The effect of viscous dissipation in thermally fully-developed electro-osmotic heat transfer in microchannels

The influence of viscous dissipation on thermally fully-developed, electro-osmotically generated flow has been analyzed for a parallel plate microchannel and circular microtube under imposed constant wall heat flux and constant wall temperature boundary conditions. Such a flow is established not by an imposed pressure gradient, but by a voltage potential gradient along the length of the tube. The result is a combination of unique electro-osmotic velocity profiles and volumetric heating in the fluid due to the imposed voltage gradient. For large ratio of the microtube radius (or microchannel half-width) to Debye length, the wall-normal fluid velocity gradients can be extremely high, which has the potential for significant viscous heating. The solution for the fully-developed, dimensionless temperature profile and corresponding Nusselt number have been determined for both geometries and for both thermal boundary conditions. It is shown that three dimensionless parameters govern the thermal transport: the relative duct radius (ratio of the duct radius or plate gap half-width to Debye length), the dimensionless volumetric source (ratio of Joule heating to wall heat flux), and a dimensionless parameter that relates the magnitude of the viscous heating to the Joule heating. Surprisingly, it is shown that the influence of viscous dissipation is only important at low values of the relative duct radius. For magnitudes of the dimensionless parameters which characterize most practical electro-osmotic flow applications, the effect of viscous dissipation is negligible.     

Thermal effects on mixed electro-osmotic and pressure-driven flows in triangle microchannels

A numerical investigation on the mixed electro-osmotic and pressure-driven flows in triangle microchannels with constant wall temperature is reported in the present study. The Galerkin method is employed to solve the Poisson equation, energy equation and Navier–Stokes equations for the flow driven by electro-osmotic and pressure gradient synchronously under the conditions of favorable pressure gradients and backpressure gradients. The physical properties of the electrolyte solution are considered to be varying with the temperature, and the dimensionless velocity profile, dimensionless temperature profile as well as dimensionless mass flux of the electrolyte solution are obtained. Furthermore, the parameters studies including pressure gradient, length ratio and Joule heating on mass flux of the electro-osmotic flows are performed, respectively. The numerical results show that a large Joule number leads to large dimensionless mass flux and dimensionless temperature of the electrolytic solution in the triangular microchannels for both conditions. For the electro-osmotic flows under the favorable pressure gradient, the increase in dimensionless mass flux resulted from Joule heating is enlarged with increasing pressure gradient and length ratio. However, for the electro-osmotic flows under the backpressure gradient, Joule heating results in a reverse flow in the channel, and the dimensionless mass flux of the reverse flow increases with increasing backward pressure gradient and decreasing length ratio. It is further found that the Joule heating induces a more significant increase in the dimensionless mass flux under favorable pressure gradient compared with that under backpressure gradient.     

Effect of Joule heating on electro-osmotic flow in a closedend micro-channel with isothermal and convective boundary conditions

The effect of Joule heating on the steady state electro-osmotic flow in a closed-end micro-channel is studied through numerical simulation with the finite volume method. The velocity field and the temperature field are described by a rigorous mathematical model. Thermophysical properties including viscosity and thermal conductivity are considered to be temperature-dependent. The simulations show that the presence of Joule heating causes an increase in temperature and a decrease in viscosity in the whole micro-channel, which, thereafter, induce a large velocity near the wall and an increase in fluid velocity at the central region in order to maintain a zero flow rate at the cross section of the micro-channel. The effect of Joule heating on the induced pressure gradient is also studied, which is very important for the application of the closed-end micro-channel as a microactuator. The results reveal that the induced pressure gradient, taking into consideration Joule heating, is significantly smaller than that without considering Joule heating when the wall temperature of the micro-channel is constant. The induced pressure gradient difference between considering Joule heating and without considering Joule heating is small under the convective boundary condition.     

