Analysis of heat transfer and entropy generation for a low-Peclet-number microtube flow using a second-order slip model: an extended-Graetz problem

Cataloged from PDF version of article.The classical Graetz problem, which is the problem of the hydrodynamically developed, thermally developing laminar flow of an incompressible fluid inside a tube neglecting axial conduction and viscous dissipation, is one of the fundamental problems of internal-flow studies. This study is an extension of the Graetz problem to include the rarefaction effect, viscous dissipation term and axial conduction with a constant wall temperature thermal boundary condition. The energy equation is solved to determine the temperature field analytically using general eigenfunction expansion with a fully developed velocity profile. To analyze the low-Peclet-number nature of the flow, the flow domain is extended from −∞ to +∞. To model the rarefaction effect, a second-order slip model is implemented. The temperature distribution, local Nusselt number, and local entropy generation are determined in terms of confluent hypergeometric functions. This kind of theoretical study is important for a fundamental understanding of the convective heat transfer characteristics of flows at the microscale and for the optimum design of thermal systems, which includes convective heat transfer at the microscale, especially operating at low Reynolds number

Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel : mathematical model

A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic nonNewtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption and lubrication theory approximations. Debye-Hückel linearization (i.e. wall zeta potential ≤ 25mV) is also considered. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design

Electrothermal transport in biological systems : an analytical approach for electrokinetically-modulated peristaltic flow

A mathematical model is developed to investigate the combined viscous electro-osmotic flow and heat transfer in a finite length micro-channel with peristaltic wavy walls. The influence of Joule heating is included. The unsteady two-dimensional conservation equations for mass, momentum and energy conservation with viscous dissipation, heat absorption and electro-kinetic body force, are formulated in a Cartesian co-ordinate system. The Joule heating term appears as a quadratic function of axial electrical field in the energy conservation equation. The axial momentum and energy equations are coupled via the thermal buoyancy term. The peristaltic waves propagating along the micro-channel walls are simulated via a time-dependent co-sinusoidal wave function for the transverse vibration of the walls. Both single and train wave propagations are considered. Constant thermo-physical properties are prescribed and a Newtonian viscous model is employed for the fluid. The electrical field terms are rendered into electrical potential terms via the Poisson-Boltzmann equation, Debye length approximation and ionic Nernst Planck equation. The dimensionless emerging linearized electro-thermal boundary value problem is solved using integral methods. A parametric study is conducted to evaluate the impact of isothermal Joule heating term on axial velocity, temperature distribution, pressure difference, volumetric flow rate, skin friction and Nusselt number. The modification in streamline distributions with Joule heating and electro-osmotic velocity is also addressed to elucidate trapping bolus dynamics

Microfluidic manipulation by AC Electrothermal effect

AC Electrokinetics (ACEK) has attracted much research interest for microfluidic manipulation for the last few years. It shows great potential for functions such as micropumping, mixing and concentrating particles. Most of current ACEK research focuses on AC electroosmosis (ACEO), which is limited to solutions with conductivity less than 0.02 S/m, excluding most biofluidic applications. To solve for this problem, this dissertation seeks to apply AC electrothermal (ACET) effect to manipulate conductive fluids and particles within, and it is among the first demonstration of ACET devices, a particle trap and an ACET micropump. The experiments used fluids at a conductivity of 0.224 S/m that is common in bio-applications. Pumping and trapping were demonstrated at low voltages, reaching ~100 um/s for no more than 8 Vrms at 200 kHz. The flow velocity was measured to follow a quadratic relationship with applied voltage which is in accordance with theory. This research also studies ACET effect on low ionic strength microfluidics, since Joule heating is ubiquitous in electrokinetic devices. One contribution is that our study suggested ACET as one possible reason of flow reversal, which has intrigued the researchers in ACEK field. Electrically, a microfluidic cell can be viewed as an impedance network of capacitances and resistors. Heat dissipation in those elements varies with AC frequency and fluid properties, so changes the relative importance of heat generation at the electrode/electrolyte interface and in the resistive fluid bulk, which could change the temperature gradient in the device, hence changing the flow direction. Another contribution of this dissertation is the reaction enhanced ACET micropumping. A dramatic improvement in flow rate over conventional ac micropumps is achieved by introducing a thin fluid layer of high ionic density near the electrodes. Such an ionic layer is produced by superimposing a DC offset on AC signal that induces Faradaic reaction. The velocity improvement, in some cases, is over an order of magnitude, reaching a linear velocity of up to 2.5 mm/s with only 5.4Vrms. This discovery presents an exciting opportunity of utilizing ACET effect in microfluidic applications

Electrothermal transport of nanofluids via peristaltic pumping in a finite micro-channel : effects of joule heating and Helmholtz-Smoluchowski velocity

The present article studies theoretically the electrokinetic pumping of nanofluids with heat and mass transfer in a micro-channel under peristaltic waves, a topic of some interest in medical nano-scale electro-osmotic devices. The microchannel walls are deformable and transmit periodic waves. The Chakraborty-Roy nanofluid electrokinetic formulation is adopted in which Joule heating effects are incorporated. Soret and Dufour cross-diffusion effects are also considered. Under low Reynolds number (negligible inertial effects), long wavelength and Debye linearization approximations, the governing partial differential equations for mass, momentum, energy and solute concentration conservation are derived with appropriate boundary conditions at the micro-channel walls. The merging model features a number of important thermo-physical, electrical and nanoscale parameter, namely thermal and solutal Grashof numbers, the Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity) and Joule heating to surface heat flux ratio. Closed-form solutions are derived for the solute concentration, temperature, axial velocity, averaged volumetric flow rate, pressure difference across one wavelength, and stream function distribution in the wave frame. Additionally expressions are presented for the surface shear stress function at the wall (skin friction coefficient), wall heat transfer rate (Nusselt number) and wall solute mass transfer rate (Sherwood number). The influence of selected parameters on these flow variables is studied with the aid of graphs. Bolus formation is also visualized and analyzed in detail