This investigation aims to study Hall's current effect on the peristaltic flow of a Jeffrey nanofluid with variable thermal conductivity in an inclined asymmetric channel. Joule heating and oblique magnetic field effects are taken into consideration. A system of ordinary differential equations is obtained under the approximation of low Reynolds number and long wavelength, which consists of momentum, energy, and concentration equations. The influences of penitent physical parameters on the distribution of velocity, temperature, and concentration have been discussed graphically. Streamline graphs are offered in the terminus, which elucidates the trapping bolus phenomenon. The resulting equations are solved numerically using the ND Solver technique. The thermal conductivity parameter causes the pressure gradient to increase while reducing the pressure rise. Our present model can be applied to physiological flow transportation in the veins with heat transfer. K E Y W O R D S Hall current, Jeffrey nanofluid, ND Solver, peristaltic flow, variable thermal conductivity

This investigation aims to introduce a new solution with aid of numerical methods to the blood flow of Carreau-Yasuda fluid through a microvessel. Swimming of gyrotactic microorganisms with nanoparticles is considered. A resulting system of partial differential equations is simplified by the meaning of low Reynolds number and long wavelength. This system of partial differential equations was formulated and transformed mathematically using new theories of differential transform method. Variable nonndimensional physical parameters effects, such as numbers of bioconvection Peclet and bioconvection Rayleigh, and so forth on velocity, temperature, and concentration distribution as well as oxytactic microorganism and oxygen concentration profiles are studied. All results are constructed in two cases of viscosity on the same figure, one of them in the case of variable parameters and the other in constant parameters. The existing study assured that the microorganism density in the direction near to the hypoxic tumor tissues regions grows with a rise in oxygen concentrations and the blood viscosity diminutions.

As thermal radiation is one of the fundamental means of heat transfer, therefore, this study analyzes the impacts of thermal radiation and magnetic field on the peristaltic transport of a Jeffrey nanofluid in a nonuniform asymmetric channel. Further, Two models of viscosity are debated: Model (I), in which all parameters dependent on viscosity behave as a constant (as treated before in nanofluid research); Model (II), in which these known parameters are considered to vary with the temperature of the flow. Under the condition of long wavelength and low Reynolds number, the problem is rearranged. The resulting system of partial differential equations (PNE) is solved with aid of Mathematica 11. Furthermore, the streamline graphs are presented by significance of trapping bolus phenomenon. To emphasize the quality of solutions, comparisons between the previous results and recent published results by Reddy et al. have been made and signified. The comparisons are shown in Table 1 and are found to be in good agreement. As the thermal radiation increases, the diameter of nanoparticles rises (thermal radiation is a diminishing function of temperature, and with a decrease in the temperature, the diameter of the nanoparticles increases, that is, the size of nanoparticles increases and they become more active near malignant tumor tissues). Therefore, its work as agents for radiation remedy, produce limited radiation quantities, and selectively target malignant tumor for controlled mutilation (radiotherapy of oncology). Such a model is appropriate for the transportation of physiological flows in the arteries with heat and mass transfer (blood flow models).