<p>This study examines the flow of Williamson fluid over a steadily expanding permeable stretching sheet under the influence of the inclined magnetic field. The sheet is assumed to be stretching in two-dimensional. A suitable approach has been set up to solve the modeled problem. The nonlinear PDE is transformed to ODE by similarity transformation, and the newly devised Chebyshev wavelet operational matrix method transforms nonlinear ordinary differential equations into nonlinear algebraic equations. This novel method is computationally flexible and facile due to the generation of integral matrices in comparison with the series collocation method and the convergence rate of Chebyshev wavelet is higher than other wavelets. The unresolved Chebyshev wavelet coefficients are determined using the Newton–Raphson method. Thus, a solution to the given Williamson fluid flow is achieved. The convergence of the approach is currently demonstrated through computation. The findings are validated with previous data thus demonstrating perfect synchrony in the physical parameters. It is discovered that when the magnetic field’s angle of inclination grows, the skin friction coefficient rises, the Nusselt number decreases as the Brownian parameter increases, and the Sherwood number increases as the Lewis number rises.</p>