The research of non-Newtonian fluids has gained the attention of scientists because of its assorted uses in biological sciences, drug reduction, damping device production and industry. Second-grade nanofluid is one of the non-Newtonian fluids. This study includes the study of second-grade nanofluid flow passing through a stretchable vertical Riga surface of variable thickness. Thermal conductivity and viscosity are taken as variables, as the function of temperature. For heat transfer, this study includes the influences of thermophoresis and Brownian motion. The Cattaneo–Christov double diffusive (CCDD) model is considered and buoyancy forces’ effects are examined. The governing equations are converted to the nonlinear ordinary differential equations (ODEs) to solve these equations easily. The solution is obtained using the MATLAB package with its bvp4c technique. Consequences of different parameters like second-grade fluid parameter modified Hartmann number, thermal time relaxation parameter, concentration time parameter, variable thermal conductivity parameter, buoyancy forces, Brownian motion parameter, Schmidt number and thermophoresis parameter are interpreted through graphs and tables. This research exposes that Buoyancy forces’ parameters have antagonistic behavior on velocity curves. Depreciation in temperature and concentration is also noted with the rise in thermal time relaxation and concentration time relaxation.

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