Thermo-entropic analysis of unsteady MHD nanofluid Couette flow: A classical spectral approach with an exploratory quantum linear-solver application

Source abstract

This study presents a thermo-entropic analysis of unsteady MHD nanofluid Couette flow, combining a classical bivariate spectral quasilinearisation (BI-SQLM) and Crank--Nicolson solution with an exploratory application of quantum linear solvers. An incompressible, electrically conducting nanofluid flows between parallel plates under partial slip and convective heat exchange; the discretised linear systems are additionally solved via the Harrow--Hassidim--Lloyd (HHL) algorithm and the Variational Quantum Linear Solver (VQLS). Results are presented for Pure Water, Cu-Water, and Al2O3-Water across seven parameter variations. The Hartmann number dominates velocity suppression and entropy amplification, while velocity slip reduces upper-wall entropy generation more than nine-fold. VQLS achieves $0.007\%$ solution error at a transpiled circuit depth of only 5 gates, versus HHL's 43,127, confirming near-term hardware feasibility. This is the first thermo-entropic analysis of unsteady MHD nanofluid Couette flow to combine validated classical spectral/finite-difference solvers with an exploratory quantum linear-solver demonstration, establishing a foundation for future full quantum treatment.