Viscous dissipation effects on thermal transport characteristics of combined pressure and electroosmotically driven flow in microchannels

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 unchanged. Depending on the value of flow parameters, a singularity may occur in Nusselt number values even in the absence of viscous heating, especially at great values of dimensionless Joule heating term. For a given value of Brinkman number, as dimensionless Debye–Huckel parameter increases, the effect of viscous heating increases. In this condition, as dimensionless Debye–Huckel parameter goes to infinity, the Nusselt number approaches zero, regardless of the magnitude of Joule heating. Furthermore, it is realized that the effect of Brinkman number on Nusselt number for pressure opposed flow is more notable than purely electroosmotic flow, while the opposite is true for pressure assisted flow.     

On laminar hydromagnetic mixed convection flow in a vertical channel with symmetric and asymmetric wall heating conditions

The problem of hydromagnetic fully developed laminar mixed convection flow in a vertical channel with symmetric and asymmetric wall heating conditions in the presence or absence of heat generation or absorption effects is considered. Through proper choice of dimensionless variables, the governing equations are developed and three types of thermal boundary conditions are prescribed. These thermal boundary conditions are isothermal-isothermal, isoflux-isothermal, and isothermal-isoflux for the left-right walls of the channel. Analytical solutions for the velocity and temperature profiles for various special cases of the problem are reported. In addition, closed-form expressions for the Nusselt numbers and reversal flow conditions at both the left and right channel walls are derived. The general problem which includes the effects of both viscous dissipation and Joule heating is solved numerically by an implicit finite-difference scheme. Favorable comparisons of special cases with previously published work are obtained. A selected set of graphical results illustrating the effects of the various parameters involved in the problem including viscous and magnetic dissipations on the velocity and temperature profiles as well as flow reversal situations and Nusselt numbers is presented and discussed.     

Joule heating effect on electroosmotic flow and mass species transport in a microcapillary

This study presents a numerical analysis of Joule heating effect on the electroosmotic flow and mass species transport, which has a direct application in the capillary electrophoresis based BioChip technology. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including the Poisson-Boltzmann equation, the modified Navier-Stokes equations and the energy equation is developed. All these equations are coupled through the temperature-dependent liquid dielectric constant, viscosity, and thermal conductivity. By numerically solving the aforementioned equations simultaneously, the double layer potential profile, the electroosmotic flow field, and the temperature distribution in a cylindrical microcapillary are computed. A systematic study is carried out to evaluate the Joule heating and its effects under the influences of the capillary radius, the buffer solution concentration, the applied electric field strength, and the heat transfer coefficient. In addition, the Joule heating effect on sample species transport in a microcapillary is also investigated by numerically solving the mass transfer equation with consideration of temperature-dependent diffusion coefficient and electrophoresis mobility. The simulations reveal that the presence of the Joule heating could have a great impact on the electroosmotic flow and mass species transport.     

Analysis of dissipative non-Newtonian magnetic polymer flow from a curved stretching surface with slip and radiative effects

The convective–radiative magnetohydrodynamic non-Newtonian second-grade fluid boundary layer flow from a curved stretching surface has been scrutinized in the present study. The Reiner–Rivlin second-grade viscoelastic model is deployed which provides a good approximation for certain magnetic polymers. High temperature invokes the presence of radiative heat transfer, which is simulated with the Rosseland diffusion approximation. Viscous dissipation and Joule heating are also featured in the model and hydrodynamic (velocity) slip at the wall is also incorporated in the boundary conditions. The emerging nonlinear coupled dimensionless transport equations are solved with a Runge–Kutta method and a shooting numerical scheme. The influence of emerging multiphysical flow parameters on the dimensionless profiles is examined with the help of plots for comparative analysis of both non-Newtonian fluid and Newtonian fluid. The numerical solutions are validated for special cases with existing works. The velocity declines for a higher magnetic field, whereas the reverse trend is noted for the temperature function. The augmentation in the thermal field is noted with increments in radiation parameters. Furthermore, the fluid temperature of the second-grade fluid is higher with increasing Brinkmann number. The wall slip induces deceleration. Contour plots for streamlines and isotherms are also visualized and analyzed.     

