Coupled heat transfers resolution by Monte Carlo in urban geometry including direct and diffuse solar irradiations

Modelling transient combined heat transfer in complex urban geometry is a key step to predict human exposure or energy consumption and to quantify the effect of climate change mitigation and adaptation measures. A difficulty lies in the possibility for a model to scale up and integrate large and complex urban morphology. We develop a probabilistic approach to solve heat transfers with the Monte Carlo method that is insensitive to the complexity of both the urban geometry and the boundary conditions. The integral formulation that includes random walks for each heat transfer mode is presented and the computation of absorbed solar irradiations at walls with the double randomization technique is detailed. Numerical validations are given through comparisons with deterministic method results for single and two-layer slabs, but also a three-dimensional thermal bridge geometry. The developed probabilistic heat transfer model is then used in a demonstration heat wave scenario where are computed: the outdoor mean radiant temperature showing the influence of trees; and the indoor average wall temperature showing the influence of solar gains through windows.