Theoretical study of the thermal state of building envelop in the neighborhood of embedded item

• A cell model of heat conduction in a building wall near embedded item is proposed.
• The model takes into account freezing moisture in the wall near embedded items.
• The model allows estimating the heat resistance loss in the neighborhood of the item.

A cell mathematical model of two-dimensional thermal state of a building envelop near an embedded item is proposed. The model is based on the recurrent matrix equality that describes the thermal state evolution taking into account the phase transformation in the wall material. The main operator of the model is the matrix of heat conduction for a complex two-dimensional domain, in which the physical properties have jump variation at the borders of zones that are presented by the shape matrix and take into account the embedded item configuration. An example of calculating the temperature field and calculating the configuration of the freeze-up zone at different positions of the wall-embedded item is presented.

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