**Introduction**

It is well known that one of the clearest effects of climate change is the increase of the frequency, length and severity of heat waves, in particular at mid-latitudes. This over-heating is accentuated in cities due to the so-called urban heat island effect which is induced by the way in which buildings store and exchange heat with the atmosphere.

Understanding and correctly modeling the building-atmosphere interactions during heat waves allows to design and evaluate strategies to mitigate negative effects on people’s thermal stress.

However, one of the main problems is that heat waves are essentially meso-to-synoptic scale phenomena, while building-atmosphere heat exchanges are strongly influenced by the heterogeneities that exist in urban environment at the microscale. The modelling challenge is to combine these two scales. One of the most common approaches is to use mesoscale models (e. g. with spatial resolution of the order of 1 km), with detailed urban canopy parameterizations. However, such schemes heavily rely on the accuracy of the heat exchange coefficients used to estimate the heat fluxes from walls, roofs and road.

The objective of this work is to propose and use a new methodology, based on Computational Fluid Dynamic (CFD) microscale simulations, to derive the local heat transfer coefficients (LHTCs) between the building envelopes and air flow, as a function of mean variables and parameters that are used in Urban Canopy Parameterizations of mesoscale models.

**CFD model description**

The CFD modelling is focused on a real urban environment, particularly a fraction of the Salamanca district of Madrid (Spain), characterized by a very regular morphology, see Fig. 1. The computational domain is 1 km x 1 km x 1 km and contains 9 aligned blocks (3 x 3) of 15 m height.

A quasi-steady conjugate heat transfer model between indoor air and outdoor air through the building envelopes has been used in the CFD, accounting for: forced convection in the outdoor side, conduction through the envelopes and natural convection in the indoor side. Additionally, radiative exchanges between the sun and atmosphere with the urban surfaces and between each surface have been considered.

It has been assumed that building envelopes are made up of roofs, walls, floors and windows (30 % of the wall surface), considering that the first three building elements store energy (1.0 m, 0.5 m and 1.0 m thicknesses respectively) but the last one does not (un-thickness).

The mesh is a combination of polyhedral and tetrahedral cells and includes suitable refinements around the surfaces (up to 0.25 m). The total number of cells is approx. 5.2·10^{6}.

Numerical simulations are based on a RANS approach with the Realizable K-Epsilon Two Layer model using the All Y+ wall hybrid treatment of STAR-CCM+9.04.011^{®}.

The thermal properties in all physical media have been assumed temperature independent, except in the air, where Boussinesq approximation has been employed.

And, the spectral behavior of both walls and windows has been considered.

To fix the model boundary conditions, the hourly Temperature and Radiation (Direct and Diffuse) data from the nearest urban meteorological station during the central day of the second heat wave registered in Madrid in 2015 have been chosen. The following cases have been simulated:

- consecutive hours (from 7 a.m. to 9 p.m.), considering the real solar position (elevation and azimuth) but fixing the wind direction (NW) and speed
- specific hours fixing the wind direction (NW) but varying speed

A thermal equilibrium situation has been assumed as initial condition.

Finally, model evaluation will be conducted by the COSMO experiment.

**LHTCs methodology**

Considering as reference air the highlighted volume in Fig. 1 (15 m height), which can be considered representative of the air temperature computed by a mesoscale model, the LHTCs has been estimated according to the expression in the Fig. 1, for each of the facades j (j=N, S, E, W), where, for each hour i, Q is the total boundary heat flux, Tw is the surface average temperature and Tbulk the volume air average temperature.

**Results**

For this urban configuration and meteorological conditions:

- when wind speed is fixed, the LHTCs on illuminated facades change mainly with the air temperature. The values obtained range from 10 W·m
^{-2 }K^{-1}(minimum value) given on the east facade during the morning up to 28 W·m^{-2}K^{-1}(maximum value) on the west facade during the afternoon, with intermediate values on the south facade, as sun position evolves. - when wind speed is varied, the values obtained depend only on wind speed above a certain threshold. For low values, the coefficients are independent of wind speed. This behavior may be due to the fact that the convective contribution to LHTCs depends on the balance between buoyancy and inertial forces. When the velocities are very low, this contribution is by natural convection (dependent on the temperature differences between the urban surfaces and bulk air), whereas when the velocities are very high this contribution is by forced convection (dependent on the wind velocity).