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Thermal performance analysis of a naturally ventilated system using PMV models for different roof inclinations in composite climatic conditions


Computational analysis has become a very useful tool for a detailed understanding of building physics before actual building constructions and for predicting such system behaviors where massive urbanizations are envisaged. The present study attempts to describe the efficacies of CFD as an “analysis led design” tool, where a computationally modeled cross-ventilation system with asymmetric positions of openings is analyzed to estimate the comfort zones according to the PMV (predicted mean vote) model for evaluating the influence due to roof inclinations, thereby providing opportunities in rectifying any anomalies pertaining to it, prior to the actual construction. A numerical analysis has been carried out to examine the effects of natural ventilation in a wind-driven system using the established extended PMV model (PMVe). The study focuses on thermal comfort and the effect of roof inclination angle over the three different weather conditions in Delhi—winter season (high humidity and low temperature), summer season (low humidity and high temperature) and monsoon season (high humidity and mild temperature). Appropriate roof inclination angles provide a better ventilation rate and air distribution pattern, which significantly affects comfort condition. Study shows that for winter season, the PMV values decrease as the roof inclination angle is increased and the ventilation rate for 30° inclined roof increases about 16% as compared to the flat roof case, while PMV values increase with roof inclination for summer season, signifying zone of discomfort. It also concludes that a moderate roof inclination is beneficial for monsoon season.

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\( {A_{\text{eff}}} \) :

Effective area of the openings (m2)

a :


\( {C_{\text{d}}} \) :

Discharge coefficient

\( \Delta {C_{\text{P}}} \) :

Difference between the values of pressure coefficient on both the openings

\( {C_\mu} \) :

Empirical constant (= 0.09)

\( E \) :

Internal energy (J)

\( e \) :

Expectancy factor

\( {F_{p - i}} \) :

View factor of the point p from the face of the cell grid present on the radiative wall

\( {I_{\text{U}}}(z) \) :

Turbulence intensity (%)

\( K \) :

Von Karman constant (= 0.42)

\( k(z) \) :

Turbulent kinetic energy (m2/s2) at the height coordinate \( z \) (mm)

\( L \) :

Thermal load on the body (W/m2)

\( M \) :

Metabolic rate (W/m2)


Static pressure (Pa)

P ref :

Reference static pressure (Pa)


Predicted mean vote

PMVe :

Extended model of PMV

PMVtrad :

Traditional PMV value

\( \dot{q} \) :

Volumetric heat addition per unit mass (J/kg)

\( {T_i} \) :

Temperature of that face (K)

T r :

Mean radiant temperature (K)

\( U_{\text{ABL}}^* \) :

Atmospheric boundary layer friction velocity (m/s)

\( {U_{\text{ref}}} \) :

Velocity (m/s) at the reference height \( {z_{\text{ref}}} \) (mm)

\( U(z) \) :

Inlet wind velocity (m/s) at the height coordinate \( z \) (mm)

\( z \) :

Height coordinate (mm)

\( {z_0} \) :

Reduced-scale aerodynamic roughness length (mm)

\( \varepsilon (z) \) :

Dissipation rate of turbulent kinetic energy (m2/s3) at height coordinate z (mm)

\( \omega (z) \) :

Specific dissipation rate (1/s)

\( \rho \) :

Density of the fluid (m3/s)

\( {\rho_{air}} \) :

Air density (m3/s)


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This study was conducted under the joint call proposal between the Ministry of Science and Technology (MOST) of Taiwan and Department of Science and Technology (DST) of India.

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Correspondence to Dibakar Rakshit.

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Vaishnani, Y., Ali, S.F., Joshi, A. et al. Thermal performance analysis of a naturally ventilated system using PMV models for different roof inclinations in composite climatic conditions. J Braz. Soc. Mech. Sci. Eng. 42, 124 (2020).

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  • Thermal comfort
  • PMV (predicted mean vote) model
  • Indoor environmental quality
  • Natural ventilation
  • Roof inclination