**3. Numerical setup**

Unsteady Reynolds-Averaged Navier–Stokes (URANS) approach has been used to model both free and forced convective flows around the structure. For this purpose, Ansys Fluent 2021 code has been used. The working fluid (air) is considered to follow the ideal gas behaviour. The governing equations of the current problem, i.e., conservation of mass, momentum, and energy are:

$$\frac{\partial \rho}{\partial t} + \frac{\partial (\rho u\_j)}{\partial x\_j} = \mathbf{0} \tag{2}$$

$$\frac{\partial(\rho u\_i)}{\partial t} + \frac{\partial(\rho u\_i u\_j)}{\partial \mathbf{x}\_j} = -\frac{\partial p}{\partial \mathbf{x}\_i} + \frac{\partial \sigma\_{\bar{\eta}}}{\partial \mathbf{x}\_j} + \left(\rho - \rho\_{r\bar{\eta}}\right) \mathbf{g}\_i \tag{3}$$

$$\frac{\mathbf{C}\_p \partial(\rho T)}{\partial t} + \frac{\mathbf{C}\_p \partial(\rho u\_i T)}{\partial \mathbf{x}\_j} = k \frac{\partial}{\partial \mathbf{x}\_j} \left(\frac{\partial T}{\partial \mathbf{x}\_j}\right) + \frac{\partial q\_j}{\partial \mathbf{x}\_j} \tag{4}$$

In Eqs. (2)–(4), *g*, *ρref* , *u*, *T*, *P*, *Cp*, σij, *k*, and *qj* show the gravity vector, reference density, velocity vector, temperature, dynamic pressure, the specific heat capacity of constant pressure, stress tensor, thermal conductivity, and turbulent thermal flux vector, respectively.

To model the turbulent flow, the *k* � *ωSST* model has been used. *SST* is a hybrid model that utilises *k* � *ω* formulation within the boundary layer where viscous forces are dominant and then switches to *k* � *ε* formulation outside the boundary layer making it suitable for a wide range of engineering applications [9]. A pressure-based solver along with a second-order discretization scheme has been used to solve the flow variables, and the coupled algorithm has been used for velocity–pressure coupling. The solution residual target is set to 10�<sup>5</sup> .

An unstructured mesh with 2.06 million cells has been used to model the flow. It was found that a further increase in the number of cells did not affect the results. To correctly capture the flow behaviour within the boundary layer, inflation has been used on the solid boundaries. Generally, the mesh has been refined around the structure, within the gap between the panel and roof, and close to walls where a sharp gradient of flow variables such as velocity or temperature is expected.

The surface-to-surface radiation model has been used to simulate the radiation effects. This model uses the following formulation to compute the radiative energy transfer from surfaces:

$$q\_{out,m} = \epsilon\_m \alpha T^4 + \Omega\_m \cdot \sum\_{j=1}^{N} F\_{jm} q\_{out,j} \tag{5}$$

where *qout*,*<sup>m</sup>* is the energy flux leaving the surface *m*, *α* is the Stefan–Boltzmann constant, Ω*<sup>m</sup>* ¼ 1 � *ϵ<sup>m</sup>* is the reflectivity of surface m, *ϵ<sup>m</sup>* is the emissivity of the surface m, and *Fjm* is the view factor between surface *m* and surface *j*.
