<p>We present a rotating viscous-fluid (RVF) model, formulated within a Newtonian framework, that reproduces the rotation curves of both unbarred and barred spiral galaxies. The model incorporates three principal features: differential rotation, radial temperature gradients and a radially varying kinematic viscosity. In this framework, the galaxy is treated as a differentially rotating viscous medium whose effective viscosity increases with distance from the hot central regions, while the galactic mass is provided by baryonic matter distributed throughout the disc. On galactic scales, viscous stresses alter the orbital velocities of stars and gas, becoming dynamically significant in the outer disc and producing flattened rotation profiles. From observed rotation curves of a sample of spiral galaxies we estimate a radius-dependent viscosity angle <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha (r)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and discuss how these estimates might, in principle, be constrained by high-resolution kinematic and thermal observations. We review relevant observational and simulation-based evidence on galactic composition, temperature structure and viscous transport, and compare the RVF predictions with those of cold dark matter (CDM) and modified Newtonian dynamics (MOND), emphasising that the explicit inclusion of temperature-dependent kinematic viscosity is the principal distinguishing feature of the RVF model.</p>