This paper examines the influence of magnetic field on peristaltic flow of synovial nanofluid in an asymmetric channel. Hall current, thermophoresis, and Brownian motion effects are taken into account. Our problem is discussed for two models, in the first model which referred as Model (I), viscosity is considered exponentially dependent on the concentration, and Model (II) Shear thinning index is considered function of concentration. The governing problem is reformulated under the assumption of low Reynolds number and high wavelength. Resulting system of equations are solved numerically with the aid of Parametric ND Solve. Detailed comparisons have been made between Model (I) and Model (II) and found unrealistic results between them. Results for velocity, temperature and nanoparticle concentration distributions as well as pressure gradient and pressure rise are offered graphically for different values of various physical parameters. It is found that the velocity of fluid decreases in semi‐curved lines in case of Model (I) with the increase of Nb while, in Model (II) it decreases in the left side of the channel and increases in the right side of that channel. Such models are applicable to rheumatoid arthritis treatment.