Combined influences of viscous dissipation,non-uniform Joule heating and variable thermophysical properties on convective heat transfer in microtubes

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 neglected at low values of the dimensionless Debye–Hückel parameter. Moreover, uniform Joule heating assumption, even at low zeta potentials, may reduce the accuracy of the predicted thermal features considerably. The wall shear stress is found to be strongly dependent upon the zeta potential, which is underestimated by the Debye–Hückel linearization. Compared with the constant fluid properties case, decreasing electrical resistivity of the fluid by increasing temperature, amplifies the total energy generation due to the Joule heating and reduces the Nusselt number.     

Micro-scale thermo-fluidic transport in two immiscible liquid layers subject to combined electroosmotic and pressure-driven transport

A theoretical analysis is presented for fully developed convective heat transfer in two immiscible fluid layers confined within parallel plate microchannels subject to combined effects of axial pressure gradients and imposed electrical fields. Assuming desperate zeta potentials at the interfaces thus formed, closed-form expressions are derived for the velocity and temperature distributions under fully developed conditions, with uniform wall heat flux boundary conditions. For the heat transfer analysis, the viscous dissipation effects are neglected as compared to the Joule heating effects. Results are subsequently obtained for different ranges of the ratios of various electrical properties of the two fluid layers and various relative strengths of the ratios of the electrical fields and the imposed pressure gradients. These results demonstrate the effects of the applied electric fields and pressure gradients, presence of external heat source or sink and interfacial positions on the temperature distributions in the two layers and the corresponding Nusselt numbers.     

Solidification of electrically conducting liquid flow driven by shear and pressure gradients subject to viscous and Joule heating

Solidification of a liquid in motion driven by shear and pressure gradients occurs in many natural settings and technological applications. When the liquid is electrically conducting, its solidification rates can potentially be modulated by an imposed magnetic field. The shearing motion results in viscous dissipation and the Lorentz force induced by the magnetic field causes Joule heating of the fluid, which can influence the structure of the flow, thermal fields, and thereby the solidification process. In this study, a mathematical model is developed to study the combined effects of shear and pressure gradients in the presence of a magnetic field on the solidification of a liquid between two parallel plates, with one of them being insulated and under constant motion, and the other being cooled convectively and at rest. Under the quasi-steady assumption, closed-form semianalytical solutions are obtained for the instantaneous location of the solid–liquid interface, Nusselt number, and dimensionless power density as a function of various characteristic parameters such as the Hartmann number, pressure gradient parameter, Brinkman number, and Biot number. Furthermore, an interesting remelt or steady-state condition for the interfacial location is derived as arising from the competing effects of the solid side heat flux and viscous dissipation and Joule heating on the liquid side. The newly derived analytical results are shown to reduce to the various classical results in the limiting cases. A detailed systematic study is performed by the numerical solution of the semianalytical formulation, and the effects of different characteristic parameters on the solidification process are discussed.     

Fully developed electro-osmotic heat transfer in microchannels

Thermally fully developed, electro-osmotically generated convective transport has been analyzed for a parallel plate microchannel and circular microtube under imposed constant wall heat flux and constant wall temperature boundary conditions. Such a flow is established not by an imposed pressure gradient, but by a voltage potential gradient along the length of the tube. The result is a combination of unique electro-osmotic velocity profiles and volumetric heating in the fluid due to the imposed voltage gradient. The exact solution for the fully developed, dimensionless temperature profile and corresponding Nusselt number have been determined analytically for both geometries and both thermal boundary conditions. The fully developed temperature profiles and Nusselt number are found to depend on the relative duct radius (ratio of the Debye length to duct radius or plate gap half-width) and the magnitude of the dimensionless volumetric source.     

