Scott-Blair model with unequal diffusivities of chemical species through a Forchheimer medium

•Non-integer derivatives are explored for unequal diffusivity of chemical spices Forchheimer Medium.•Theoretical Error and convergence analysis are carried out.•The Finite Difference method is constructed along with the L1 algorithm.•Average mass transfer rates are analyzed through plots for different physical parameters. Owing to the fact that fractional viscoelastic models contribute significantly with application point of view, a good number of researchers have diverted their attention to this area. In the current study, we have carried out a numerical investigation of the fractional viscoelastic fluid model with unsteady convection, on an inclined plane, via Forchheimer medium. Furthermore, we have presented the generalized Scott-Bliar model to Caput-type fractional derivatives with homogeneous-heterogeneous reactions in the constitutive relations. The viscoelastic features of the proposed model are explored by introducing three memory parameters. The homogeneous-heterogeneous reactions in the flow domain cause variations in the concentration, leading to one of the long-lasting chemical species. One can witness the homogeneous reactions in the flowing region, whereas the heterogeneous reactions occur at the boundary. A broader cluster of physical and chemical processes is tackled by considering diffusion coefficients of a different order. The well-known finite difference technique combined with the “L1 algorithm” is utilized to discretize the principal nonlinear boundary layer equations. The proposed numerical scheme is being validated by performing error and convergence analysis so that a thorough investigation of the chemical reaction process through the Forchheimer medium in the viscoelastic fluid model may be carried out. The proposed mathematical approach may be regarded as a valuable technique for studying the viscoelastic model and chemical reaction processes in a fluid to formulate schemes dealing with unsteady convection. Resultantly, this model can be utilized in the chemical industry.