A review on Rayleigh-Bénard convection influenced by the complicating factors

Jia, Song; Li, Panxin; Chen, Lu; Li, Chen-Hao; Li, Ben-Wen; Huang, Lingyun

doi:10.1016/j.icheatmasstransfer.2023.106784

Cited by 12 publications

(1 citation statement)

References 305 publications

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“…Exact solutions for unidirectional thermal diffusion flows are built on the basis of the Ostroumov-Birich class of exact solutions for a horizontal fluid layer or the Gershuni-Bachelor family of exact solutions for a vertical fluid layer [7,[32][33][34][35][36][37][38]. Reviews on exact solutions for problems of convective, concentration, and thermal diffusion flows are contained in bibliographic sources [39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows

Ershkov,

Burmasheva,

Leshchenko

et al. 2023

Symmetry

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We present a new exact solution of the thermal diffusion equations for steady-state shear flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale currents of the world ocean, motions in thin layers of fluid, fluid flows in processes, and apparatuses of chemical technology. To describe the steady shear flows of an incompressible fluid, the system of Navier–Stokes equations in the Boussinesq approximation is redefined, so the construction of exact and numerical solutions to the equations of hydrodynamics is a very difficult and urgent task. A non-trivial exact solution is constructed in the Lin-Sidorov-Aristov class. For this class of exact solutions, the hydrodynamic fields (velocity field, pressure field, temperature field, and solute concentration field) were considered as linear forms in the x and y coordinates. The coefficients of linear forms depend on the third coordinate z. Thus, when considering a shear flow, the two-dimensional velocity field depends on three coordinates. It is worth noting that the solvability condition given in the article imposes a condition (relation) only between the velocity gradients. A theorem on the uniqueness of the exact solution in the Lin–Sidorov–Aristov class is formulated. The remaining coefficients of linear forms for hydrodynamic fields have functional arbitrariness. To illustrate the exact solution of the overdetermined system of Oberbeck–Boussinesq equations, a boundary value problem was solved to describe the complex convection of a vertical swirling fluid without its preliminary rotation. It was shown that the velocity field is highly stratified. Complex countercurrents are recorded in the fluid.

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