Abstract: The study of non-axisymmetric Homann stagnation-point flow of Walter’s B nanofluid along with magnetohydrodynamic (MHD) and non-linear Rosseland thermal radiation over a cylindrical disk in the existence of the time-independent free stream is considered. Moreover, the notable impacts of thermophoresis and Brownian motion are analyzed by Buongiorno’s model. The momentum, energy, and concentration equations are converted into the dimensionless coupled ordinary differential equations via similarity transformations, which are later numerically solved by altering the values of the pertinent parameters. The numerical and asymptotic solutions for the large shear-to-strain rate ratio γ = a/b for the parameters of the displacement thicknesses and the wall-shear stress are computed by perturbative expansion and analyzed. Furthermore, the technique bvp4c in MATLAB is deployed as an efficient method to analyze the calculations for the non-dimensional velocities, temperature, displacement thickness, and concentration profiles. It is observed that the two-dimensional displacement thickness parameters α and β are reduced due to the viscoelasticity and magnetic field effects. Moreover, when the shear-to-strain rate ratio approaches infinity, α is closer to its asymptotic value, while β and the three-dimensional displacement thickness parameter δ₁ show the opposite trend. The outcomes of the viscoelasticity and the magnetic field on the skin friction are also determined. It is concluded that f″(0) reaches its asymptotic behavior when the shearto-strain rate ratio approaches infinity. Meanwhile, ge(0) shows different results.

Key words: Walter's B fluid, cylindrical disk, nanofluid, magnetic field, non-linear thermal radiation, stagnation-point flow