Abstract Blood flow in narrow channels such as veins and arteries is the major topic of interest here. The Casson fluid with its shear-thinning attribute serves as the blood model. Owing to the arterial walls, the channel is configured curved in shape. The activation energy and nonlinear thermal radiation aspects are highlighted. The channel boundaries are flexible with peristaltic wave travelling along the channel. The mathematical description of the problem is developed under physical laws and then simplified using the lubrication technique. The obtained system is then sketched in graphs directly using the numerical scheme NDSolve in Mathematica software. The physical interpretation of parameters on axial velocity, temperature profile, concentration, and streamline pattern is discussed in the last section.