Analysis of Free-Convection Hydrothermal Fields in a Rectangular Cavity under Thermal Boundary Conditions of the Second Kind

On the basis of the Oberbeck–Boussinesq equations, this study formulates the problem of a Newtonian fluid motion in a rectangular cavity under the Stokes hydrodynamic approximation. The thermal and hydrodynamic subproblems are presented, and an analytical solution of the model equations is obtained using integral Fourier transforms with thermal boundary conditions of the second kind. As an application example, this study analyzes the dynamics of hydrothermal fields during liquid nitrogen storage, taking into account the incoming heat through the wetted surface.