This paper focuses on flow structures and thermal fields of the Carreau–Yasuda (CY) nano°uid model through a two-dimensional, wavy, complicated vertical asymmetrical conduit ¯lled with porous elements. Formulations of the viscous dissipation in the case of CY nano°uids are derived and nonlinear radiation °ux as well as joule heating are examined. Buongiorno's nano°uid approach, which involves Brownian motion and thermophoresis aspects is considered. The electrical conductivity of the suspension is considered as a variable where it depends upon the ambient temperature and concentration distributions and the Joule heating impacts are not neglected. The approach of solving the problem is contingent upon converting the system to dimensionless form then the lubrication approach with low magnetic Reynold numbers is applied. Numerical solutions are found for the resultant system, and wide ranges are considered for Weissenberg number We, non-Newtonian parameter n and Darcy number Da, namely, 0
We
2, 0:5
n
1:5 and 0
Da
1:6, respectively. The major results indicated that gradients of the pressure are higher in case of shear thickening ðn > 1Þ comparing to in the instance of shear thinning ðn < 1Þ. Also, the velocity is enhanced, close to the channel's lowest portion, as the Weissenberg number is growing. The variable electrical conductivity gives a higher mass transfer rate compared to the constant property.