252 Zeeshan et al: Heat Stress Mitigation in a Hot-Humid Urban Environment the inflated volume of green vegetation and an under- estimation of the drag coefficient. Thus, a drag cor- rection factor for different canopy-shaped trees was incorporated to model the realistic canopy shape (Zeng et al. 2020) and is described as: (9) where F was the corrective factor for each canopy shape and was taken from the study of Zeng et al. (2020). The value of drag corrective factors for representative paraboloid-shaped, cone-shaped, and spherical-shaped canopy trees is compiled in Table 2. Tree Classification Characterization Scheme This study applied a generalized classification scheme based on 5 important structural parameters, assessed mainly by the landscape tree databank (National Parks Board 2017). Based on this scheme, 5 cases were compiled to model trees in ANSYS FLUENT. Each of the morphological parameters is divided into 2 classes: foliage density (sparse ≤ 3 and dense), crown height (short vs. tall), crown width (narrow and wide ≤ 9), and trunk height (high and low ≤ 2). For the selected tree species (i.e., Guaiacum offinale, Azadirachta indica, Peltophorum pterocarpum, and Bauhinia × blakeana), the average values of their morphological characteristics (i.e., tree height [HT], trunk height [TH – height of tree trunk from ground base to the bottom of live crown], crown height [CH], crown width [CW], and leaf area density [LAD]) are tabulated in Table 3. All selected tree species present inside the studied urban area were evergreen and rep- resented a specific canopy shape structure. In addition to common species, the effect of the Bauhinia × blakeana tree was also simulated with its greater LAD and was proposed for planting in Karachi for its capability of reducing temperature. The LAD distribution for Bauhinia × blakeana was 0 m2/m3, 0.17 m2/m3, 0.30 m2/m3, 0.52 m2/m3, 0.87 m2/m3, 1.27 m2/m3, 1.28 m2/m3, 0.03 m2/m3, and 0 m2/m3 at crown height of 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, and 9 m, respectively. In ANSYS, vegetation was mod- eled as a porous zone incorporated with canopy shape correction (i.e., form drag coefficient and heat transfer occur through its interaction with the surroundings through energy absorption and evapotranspiration). It is pertinent to mention that Guaiacum offinale is recognized with sparse foliage density, low trunk height, short crown height, and narrow crown width (Tree Case [TC]-1), while Bauhinia × blakeana is characterized ...... . .. ....... by dense foliage density, low trunk height, short crown height, and narrow crown width (TC-2)(Table 4). By contrast, Azadirachta indica has sparse foliage density, high trunk height, tall crown height, and narrow crown width (TC-5), while Peltophorum pterocarpum has sparse foliage density, low trunk height, tall crown height, and wide crown width (TC-3 and TC-4)(Table 4). Heat Stress (Thermal Comfort) A simple bioclimatic index (apparent temperature) was adopted to represent heat stress or thermal com- fort to study an adjustment of temperature at different humidity levels. Mathematically, it was a function of vapor pressure, velocity, relative humidity, and air temperature (Steadman 1984) and is given as: (10) where represented vapor pressure and RH represented the relative humidity. Q was the net radiation absorbed per unit area of the body surface in W/m2. U, Ta, and TA represented flow velocity, air temperature, and appar- ent temperature, respectively. RESULTS The evaluation zones and points selected for species analysis were based upon surface temperature distri- bution of the reference case which was simulated for a 5-day heatwave period from 2015 June 18–22. First, the base case for vegetation (TC-1)(Table 4) was modeled for 2015 June 19 by employing the tuned value of drag coefficient and energy source terms for Equations 7 and 8 in the flow governing equations through user-defined functions. The same vegetation model was first validated using the sub-configuration method, for which the experimen- tal study of Shashua-Bar et al. (2011) was referenced, to simulate its transpiration cooling power (Appendix). After the base case, separate simulations, as articulated in Table 4, were performed with different morpholog- ical parameters. However, the results were compared as averaged data of the evaluation parameters, due to the localized vegetation effect, and as box plots based on discrete data taken at some discrete locations. Evaluation Zones Identification and Validation of Surface Temperatures To make a comparative assessment of the cooling effect of street trees inside a hot-humid urban area, .. . .. . ......... . .... . ..... . ..... . ..... .. . .. ... ..................................
