ELECTROOSMOTIC FLOW AND HEAT TRANSFER OF NEWTONIAN/NON-NEWTONIAN FLUID IN MICRO AND NANO CHANNEL

Abstract

The enhancement of fluid flow, mixing efficiency and heat transfer by surface modulation in micro and macro domains have been addressed in this thesis. The present work focused on both analytical and numerical overview of electrokinetic theory to reveal the underlying physics for the flow enhancement and heat transfer, since the available literature could not provide a con crete information about complex fluids dealing in different flow domains (micro/macro) under different physical scenario. The performance of any mechanical system can be enhanced with the best optimal design to save the energy efficiency of the system in the sense of time as well as production with optimal cost. In this work major concern is to deal with the mathematical modeling of open and close domain problems including the heat and mass transfer effects in volving several external activated energy and boundary effects. Major portion of this thesis dealt with the analytical and numerical investigation of the effects of surface modulations on the electroosmotic flow (EOF), heat and mass transfer of Newtonian and non-Newtonian fluids in micro/nano channels as well as in enclosures. The mathematical model is based on the conservation principles and the nonlinear governing equa tions are solved numerically through the staggered grid based finite volume method. Chapter 1 of the thesis is introductory, which contains the basic principles of fluid flow, electroosmotic flow and the heat transfer effects of Newtonian/non-Newtonian fluids along with the corresponding governing equations. The effect of surface heterogeneity in wall potential on EOF is investigated in Chapter 2. The surface potential heterogeneity in micro/nano fluidic systems are used to generate the strong effects of convections restricting the pure molecular diffusion to enhance the mixing efficiency in multi component species solutions. The aim of this chapter is to enhance mixing of different eluted species in a nano-circular channel due to step change of wall potential which produces a strong recirculation zone in the bulk EOF. The mathematical model is based on the coupling between Maxwell’s equation for potential, Nernst-Planck equation for ion transport and the Navier-Stokes equations for momentum transport and are solved numerically by using finite volume method based on the pressure correction iterative algorithm SIMPLE (Semi-Implicit Method for Pressure Linked Equations) method. Flow recirculation zones are induced due to strong pressure gradient along the over potential region which increases the mixing efficiency. The streamlines and mole fraction distribution follows a tortuous path above the non-uniform potential region and the flow properties of strong solution deviates more compared to weaker solution due to the presence of strong pressure gradient inside the channel. An enhanced EOF of power-law fluid through a hydrophobic micro-channel has been ana lyzed by semi-analytic method in Chapter 3. The aim of the study is achieve an EOF augmen tation in a micro-channel without using the pressure gradient by creating a hydrophobic zone along the channel wall. The analytical expressions are derived on the basis of Debye-H¨uckel linearization principle and the closed form analytical expressions are obtained for the fluid flow and heat transfer where as the numerical results are presented for general parametric values. It is observed that the pseudoplastic (shear thinning) fluids achieve maximum flow enhancement and heat transfer as compared to dilatant (shear thickening) fluids in case of pure EOF as well as in the case of electroosmotic pressure driven flow. The expressions for Joule heating and ther mal radiation effects are derived and their contributions for classical Newtonian/non-Newtonian f luids are evaluated. Since thermal radiation plays a vital role for the therapeutic treatment of hyperthermia on thermal transport close to the surface wall and it is observed that Joule heating parameters enhance the heat transfer rate with decrease in flow behavior indices. In Chapter 4 we have studied the combined electroosmotic pressure driven flow of an electrolyte through a micro-channel where the channel walls are modulated with a periodic array of hydrophobic patches along the axial direction. It is an extension of Chapter 3 in two-dimensional form and the main motivation of this study is to find an optimum EOF over an electroosmotic pressure driven flow through the wall modulation compared to a slit micro channel under the same physical parameters. We have arranged the rectangular hydrophobic slippage in order to obtain the maximum flow enhancement. It is a big challenge for the trans portation and mixing of ionized fluids in BioMEMS as the drag effect is very strong along the walls and this effect can be minimized by imposing periodic hydrophobic slippage along the boundary. The results are presented in terms of flow enhancement factor, average heat transfer rate and the average entropy generation due to fluid friction, heat transfer and Joule heating effect. The results show that the electroosmotic flow enhancement in the patterned channel depends on the hydrophobic slip thickness and the length of the hydrophobic region. iii A generalized mixed convective flow inside a cubical enclosure filled with non-Newtonian power-law fluids is carried out numerically in Chapter 5. The aim of this study is to analyze the heat and mass transfer effect in an enclosure due to augmentation of wall heating effects for four different cases. The flow is influenced by the wall shear effects where the discrete temperature and mass gradients are acting along its bottom wall. A detailed physical insights into the flow, heat and mass transfer effects due to the variation of physical parameters such as Reynolds number, Grashof number, power-law index, Lewis number and Richardson number are presented graphically. The fluid flow and thermal fields are analyzed over a wide range of Reynolds number and Grashof number so as to achieve the effects associated with the Richard son number greater or less than 1. Our computed results showed that a decrease in flow behavior indices enhance the velocity boundary layer regime because shear thinning nature is increased. It is also revealed that the heat and mass transfer rate are sensitive to the location and length of the heating and soluting zones. The heat and mass transfer rate increases with the decrease of flow behavior indices, since the convection effect increases. Subsequently, the double diffusive magneto convection of a power-law fluid inside an enclo sure is studied numerically in Chapter 6. A comparative study is conducted between the shear thinning and shear thickening fluid in the case of co-operating buoyancy and opposing buoyancy driven flows to obtain the maximum heat and mass transfer rate. The flow is generated by the combined effect of time periodic thermal and solutal sources acting along short side walls. The aim of this study is to analyze the time periodic effect of the thermal and solutal gradients on the flow field, heat and mass transfer rate. A time history analysis is made for the fluid flow, heat and mass transfer characteristics. The analysis for entropy generation mechanism is made to characterize the thermodynamic optimization of the conjugate double diffusive convection. The entropy generation minimization (EGM) technique is used for the modeling and optimiza tion of the mechanical system. Bejan number is calculated to measure the relative contribution of heat transfer and the fluid friction irreversibility on the total entropy generation. It is found that the magnetic field strength induces the fluid flow rate and is strongly supported by the f low behavior index. It is also observed that, with the decrement of flow behavior index, the buoyancy effect and the hydrodynamic behavior of the fluid is getting increased.