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An analytical solution is presented to study the heat transfer characteristics of the combined pressure - electroosmotically driven flow in planar microchannels. The physical model includes the Joule heating effect to predict the convective heat transfer coefficient in two dimensional microchannels. The velocity field, which is a function of external electrical field, electroosmotic mobility, fluid viscosity and the pressure gradient, is obtained by solving the hydrodynamically fully-developed laminar Navier-Stokes equations considering the electrokinetic body force for low wall zeta potentials. Then, assuming a thermally fully-developed flow, the temperature distribution and the Nusselt... 

This is a theoretical study dealing with mixed electroosmotic and pressure-driven flow of a Newtonian liquid in a rectangular microchannel. Both and thermal boundary conditions are considered and the Debye-Hückel linearization is invoked. The governing equations are made dimensionless assuming fully developed conditions and then analytically solved using an infinite series solution. The governing factors are found to be the dimensionless Debye-Hückel parameter, velocity scale ratio, dimensionless Joule heating parameter, and channel aspect ratio. The results indicate that the Nusselt number is an increasing function of the channel aspect ratio, whereas the opposite is true for the velocity... 

This essay investigates a steady three-dimensional laminar boundary layer flow of magnetohydromagnetic radiative of graphene oxide-water nanofluid over an extensible surface in the attendance of couple stress, thermal ray, and Joule heating impact. Governing equations are solved numerically using the Runge-Kutta-Fehlberg 4.5 approach after the transformation of partial differential equations into ordinary differential equations. The main goal of this essay is to check the impacts of variations in the value of numerous parameters on the velocity along x and y-axis directions ((Formula presented.)) and temperature ((Formula presented.)) profiles, and also on the local skin friction coefficient... 

In this paper, a three-dimensional numerical model is developed to analyze the influence of the Joule heating on flow characteristics of an electroosmotic flow through square cross section micro-channels. The governing system of equations consists of three sets of equations: electric potential distribution, flow-field and energy equations. The solution procedure involves three steps. The net charge distribution on the cross section of the micro-channel is computed by solving two-dimensional Poisson-Boltzmann equation using the finite element method. Then, using the computed fluid's charge distribution, the magnitude of the resulting body force due to interaction of an external electric field... 

An analytical solution is presented to study the heat transfer characteristics of the combined pressure - electroosmotically driven flow in planar microchannels. The physical model includes the Joule heating effect to predict the convective heat transfer coefficient in two dimensional microchannels. The velocity field, which is a function of external electrical field, electroosmotic mobility, fluid viscosity and the pressure gradient, is obtained by solving the hydrodynamically fully-developed laminar Navier-Stokes equations considering the electrokinetic body force for low wall zeta potentials. Then, assuming a thermally fully-developed flow, the temperature distribution and the Nusselt... 

Electroosmosis is the main mechanism for flow generation in lab-on-a-chip (LOC) devices. The temperature rise due to the Joule heating phenomenon, associated with the electroosmosis, may be detrimental for samples being considered in LOCs. Hence, a complete understanding of the heat transfer physics associated with the electroosmotic flow is of high importance in design and active control of LOCs. The objective of the present study is to estimate the temperature rise and the thermal entry length in electroosmotic flow through rectangular microchannels, having potential applications in LOC devices. Along this line, the power-law rheological model is used to account for non-Newtonian behavior... 

The present investigation considers the fully developed electro-osmotic flow of power-law fluids in a planar microchannel subject to constant wall heat fluxes. Using an approximate velocity distribution, closed form expressions are obtained for the transverse distribution of temperature and Nusselt number. The approximate solution is found to be quite accurate, especially for the values of higher than ten for the dimensionless Debye-Huckel parameter where the exact values of Nusselt number are predicted. The results demonstrate that a higher value of the dimensionless Debye-Huckel parameter is accompanied by a higher Nusselt number for wall cooling, whereas the opposite is true for wall... 

The limitations of the microfabrication technology do not allow producing perfectly smooth microchannels. Hence, exploring the influences of roughness on transport phenomena in microtubes is of great importance to the scientific community. In the present work, consideration is given toward the corrugated roughness effects on fully developed electroosmotic flow and heat transfer in circular microtubes. Analytical solutions based on perturbation technique are presented for the problem assuming a low zeta potential under the constant heat flux boundary condition of the first kind. It is revealed that higher values of the corrugation number and relative roughness give rise to smaller Nusselt... 

Thermally developing electroosmotically generated flow of two viscoelastic fluids, namely the PTT and FENE-P models, through a slit microchannel is considered. Both the viscous dissipation and Joule heating effects are taken into account and a step change in wall temperature is considered to represent physically conceivable thermal entrance conditions. Expressions for the dimensionless temperature and Nusselt number in the form of infinite series are presented. In general, the resultant eigenvalue problem is solved numerically; nevertheless, an analytical solution is presented for the regions close to the entrance. A parametric study reveals that increasing amounts of the Peclet number... 

