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An unconventional method for solving the heat transfer problem for free convection near the vertical surfaces of the enclosing structures is proposed. It is based on the laws of thermodynamics of irreversible processes. A variational principle is used to find the unknown functions that analytically express the velocity fields and other flow quantities in the boundary layer near the vertical walls. A variational formulation of the hydrodynamic and thermal boundary layer near a vertical plane surface in conditions of free convection is given. It is given an analytical solution of the problem of the distribution of the vertical component of velocity and temperature in the wall boundary layer in the laminar flow. Theoretical formulas for the thickness of the boundary layer are obtained, as well as for the local and mean values of convective heat transfer coefficient.

A variational method in the problem of convective heat transfer near the vertical plane of the outer building fence in terms of free air movement