Peristaltic activity in frames of hydromagnetics and rotation

Abstract

Peristalsis has pivotal role due to its applications in both industry and physiology under different conditions. Especially in mechanical discipline it has motivated engineers to construct pumps where fluid does not come in direct contact with any part of the machine. Applications include dialysis machines, open-heart bypass pump machines and infusion pumps. In addition, the study of hydro-magnetic peristaltic flow under the effect of magnetic field has played vital role in many engineering problems such as meteorology, biomedical engineering, solar physics, motion of earth's core and chemical engineering etc. Particularly the treatment of pathologies like gastroenric pathologies, rheumatisms, constipation, hypertension, targeted transport of drugs using magnetic particles as drug carriers are some applications. Blood is also known as the bio-magnetic fluid. It is because of complex interaction of the intercellular protein, cell membrane and the hemoglobin. The study of fluid flow in rotating frame of reference has promising applications in cosmic and geophysical flows. In such situation, Coriolis and Centrifugal forces are significant in relevant equations. The earth's liquid is strongly affected by the Coriolis force produced due to earth's rotation. Therefore, it is of great interest to study the flow of Newtonian/non-Newtonian fluids in rotating frame. Keeping this in mind the present thesis focus on the flow problems under different situation. Complex nonlinear differential systems for peristalsis of fluids under the aforementioned aspects are simplified through appropriate transformations. Suitable methods are employed to solve the nonlinear mathematical problems. Effects of rotation and heat/mass transfer are given due attention. Keeping all such facts in mind we structure the present thesis as follows: The review of some existing literature relevant to peristaltic transport and some fundamental equations is given in chapter one. Chapter two addresses the peristaltic flow Jeffrey fluid in a symmetric rotating channel. Channel walls are considered compliant in nature. Fluid is electrically conducting. Thermal radiation and Joule heating effects are employed in energy equation. Long wavelength and low Reynolds number approximation is applied for problem simplification. Analysis has been carried out for axial and secondary velocity. Moreover, heat transfer analysis is also discussed. Several graphs of physical interest are displayed and discussed. The results of this chapter are published inInternational Journal of Biomathematics8(2015)1550061(21 pages) DOI: 10.1142/S1793524515500618. Chapter three dealswith the peristaltic transport of Jeffrey fluid in a rotating channel. The channel walls satisfy the dynamic boundary conditions. This chapter is generalized work of previous chapter forSoret and Dufour and porous medium. The relevant flow analysis is first modeled and then computed for the exact solutions of velocities, temperature and concentration fields. Closed form expression of stream function is constructed. Plots are prepared for a parametric study reflecting the effects of Taylors, Soret, Dufour, Prandtl, Eckert and permeabilityparameters. The findings of this chapter have been published inPLoS ONE11 (2016) e0145525DOI: 10.1371/journal.pone.0145525. Chapter four has been organized for the impacts of thermophoresis, chemical reaction and heat source/sink. Thermal radiation is also present.Computations of solutions are made for the velocity, temperature and concentration fields. Closed form expression of streamfunction is obtained. Results displayed and discussed for the effects ofTaylors, Hartman, Brinkman, Biot, Schmidt numbers, chemical reaction, radiation, thermophoretic and non-uniform heat source/sink para