The present investigation considers the thermally developing electroosmotic flow of power-law fluids through a parallel plate microchannel. Both the viscous dissipation and Joule heating effects are taken into account and a step change in wall temperature is considered to represent physically conceivable thermal entrance conditions. Expressions for the dimensionless temperature and Nusselt number in the form of infinite series are presented. In general, the resultant eigenvalue problem is solved numerically; nevertheless, an analytical solution is presented for the regions close to the entrance. A parametric study reveals that increasing amounts of the Peclet number result in higher wall... 

In the present study, the thermal characteristics of electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient are investigated. The governing equations for fully developed flow under H1 thermal boundary conditions are first made dimensionless and subsequently solved through a finite difference procedure for a non-uniform grid. The influence of the major parameters on thermal features of the flow such as the temperature distribution and Nusselt number is discussed by a complete parametric study. The results reveal that the channel aspect ratio and the non-Newtonian characteristic of the fluid can affect the thermal behavior of the flow. It is... 

The influence of variable fluid properties on mixed electroosmotic and pressure driven flow of non-Newtonian fluids is investigated in this paper. The non-linear coupled energy and momentum equations are solved by means of an iterative numerical approach. The results reveal that the temperature dependent effects only become significant at very high values of the Debye-Hückel parameter in case of combined electroosmotic and pressure driven flow and could safely be neglected in other cases. It is observed that the physical properties variation lead to a higher mean velocity in case of pressure assisted flow and a lower mean velocity in case of pressure opposed flow. Furthermore, the... 

The present study considers both the hydrodynamic and thermal characteristics of combined electroosmotic and pressure driven flow in a microannulus. Analytical solutions are presented using the Debye-Hückel linearization along with the uniform Joule heating and negligible viscous dissipation assumptions, whereas exact results are achieved numerically. Here, the range of validity for the Debye-Hückel linearization is found to be about two times of that for a parallel plate microchannel. Accordingly, this linearization may successfully be used to evaluate the potential and velocity distributions up to the zeta potentials of 100 mV, provided that the dimensionless Debye-Hückel parameter is... 

Thermal transport characteristics of electroosmotic flow of power-law fluids in the presence of pressure gradient through a slit microchannel are studied in this paper. Considering a fully developed flow with a constant wall heat flux as the boundary condition, the governing equations are numerically solved by means of the finite difference method. A complete parametric study is done in order to investigate the effects of different flow parameters on the thermal behaviors of the flow. The results show that the non-Newtonian characteristic of the fluid can influence the thermal behaviors of the flow by affecting the rate of heat convection and viscous dissipation; however, its influence... 

The bio-microfluidic systems are usually encountered with non-Newtonian behaviors of working fluids. The rheological behavior of some bio-fluids can be described by differential viscoelastic constitutive equations that are related to PTT and FENE-P models. In the present work, thermal transport characteristics of the steady fully developed electroosmotic flow of these fluids in a slit microchannel with constant wall heat fluxes have been investigated. The Debye-Huckel linearization is adopted and the effects of viscous dissipation and Joule heating are taken into account. Analytical solutions are obtained for the transverse distributions of velocity and temperature and finally for Nusselt... 

This study investigates the influence of viscous dissipation on thermal transport characteristics of the fully developed combined pressure and electroosmotically driven flow in parallel plate microchannels subject to uniform wall heat flux. Closed form expressions are obtained for the transverse distributions of electrical potential, velocity and temperature and also for Nusselt number. From the results it is realized that the Brinkman number has a significant effect on Nusselt number. Generally speaking, to increase Brinkman number is to decrease Nusselt number. Although the magnitude of Joule heating can affect Brinkman number dependency of Nusselt number, however the general trend remains... 

The present study attempts to analyze the extended Graetz problem in combined electroosmotic and pressure driven flows in rectangular microchannels, by employing a variational formulation. Both the Joule heating and axial conduction effects are taken into consideration. Since assuming a uniform inlet temperature profile is not consistent with the existence of these effects, a step change in wall temperature is considered to represent physically conceivable thermal entrance conditions. The method of analysis considered here is primarily analytical, in which series solutions are presented for the electrical potential, velocity, and temperature. For general treatment of the eigenvalue problem... 

This study presents a comprehensive investigation on hydrodynamic and thermal transport properties of mixed electroosmotically and pressure driven flow in microtubes. Particular emphasis is given to investigating the combined consequences of viscous dissipation, non-uniform Joule heating, and variable thermophysical properties. Analytical solutions are obtained using the Debye-Hückel linearization and constant fluid properties assumption, while a numerical solution is presented for variable fluid properties and non-uniform distribution of Joule heating. The results indicate that, viscous heating effect is pronounced significantly when a favorable pressure gradient exists and cannot be...