AbstractThis article attempts to report the flow mechanism of Jeffrey nanofluid flow on a Riga plate integrating the influences of viscous dissipation, irregular heat source/sink, Brownian motion, and thermophoretic force. Nondimensionalization of mathematical model describing the flow system is accomplished by a set of compatible transformations. An accurate solution of ordinary differential equations is achieved by practicing spectral quasilinearization method. The present method is capable of giving results with good accuracy in few iterations, which infers speedy convergence. Solution‐based error norm (a measure of difference of approximate solution in two consecutive iteration level) is presented to authenticate precision of obtained approximate solution. The similarity between present approximate results and previously reported results is noted to check correctness. Obtained numerical solutions were replicated in a diagrammatic form to visualize the impact of flow parameters. Ratio of relaxation to retardation time produces an enhancing influence on momentum and nanoparticle concentration and a declining effect on the fluid temperature. Riga plate strengthens the momentum, which intensifies the transport of heat energy from boundary layer region, resulting in a reduction in fluid temperature.