This paper aims to present a comprehensive study of the non-linear peristaltic transport within a vertical uniform/non-uniform channel filled with a Jeffery non-Newtonian nanofluids in the presence of oxytactic microorganisms. The thermal conductivity of the used physiological fluids is varied linearly with the temperature while Arrhenius function is applied for the activation energy. The significance of electrical and magnetic fields together with a linear radiation and viscous dissipation are analyzed. The flow and heat transfer analysis has been performed under wall slip and compliant conditions. Additionally, optimization of the system entropy under the impacts of these aspects is examined. Numerical solutions for the governing system are introduced and profiles of the velocity 𝑢, temperature 𝜃, nanoparticle distributions 𝜑, heat transfer coefficient 𝑧 and extra stress tensor distribution 𝑆 𝑥𝑦 for the variations of the considered parameters are discussed. The main outcomes revealed that the maximizing of the Brinkman number 𝐵𝑟 is better to get higher features of the extra stress tensor 𝑆 𝑥𝑦 . Also, the velocity 𝑢, density of the microorganisms 𝜉 and the NP distributions in the interval −0.5 < 𝑦 < 0.5 get lower features as 𝑚 𝑒 is altered. However, the temperature distributions are maximized as 𝑚 𝑒 is growing.

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The main objective of this work is to present a comprehensive study that scrutinize the influence of DD convection and induced magnetic field on peristaltic pumping of Boron Nitride—Ethylene Glycol nanofluid flow through a vertical complex irregular microchannel. Experimental study showed that the nanofluid created by suspending Boron Nitride particles in a combination of Ethylene Glycol exhibited non-Newtonian characteristics. Further, the Carreau's fluid model provides accurate predictions about the rheological properties of BN-EG nanofluid. In order to imitate complicated peristaltic wave propagation conditions, sophisticated waveforms are forced at the walls. The essential properties of Brownian motion and thermophoresis phenomena are also included in simulating of heat equation as well as viscous dissipation. Mathematical simulation is performed by utilizing the lubrication approach. The resulting nonlinear coupled differential equation system is solved numerically using the built-in command (ND Solve function) in the Mathematica program. Numerical and pictorial evidence is used to illustrate the importance of various physiological features of flow quantities. The major findings demonstrated that the thermal resistance is observed to rise as the Soret and Dufour numbers increase, while the dissolvent concentration and nanoparticles volume fraction have the opposite effect.