Peristaltic transport of fluids with convective conditions

Abstract

hysiology and industry. Especially the dynamics of non-Newtonian fluids by peristaltic mechanism is hottopic of research. Peristalsis is quite significant in various engineering problems associated with powder technology, sedimentation, combustion, fluidization, heart-lung machine and paint spraying. In plant physiology, such mechanism is involved in phloem translocation by driving a sucrose solution along tubules by peristaltic contractions. Heat transfer analysis in peristalsis has been also used to obtain information about the properties of tissues and thus quite significant in the biomedical sciences. In fact heat transfer is important because nutrients diffuse out from blood. Further the temperature difference in any situation results from energy flow into a system or energy flow from a system to surroundings. The former leads to heating whereas latter leads to cooling of an object. This is known as convection heat transfer. Bulk motion of fluid boosts heat transfer in many physical situations. It is supportive to predict how long it takes for a hot object to cool down at a certain temperature.Heat transfer subject to convective conditions is involved in processes such as thermal energy storage, gas turbines, nuclear plants etc. This concept is of great value because the thermodynamic aspects of blood are quite prevalent in processes such as oxygenation and hemodialysis. Moreover the energy flux is not only induced by the temperature gradient but by composition gradient as well. The simultaneous effects of heat and mass transfer with convective boundary conditions provide complicated expressions relating the fluxes and driving potentials. Keeping this in mind the present thesis highlights the heat transfer in peristaltic transport of fluids in a channel with convective boundaries. The relevant equations are modeled and solved for the approximate and numerical solutions. Salient features of heat transfer in view of convective boundary conditions are emphasized. Motivated by all such facts 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 of third order fluid in an asymmetric channel. Channel walls are subjected to the convective boundary conditions. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. Long wavelength approximation and perturbation method yield the series solutions for the stream function, temperature and longitudinal pressure gradient. Analysis has been further carried out for pressure rise per wavelength through numerical integration. Several graphs of physical interest are displayed and discussed. The results of this chapter are published inJournal of Mechanics 29(2013) pp. 599-607. Chapter three dealswith the peristaltic transport of viscous nanofluid in an asymmetric channel. The channel walls satisfy the convective conditions. Effects of Brownian motion and thermophoresis are taken into account. The relevant flow analysis is first modeled and then computed for the series solutions of temperature and concentration fields. Closed form expression of stream function is constructed. Plots are prepared for a parametric study reflecting the effects of Brownian motion, thermophoresis, Prandtl, Eckert and Biot numbers. The findings of this chapter have been published inJournal of Molcular Liquids 193 (2014) pp. 74-82. The peristaltically driven Casson fluid flow in an asymmetric channel with convective conditions is investigated in chapter four. The Soret and Dufour effects are studied in the presence of chemical reaction. The relevant flow analysis is modelled for Casson fluid in a wave frame. Computations of solutions are made for the velocity, temperature and concentration fields. The performed analysis shows that the two yield planes exist because of channel asymmetry. These planes are described in terms of the core width by working on the transcendental equation. Closed form expression of streamfunction is obtained. Results displayed and discussed for the effects ofCasson fluid parameter, chemical reaction parameter, Prandtl, Schmidt, Soret, Dufour and Biot numbers. The research presented in this chapter is published inComputers & Fluids 89 (2014) pp. 242-253. Chapter five explores the heat transfer effects in peristaltic flow of couple stress fluid. An incompressible fluid is considered in a channel with convective boundary conditions. This study is motivated towards investigating the physiological flow through particle size effect. Long wavelength and low Reynolds number approach is adopted. Effects of various physical parameters like couple stress parameter and Brinkman and Biot numbers on the velocity profile, streamlines pattern, temperature profile, pumping action and trapping are studied. Computational results are presented in graphical form. The contents of this chapter have been accepted for publication inHeat Transfer Research(2013). Chapter six is concerned with the peristaltic transport of JohnsonSegalman fluid in an asymmetric channel with convective boundary conditions. Mathematical modelling is based upon the conservation laws of mass, linear momentum and energy. Resulting equations have been solved after using long wavelength and low Reynolds number considerations. Results for the axial pressure gradient, velocity and temperature profiles are obtained for small Weissenbergnumber. Expressions of the pressure gradient