In dire situations, such as the restricted spatial scale in nanoparticle systems and the analogous analysis of non-Fourier heat conduction and conventional heat conduction, the transmission of heat and momentum will exhibit non-linear and nonlocal behavior. The mechanisms of heat and mass transfer for non-Newtonian fluid flow between two inclined planes (convergent channel) with porous walled are taken into consideration. The Jaffrey-Hamel flow equation is renovated with the contribution of Carreau rheological model. The Cattaneo heat flux is presented to designate the anomalous heat, mass transport of Carreau nanofluid considering the influences of radiation flux, Brownian diffusion, and thermophoresis. Assumption, theories, and conservation law's leads to governing PDEs, which are solved numerically by invoking the Keller-Box scheme. It was concluded that for both conduit, flow reversal occurs only in the divergent domain of the channel but not in the converging where rapid acceleration of flow occurs, and inertial forces dominate the transport process. The flow instability in a porous media incorporate fluid inertia. The renovated model, which incorporates non-Fourier's law of heat conduction, can explain the anomalous thermal conductivity enhancement. The thermal relaxation effects the heat flux significantly, the conduction mechanism switches to oscillatory conduction with narrower temperature.