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

Abstract

PurposeThe paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade.Design/methodology/approachReduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.FindingsThis 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 implicationsThe 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/valueTo the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.