate on the roof pith is remarkably different from that of the atti ooling load. As the roof pith inreases from 3/12 to 18/12, both the heat gain from the roof and the mass flow rate of the ventilating air inrease by over 100%. On the other hand, the atti ooling load dereases by around 9% when the roof pith inreases from 3/12 to 8/12, and keeps essentially

15 Energies 2012, unhanged for roof pithes higher than 8/12. Suh a dependene of the ooling load on the roof pith shown in Tables 2 5 is onsistent with the average atti temperature results shown in Figures 6(b) and 8(b), sine a higher ooling load is a natural onsequene of a higher atti air temperature. Table 2. Summary of numerial results for R-40 ases. Roof Pith 3/12 5/12 8/12 12/12 18/12 Q (W/m) Q r (W/m) m (kg/s m) T t (K) T av (K) T rb (K) Table 3. Summary of numerial results for R-20 ases. Roof Pith 3/12 5/12 8/12 12/12 18/12 Q (W/m) Q r (W/m) m (kg/s m) T t (K) T av (K) T rb (K) Table 4. Summary of numerial results for R-10 ases. Roof Pith 3/12 5/12 8/12 12/12 18/12 Q (W/m) Q r (W/m) m (kg/s m) T t (K) T av (K) T rb (K) Table 5. Summary of numerial results for R-1.2 ases. Roof Pith 3/12 5/12 8/12 12/12 18/12 Q (W/m) Q r (W/m) m (kg/s m) T t (K) T av (K) T rb (K) A omparison between Tables 2 5 indiates that the atti ooling load inreases remarkably with the derease of eiling insulation. For the 5/12 pith, for example, the ooling load inreases by 75%, 170%, and 440%, respetively, as the eiling insulation drops from R-40 to R20, R10, and R-1.2. In ontrast to its ontrol role on the ooling load, the eiling insulation has a relatively weak influene on

16 Energies 2012, the roof heat gain and the ventilating flow rate. As the eiling insulation dereases from R-40 to R-1.2, both the inrease in the heat gain from the roof and the derease in the mass flow rate of the ventilating air are less than 10%, regardless of the roof pith. The general trend of the roof heat gain and the air flow rate depending on the eiling insulation shown in the tables an be explained as follows. As the eiling insulation dereases, the total thermal resistane of the roof-atti air-eiling system dereases as well, this explains the predited inrease in the roof heat gain, sine the total temperature differene aross the roof-atti air-eiling system is fixed to 50 K. However, sine the derease in the total thermal resistane is at a muh lower perentage than that in the eiling insulation derease, the inreased roof heat gain annot ompensate the inreased eiling heat loss, resulting in a derease in the net heating to the ventilating air. This dereased heating effet explains the predited derease in the ventilating air flow rate along with the eiling insulation derease. The average eiling-top temperature (T t ) and the average roof-bottom temperature (T rb ) listed in Tables 2 5 are determined in terms of the eiling thermal resistane (R ) and the roof thermal resistane (R r ), respetively, i.e.: T t Tb RQ / W (5) T rb T rt R Q W r 2 2 W H 1/ 2 r (6) whereas the average air temperature (T av ) is determined based on the overall energy balane of the atti air, i.e.: T Q Q r av Tin 2m (7) p Based on the temperature differene aross the atti air, the Rayleigh number Ra m is defined by: 3 gh Trb Tt Ra m (8) and used to haraterize the ventilating mass flow. A log-log plot for the ( m, Ra m ) data is shown in Figure 9, whih indiates that the m - Ra m data points for the R-40, R-20, and R-10 ases an be approximately orrelated by: Ra m m (9) This empirial orrelation, if orreted by a fator of about 0.88, may also provide an approximate estimate for the mass flow rates for the R-1.2 ases. In order to haraterize the eiling side heat transfer, the temperature differene between the atti air and the eiling-top is used to define both the Rayleigh number Ra and the Nusselt number Nu, i.e.: 3 gh Tav Tt Ra (10) Nu Q H pw T av Tt (11)

17 Energies 2012, Figure 9. Correlation for ventilating mass flow rate ompared with numerial data. Figure 10. Correlations for atti ooling load ompared with numerial data. A log-log plot for thus obtained ( Nu, Ra ) data is shown in Figure 10. For eah of eiling insulation level, the Nu Ra data points for the roof pithes between 3/12 and 12/12 distribute linearly on the plot, resulting in the following empirial orrelations: Nu Ra R 40 (12) Nu Ra R 20 (13) Nu Ra R 10 (14)

18 Energies 2012, Nu Ra R 1.2 (15) It is also implied that these empirial orrelations need to be orreted for roof pithes higher than 12/12, sine they systematially over predit the ooling loads for the 18/12 pith ases. 4. Conlusions In this study, the k-kl-ω transition model [12] is employed to simulate summer-time buoyany-driven turbulent ventilation in triangular attis with oupled ridge and soffit vents. In partiular, the impats of roof pith and eiling insulation on the ooling load are investigated. The findings from the numerial results are summarized as follows: (1) Air flows in the attis are steady and exhibit a general streamline pattern that is qualitatively insensitive to the investigated variations of roof pith and eiling insulation. (2) For all the eiling insulation levels investigated, the atti ooling load dereases by around 9% when the roof pith inreases from 3/12 to 8/12, and keeps essentially unhanged for roof pithes between 8/12 and 18/12. At the same time, along with the pith inrease, both the heat gain from the roof and the mass flow rate of the ventilating air inrease by over 100%. (3) The atti ooling load inreases remarkably with the derease of eiling insulation. For the 5/12 pith, for example, the ooling load inreases by 75%, 170%, and 440%, respetively, as the eiling insulation drops from R-40 to R20, R10, and R-1.2. In the meantime, the heat gain from the roof inreases by less than 10%, while the mass flow rate of the ventilating air dereases by less than 10%, regardless of the roof pith. Therefore it is lear that eiling insulation plays a dominant role in ontrolling ooling load of atti spaes in summer time, ompared to ventilating fators. (4) Both the mass flow rate of the ventilating air and the ooling load of the atti an be satisfatorily orrelated by simple relationships in terms of appropriately defined Rayleigh and Nusselt numbers. In summary, these findings an provide pratial sientifi guidane for not only new residential roof and atti onstrution, but also energy retrofitting of existing residential buildings. For example, in residential onstrution pratie, inreasing roof pith will lead to ost inrease of roofs due to both roof material and labor ost inreases. These ost inreases an be signifiant with high pith. At the same time, dereasing roof pith to lower than 3/12 may lead to leakage issues and inreased ooling load. So an optimal pith design needs to onsider many fators inluding atti airflow and ooling load as well as the dependene of solar radiation on roof pith. For long time, onstrution pratitioners have very little knowledge on how the roof pithes affet atti airflows and ooling loads. Therefore, the authors expet the findings, espeially the identified orrelations, will be of partiular interest to building pratitioners for optimizing roof/atti design using low-ost natural ventilation. This researh an be furthered by employing 3D numerial models to investigate the effets of gable walls for gable-roof buildings as well as roof-vent onfigurations other than ontinuous ridge and soffit vents.

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