The weak solvability of the steady problem modelling the flow of a viscous incompressible heat-conductive fluid through the profile cascade

作者：Neustupa Tomas^*

来源：International Journal of Numerical Methods for Heat and Fluid Flow, 2017, 27(7): 1451-1466.

DOI：10.1108/HFF-03-2016-0104

• Cascade of profiles
• Existence of a weak solution
• Heat-conductive flow
• Large inflow
• Natural outlet boundary condition
• Navier-Stokes equations

Purpose -The paper aims to theoretically study the mathematical model of a steady flow of a heatconductive incompressible viscous fluid through a spatially periodic plane profile cascade.
Design/methodology/approach -Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.
Findings -This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force).
Practical implications -The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature.
Originality/value -To the author's knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.

• 出版日期2017