Physical aspects on unsteady MHD‐free convective stagnation point flow of micropolar fluid over a stretching surface

The unsteady magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid across a vertical stretching surface with second‐order velocity slip is the main concern of the present paper. The influence of electrical energy, temperature‐dependent thermal conductivity, thermal radiation, Joule heating, and heat sink/source is investigated. The basic partial differential equations are changed into ordinary differential equations with the help of appropriate similarity variables and then solved by the fourth‐order Runge‐Kutta–based shooting technique. The impact of physical parameters on the velocity, microrotation, and temperature as well as friction factor, couple stress, and local Nusselt number is thoroughly explained with the support of graphs and tables. The results divulge that the heat source/sink and thermal radiation parameters have a propensity to enhance the fluid temperature. The distribution of velocity is an increasing function of an electric field and unsteadiness parameter. The numerical results are also compared with the results available in the literature.     

Fully Developed Electroosmotically and Hydrodynamically Induced Convection Between Two Parallel Plates

An investigation was conducted to understand thermally fully developed convective transport phenomena induced by both electroosmosis and pressure gradients in a narrow parallel channel. A model was developed to describe the fluid flow and associated heat transport phenomena. Both the dimensionless temperature profile and the Nusselt number were obtained analytically with and without Joule heating with an investigation conducted to understand the importance of Joule heating and the ratio of the hydraulic flow rate to the electroosmotic flow rate. The emphasis of the comprehensive discussion is on understanding the physical significance of the singularities of the flow behavior and heat transfer.     

Laminar combined magnetoconvection in a wavy enclosure with the effect of heat conducting cylinder

In the current work, a numerical study of the flow characteristics on combined magnetoconvection in a lid-driven square enclosure, differentially heated, is carried out. This problem is solved by using finite element method of the partial differential equations, which are the heat transfer and stream function in Cartesian coordinates. The tests are performed for different solid–fluid thermal conductivity ratio, cylinder location and Richardson number while the Prandtl number, Reynolds number, magnetic and Joule heating parameters are kept constant. One geometrical configuration is used namely two undulations. The outcome obtained shows that the heat conducting inner square cylinder affects the flow and the heat transfer rate in the enclosure. The trend of the local heat transfer is found to follow a wavy pattern. Results are presented in terms of streamlines, isotherms, average Nusselt number at the heated wavy wall, average temperature of the fluid in the enclosure and dimensionless temperature at the cylinder center for different combinations of the governing parameters.     

Fully-developed thermal transport in combined electroosmotic and pressure driven flow of power-law fluids in microchannels

Thermally fully-developed heat transfer has been analyzed for combined electroosmotic and pressure driven flow of power-law fluid in a microchannel. Analytical expressions for transport parameters are presented in terms of the flow behavior index, the length scale ratio (ratio of Debye length to half channel height), dimensionless pressure gradient, and Joule heating parameter (ratio of Joule heating to surface heat flux). Closed form solutions are obtained for some specific values of the flow behavior index, while numerical solutions are presented for general cases. The results show that the temperature variation across the channel increases with increasing the pressure gradient. To reduce the length scale ratio is found to decrease the temperature variation, particularly for shear-thinning fluids. To increase the Joule heating parameter is to enlarge the temperature variation in the channel, especially for shear-thickening fluids. The Nusselt number can be increased by decreasing the length scale ratio due to the electroosmotic effect. Also, the Nusselt number increases with decreasing the values of flow behavior index and dimensionless pressure gradient.     

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

Magnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self-similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth-order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.     

