Mathematical modelling of mechanical system in microfluidics is an emerging area of interest in micro scale engineering. Since microfluidic devices use the hair like structure of artificial cilia for pumping, mixing and sensing in different fields, therefore; electro osmotic cilia driven flow help to generate the fluid velocity for the Newtonian and viscoelastic fluid. Due to the deployment of artificial ciliated walls, the present research reports the combined effect of an electro osmotic flow and convective heat transfer on Jeffrey viscoelastic electrolytic fluid flow in a two-dimensional ciliated vertical channel. Heat generation/absorption and nonlinear radiation effects are included in the present mathematical model. After applying Debye-Huckel approximation and small Reynolds number approximation to momentum and energy equation, the system of nonlinear partial differential equation is reduced into non-homogenous boundary value problem. The problem determines the velocity, pressure and temperature profiles by the application of semi-analytical technique known as Homotopy Perturbation Method (HPM) with the help of software Mathematica. The graphical results of the study suggest that HPM is a reliable methodology for thermo physical electro-osmotic rheological transport in micro channels.
To prevent the respiratory diseases in an air ways, a defense mechanism based on mucus transport by the moving cilia plays an important role. The mucus transport is affected by the thermal radiation, chemical reaction that changes the physics of fluid due to nanoparticles and thickness of mucus, also different problems in respiratory tract may occur due to the mucus efficacy. In this study, it is observed that the mucus transport can be controlled by the magnetic field that is produced by the drug delivery of nanoparticles, thermal radiation due to temperature difference, porous medium due to respiratory infection, and diffusion of the nanoparticles (chemical reaction) due to the magnetic drug delivery. In this model, flow of Jeffrey nanofluid through the ciliated tube resembles with the mucus flow in a wind pipe. The movement of the mucus is observed by the momentum, energy and concentration equation in the presence of body forces due to magnetic field, heat source due to radiation, Darcy’s resistance due to infection and chemical reaction due to the concentration of nanoparticles. Mathematical model of this study forms a complex system of partial differential equations under the low Reynolds number and long wavelength approximation. The nonlinear set of partial differential equations is solved by the Homotopy perturbation method and software “Mathematica,” results are found for velocity, temperature and concentration profiles and concluded that the mucus flow decelerates due to magnetic field produced by the drug delivery of the nanoparticles but accelerates due to the viscoelastic parameter of Jeffrey fluid and Darcy’s resistance parameter due to infection. The heat transfer rate in the mucus flow rises by increasing the random motion and reduces by the radiation and energy loss. The diffusion of the nanoparticles in the mucus rises by the growing values of thermophoresis and chemical reaction parameter and reduces by the growing values of viscoelastic and Brownian motion parameter.
In this study heat transfer effects on cilia induced mucus flow in human airways is presented. The elliptic wave pattern of cilia tips produces metachronal wave which enables the transportation of highly viscous mucus with nonzero inertial forces. Upper Convective Maxwell model is considered as mucus. The governing partial differential equations are transformed from the fixed frame to the wave frame by using Galilean transformation and viscous dissipation is also incorporated in the energy equation. The non-linear governing equations are evaluated by the perturbation technique by using software “MATHEMATICA” and pressure rise is computed by numerical integration. The impact of interested parameters on temperature profile, velocity, pressure rise and pressure gradient are plotted by the graphs. The comparison of velocities due to symplectic and antiplectic metachronal wave are also achieved graphically.
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