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

**Abstract**

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<jats:title content-type="abstract-subheading">Purpose</jats:title>

<jats:p>The 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.</jats:p>

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<jats:title content-type="abstract-subheading">Design/methodology/approach</jats:title>

<jats:p>Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.</jats:p>

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<jats:title content-type="abstract-subheading">Findings</jats:title>

<jats:p>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).</jats:p>

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<jats:title content-type="abstract-subheading">Practical implications</jats:title>

<jats:p>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.</jats:p>

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<jats:title content-type="abstract-subheading">Originality/value</jats:title>

<jats:p>To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.</jats:p>

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