Dual-Phase Thermal and Concentration Relaxation Effects on Williamson Nanofluid: A Cattaneo-Christov (C–C) Flux Approach

Abstract

This article presents a unified numerical investigation of dual-phase thermal and concentration relaxation in magneto-viscoelastic Williamson nanofluid flow over a permeable, thermally radiating stretching sheet using the Cattaneo–Christov (C–C) flux framework. The governing magnetohydrodynamic boundary-layer equations, including Joule heating, viscous dissipation and thermal radiation, are reduced via similarity transformations to a coupled nonlinear ODE system and solved with a high-accuracy spectral quasilinearization method (SQLM). Residuals below 10 −12 are achieved within six iterations on 40 Chebyshev nodes, ensuring grid-independent convergence. Parametric analysis shows that thermal relaxation ( β T = 0.1) suppresses wall heat flux by about 15.2% and thickens the thermal boundary layer by 4.48% (1% thickness criterion), confirming finite-speed heat propagation beyond classical Fourier theory. Concentration relaxation ( β C = 0.1) intensifies nanoparticle gradients, elevating the Sherwood number by nearly 4%. Suction ( S = +0.5) contracts both momentum and thermal layers, enhancing the Nusselt number by roughly 22%, whereas injection reverses this trend. Increasing the velocity ratio parameter from A = 0.1 to 0.4 reduces the skin friction by 24.4%. Radiation and thermophoresis further expand the thermal layer, while a higher Prandtl number confines heat within a thinner region. This study shows that the C–C flux model outperforms the traditional Fourier and Fick laws in representing finite-speed relaxation effects, providing valuable guidance for improving thermal and mass transport in engineering designs, including high-efficiency heat exchangers, electromagnetic coating lines, polymer extrusion dies, solar thermal collectors, and precision biomedical drug-delivery systems. These findings provide a comprehensive benchmark for designing advanced nanofluid-based technologies where simultaneous control of heat and mass transport under electromagnetic fields is required.