Abstract On explanation of biomedical applications and its complexity, the contraction and relaxation of Eyring-Powell fluid in esophagus has turned out to be notable amongst the challenging research fields of fluid mechanics. Therefore, the main idea of this paper is to classify the simultaneous significances of compliant walls and emission of electromagnetic waves from walls of electrically conducting Eyring-Powell fluid. Conductivity of the fluid is increased by adding the Brownian motion and thermophoresis effects. Moreover, the velocity of the channel and the fluid particles near the surfaces are assumed to be different. Due to vertical contraction and relaxation, the body forces are taken in the form of mixed convection. The dimensionless variables are utilized to convert the required partial differential equations including mass, momentum and energy into dimensionless form. The solutions of the reduced partial differential equations subject to the given boundary conditions are calculated by using Mathematica. Moreover, the various solutions for dimensionless fluid concentration, velocity, and temperature distributions are captured for different values of embedded parameters. The different dimensionless parameters governing the flow, heat and mass transfer characteristics are the Schmidt number, radiation parameter, Hartmann number, local temperature Grashof number, slip parameters, local nanoparticles Grashof number, thermophoresis parameter, Brownian motion parameter, fluid parameters and Prandtl number. Maximum velocity is noted an increasing function of velocity slip parameter. Further maximum temperature enhances by increasing Brownian motion and thermophoresis parameters. More specifically the effects of slip parameters, Brownian motion and thermophoresis parameters on the flow stream have been examined. The velocity profile shows enhance behavior for large values of velocity parameter and mixed convection, whereas, reverse impact is noticed for magnetic field. Increasing concentration slip parameter causes reduction in nanoparticle volume fraction, while temperature of the fluid rises by increasing thermal slip parameter.
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