Heat transfer and fluid flow analysis of non-Newtonian fluid in a microchannel with electromagnetohydrodynamics and thermal radiation

The study of electromagnetohydrodynamics (EMHD) of non-Newtonian fluid plays a significant role for optical design, thermal management of electronic components, and various operations of microfluidic devices. The use of parallel geometry is seen in the circulatory system, extrusion process, and respiratory system. By considering various practical applications, in the current study, the Poiseuille flow of an incompressible Casson liquid between the plates is investigated. The effects of MHD, Joule heating, thermal radiation, modified Darcy's law, and chemical reaction have been taken into account. The dimensional governing equations have been converted into dimensionless equations with pertinent nondimensional quantities. The resulting system of nondimensional system of equations has been analytically solved with nondimensional slip boundary conditions. The graphical results have been displayed with various fluid flow parameters. From the current study, it is concluded that the influence of Darcy number and Casson fluid parameter enhances the velocity profile, but the concentration declines with the enhancement of Casson fluid parameter. The radiation parameter and Prandtl number suppress the temperature profile.     

Electrokinetically modulated flow of couple stress magneto‐nanofluids in a microfluidic channel

In the present article, the theoretical investigation is presented for the mixed electrokinetic and pressure‐driven transport of couple stress nanoliquids in a microchannel with the effect of magnetic field and porous medium. This topic has gained a remarkable scope in nanoscale electro‐osmotic devices. The formulation of the present mathematical problem is simplified using the Debye‐Hückel linearization assumption. The merging model has important features such as the thermal Grashof number, solutal Grashof number, Joule heating, Helmholtz‐Smoluchowski velocity. The analytical solutions are presented for the axial velocity, temperature, and solute concentration. The expressions for the heat transfer rate, solute mass transfer rate, and surface shear stress function at the walls are also presented. The results display that, the velocity of the couple stress nanofluid is less in the case of pure electro‐osmotic flow as compared to that of combined electro‐osmotic and pressure‐driven flow. When the Joule heating parameter vanishes, the temperature and solute concentration profiles are linear, otherwise nonlinear. The shear stress function is larger in the case of pure electro‐osmotic flow and it is smaller for the combined effects of electro‐osmotic and pressure gradient. The present analysis places a significant observation that the various zeta potential plays an influential role in heartening fluid velocity. The analysis is relevant to electrokinetic hemodynamics and microfluidics.     

Heat transfer in micropolar fluid along an inclined permeable plate with variable fluid properties

This paper studies the heat transfer process in a two-dimensional steady hydromagnetic natural convective flow of a micropolar fluid over an inclined permeable plate subjected to a constant heat flux condition. The analysis accounts for both temperature dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim–Swigert iteration procedure. Results for the dimensionless velocity and temperature profiles and the local rate of heat transfer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that in modeling the thermal boundary layer flow when both the viscosity and thermal conductivity are temperature dependent, the Prandtl number must be treated as a variable to obtain realistic results. As the thermal conductivity parameter increases, it promotes higher velocities and higher temperatures in the respective boundary layers. The wall shear stress increases with the increase of thermal conductivity parameter. This is true of electrically conducting as well as electrically non-conducting fluids. The presence of heat generation invigorates the flow and produces larger values of the local Nusselt number compared with the case of zero heat generation.     

Flow and thermal analysis of Oldroyd 8 constant fluid in a porous channel

The present research is based on the thermal and flow properties of the viscoelastic Oldroyd 8 constant fluid in an upright microchannel. The energy and momentum equations were solved with the support of temperature Jump and velocity slip boundary conditions. To measure the irreversibility rate of the flow system, the acquired results of velocity and thermal equations were used. To crack the current mathematical model problem, the numerical Runge–Kutta–Fehlberg method was used. With the aid of graphs, the effect of physical parameters such as thermal radiation, thermal-dependent heat source, Joule heating, fluid parameters, velocity slip, and temperature Jump parameters on the fluid flow, thermal energy, and system entropy generation was discussed. Fluid parameters have different effects on the velocity profile. The Grashof and Hartmann numbers demonstrate opposite effects on the momentum field. The thermal energy of the system reduces with thermal radiation and temperature Jump factor. The thermal radiation, Hartmann number, and temperature Jump parameters reduce the system's irreversibility rate. With the Brinkman number and temperature Jump parameter, the irreversibility ratio increases.