Self-similar analysis of a viscous heated Oberbeck-Boussinesq flow system
arXiv:1905.03686 · doi:10.1088/1873-7005/ab720c
Abstract
The simplest model to couple the heat conduction and Navier-Stokes equations together is the Oberbeck-Boussinesq(OB)system which were investigated by E.N. Lorenz and opened the paradigm of chaos. In our former studies - Chaos, Solitons and Fractals 78, 249 (2015), ibid, 103, 336 (2017) - we derived analytic solutions for the velocity, pressure and temperature fields. Additionally, we gave a possible explanation of the Rayleigh-Bènard convection cells with the help of the self-similar Ansatz. Now we generalize the OB hydrodynamical system, including a viscous source term in the heat conduction equation. Our results may attract the interest of various fields like micro or nanofluidics or climate studies.
arXiv comment6 pages, 6 figures
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