This investigation discusses the influences of a chemical reaction and concentration‐dependent viscosity on a magnetohydrodynamics peristaltic pump of synovial nanofluid in a tapered channel. Chemical reaction and Hall current effects are considered in the proposed investigation. The current study is solved for two suggestion models. In Model‐(I), the concentration is considered as a function in viscosity. In Model‐(II), concentration is considered as a function of the shearthinning index. The related study is rearranged under the models of low Reynolds number and long wavelength. The system study of highly nonlinear partial differential equations is explained mathematically with the aid of ParametricNDSolve by using Mathematica 11. Both models have been compared numerically and a huge difference is found between them. Results for velocity profile, temperature, and nanoparticle concentration distributions are obtained graphically for similar values of various physical parameters in threedimensional forms. Furthermore, a trapping bolus sketch is proposed in the terminus.