Please cite this article as: N.T. Eldabe, M.A. Elogail, S.M. Elshaboury, A.A. Hasan, Hall effects on the peristaltic transport of Williamson fluid through a porous medium with heat and mass transfer, Appl. Math. Modelling (2015), doi: http://dx.
AbstractThis paper deals with the peristaltic flow of an incompressible, electrically conducting Williamson fluid in a symmetric planner channel through a porous medium with heat and mass transfer. Hall effects, viscous dissipation and Joule heating are taken into consideration. The non linear partial differential equations that govern that model were simplified under assumptions of long wavelength and low Reynolds number. Then a regular perturbation technique in the Weissenberg number (We << 1) was applied to obtain a closed form expressions for stream function, axial pressure gradient, temperature and concentration profiles. The influence of various embedded parameters on the flow were plotted through a set of graphs and discussed.
This work’s primary purpose is to implement a numerical study that simulates blood flow through a microvessel involving oxytactic microorganisms and nanoparticles. The oxytactic microorganisms exhibit negative chemotaxis to gradients of oxygen (oxygen repellents). These microorganisms are to batter infected hypoxic tumor cells as drug-carriers. The viscosity of blood is to vary with temperature, shear-thinning, and nanoparticle concentration. We have formulated a mathematical model then simplified it under assumptions of long wavelength and low Reynold’s number. The resulting non-linear coupled differential equation system is solved numerically with the MATHEMATICA software aid using the built-in command (ParametricNDSolve). This study treated all non-dimensional parameters defined in terms of viscosity to be variables (VP-Model), unlike some previous literature attempts that have considered these parameters mentioned above as constants (CP-Model). The achieved results assured the reliability of the (VP-Model) over the (CP-Model). Our results reveal that temperature and microorganism density increase with the thermophoresis parameter. The impact of increasing the Brownian motion parameter is to increase temperature and lessen microorganism density. Outcomes also indicate an enhancement in the microorganism density towards the hypoxic tumor regions located aside the microvessel walls by boosting oxygen concentrations in the streamflow. The current study is believed to provide further opportunities to improve drug-carrier applications in hypoxic tumor regions by better recognizing the flow features, heat, and mass transfer in such zones.
Recently, Hasona et al. [1] aimed to investigate the influence of thermal radiation and magnetic field on the
peristaltic flow of Carreau nanofluid in a vertical asymmetric channel. The authors have considered the Joule heating,
viscous dissipation, chemical reaction, Brownian motion, thermophoresis, Soret, and Dufour effects in their study. Several
mistakes and typos were discovered in the study mentioned above, which would affect the obtained results. This report
outlines some of these mistakes with suggested corrections to attract the readers' attention through a more in-depth insight
into analyzing and exposing these defects.
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