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In this article, we have considered the effect of metachronal ciliary wave motion on the peristaltic flow of the Buongiorno nanofluid model for the synovitis problem. This study is additionally limited by the assumption of a low Reynolds number and lubrication theory approximations. An internal energy generation is also taken into account. Shear-thinning (model I) and shear-thickening (model II) for the concentration fluids are considered. The obtained dimensionless rheological equation is solved by using the homotopy perturbation Sumudu transformation method. The influence of various physical parameters on the dimensionless velocity, pressure rise, temperature, volume fraction, multi-sinusoidal waves, triangular waves, and streamlines has been analyzed. A trapping phenomenon is thoroughly examined. It is observed from the investigation that the shear-thinning (model I) and shear-thickening (model II) have completely distinct characteristics. The synovial fluid parameter shows opposite behavior on velocity and pressure rise profiles for models I and II, whereas the multi-sinusoidal wave and triangular wave forms retain the same shape of the waves as in the pressure gradient. These models can be used to treat rheumatoid arthritis as synovial fluids are present in joints. Fluid transfer in biological organs is improved by metachronal ciliary motion. Patients with rheumatoid arthritis can be treated with nanoparticles and ciliary motion. It is primarily due to their biocompatibility, low toxicity, and controlled release as well as their capacity to boost bioavailability and bioactivity of treatments and enable targeting the injured joints through the use of nanoparticles. In the limited scenario, the current work is in good accord with the earlier research, and it is analyzed through a graph.
Kotnurkar et al. (Sun,) studied this question.