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Electrophoretic motion of hydrophobic particles has been scrutinized numerically in solid-state nanopores. The Poisson, Stokes, and Nernst–Planck equations are solved simultaneously, and the Newton–Raphson algorithm is used to compute the correct velocity at each point. For the hydrophobic surface characterization, the Navier-slip boundary condition with a wide range of slip lengths is applied to the nanoparticle's surface. The effects of the electric field intensity, the electrolyte concentration, and the particle's size on the electrophoretic velocity are examined. Then, the nanopore's size and surface charge density are manipulated to achieve the configuration for separating hydrophobic and hydrophilic particles based on their slip lengths. The results show that the hydrophobic and hydrophilic particles, under particular circumstances, would move in the opposite direction in a nanopore. Finally, the resistive pulses of the particles with various slip lengths are studied. The resistive pulse properties of the hydrophobic and the hydrophilic particles are completely distinguishable and show potential application for resistive pulse sensing as a tool for reckoning the particle's slip length.

This paper extends the analysis of solute dispersion in electrohydrodynamic flows to the case of band broadening in polyelectrolyte-grafted (soft) capillaries by accounting for the effects of ion partitioning, irreversible catalytic reaction and pulsatile flow actuation. In the Debye–Hückel limit, we present the benchmark solutions of electric potential and velocity distribution pertinent to steady and oscillatory mixed electroosmotic–pressure-driven flows in soft capillaries. Afterwards, the mathematical models of band broadening based on the Taylor–Aris theory and generalized dispersion method are presented to investigate the late-time asymptotic state and all-time evolution of hydrodynamic dispersion, respectively. Also, to determine the heterogeneous dispersion behaviour of solute through all spatiotemporal stages and to relax the constraint of small zeta potentials, a full-scale numerical simulation of time-dependent solute transport in soft capillaries is presented by employing the second-order-accurate finite difference method. Then, by inspecting the dispersion of passive tracer particles in Poiseuille flows, we examine the accuracy of two analytical approaches against the simulation results of a custom-built numerical algorithm. Our findings from hydrodynamic dispersion in Poiseuille flows reveal that, compared to rigid capillaries, more time is required to approach the longitudinal normality and transverse uniformity of injected solute in soft capillaries. For the case of dispersion in mixed electrohydrodynamic flows, it is found that the characteristics of the soft interface, including the thickness, permittivity, fixed charge density and friction coefficient of the polymer coating layer, play a significant role in determining the Taylor diffusion coefficient, advection speed and dispersion rate of solutes in soft capillaries.

Pulsating heat pipes (PHPs) are one of the new devices used for cooling in several applications such as electronic and aerospace systems. Their low cost, effectiveness at various conditions, being equipped for passive energy conversion, and well distribution of temperature compared to conventional heat pipes are among the reasons of their popularity. To investigate the effect of surface tension of the working fluid on the behavior of PHPs, a copper heat pipe is fabricated with inner and outer diameters of 2 mm and 4 mm, respectively. Five different concentrations of cetrimonium bromide (C-Tab) surfactant are dissolved in water and are tested with a filling ratio of 50% (± 1%). A piece of glass is placed in the adiabatic section to make the flow visualizations possible. Thermal resistance and flow visualization results are compared. Visualization of the flow shows that by increasing the surfactant concentration, annular and semi-annular regimes can be observed at lower powers. It is also detected that by increasing the surfactant concentration, thermal resistance will decrease, while the maximum heat flux is reduced. This can be explained by thinner film thickness in the evaporator. The lowest thermal resistance was detected to be 0.44 K/W for the 0.25 g L−1 C-Tab concentration at 25 W heat input power which shows a significant improve of 77.5% compared to pure water at the same power.

The dispersion of a neutral solute band by electrokinetic flow in polyelectrolyte layer (PEL)-grafted rectangular/slit microchannels is theoretically studied. The flow is assumed to be both steady and fully developed and a first-order irreversible reaction is considered at the wall to account for probable surface adsorption of solutes. Considering low electric potentials, analytical solutions are obtained for electric potential, fluid velocity and solute concentration. Special solutions are also obtained for the case without wall adsorption. To track the dispersion properties of the solute band, the generalized dispersion model is adopted by considering the exchange, the convection and the dispersion coefficients. The solutions developed are validated by comparing the results with the predictions of finite-element-based numerical simulations. Even though the solutions can take any form of initial solute concentration into account, the results are presented by considering a solute band of rectangular shape. The results reveal that, while the short-term transport coefficients are strongly affected by the initial concentration profile, the long-term values are not dependent upon the initial conditions. In addition, it is shown that the mass transport coefficients are strong functions of the channel aspect ratio; hence, approximating a rectangular geometry by the space between two parallel plates may lead to considerable errors in the estimation of mass transport characteristics. This is particularly important for the dispersion coefficient for which the long-term values for a slit microchannel are quite different from those for a rectangular channel of very high aspect ratio. It is also illustrated that the exchange and convection coefficients increase on increasing the Damkohler number, whereas the opposite is true for the dispersion coefficient. The convection and dispersion coefficients are generally increasing functions of the PEL fixed charge density and the PEL thickness and decreasing functions of the PEL friction coefficient. Last but not least, a thicker electric double layer is found to provide a larger degree of solute dispersion, which is the opposite of that observed in a microchannel with bare walls.

Pulsating heat pipe (PHP) is a type of wickless heat pipe that has a simple structure and an outstanding thermal performance. Nanofluid is a type of fluid in which nanoparticles are dispersed in a base fluid and have generally a better thermal conductivity in comparison with its base fluid. In this article, the performance of a nanofluid PHP is investigated. Graphene/water nanofluid with a concentration of 1 mg mL−1 and TiO2 (titania)/water nanofluid with a concentration of 10 mg mL−1 are used as the working fluids. To simultaneously investigate the thermal performance and flow regimes in the PHP, a one-turn copper PHP with a Pyrex glass attached to its adiabatic section is used. A one-turn Pyrex PHP is also used to fully visualize flow patterns in the PHP. Our results show that the material for the fabrication of a PHP and temperature of the working fluid are the most important parameters that affect the stability of a nanofluid in the PHP. The more stable nanofluid keeps its stability in the cupper PHP, while the less stable nanofluid starts to aggregate right after the injection to the cupper PHP. The more stable nanofluid has a better thermal performance than water, while the less stable nanofluid has a worse thermal performance than water. In the case of flow regimes, no significant differences are observed between the nanofluid PHP and the water PHP which is different from the previous observations. These results can help researchers to choose the best working fluid for PHPs.

Multi-stream Plate-fin heat exchangers (MSPFHEs) are among the most efficient heat exchangers in energy-based industries. They should be carefully designed to have maximum effectiveness and to avoid wasting energy. Flow maldistribution could significantly degrade the performance of heat exchangers. This study presents a novel modeling framework to capture the thermally-induced maldistribution in two-phase MSPFHEs. The developed model is used to show how thermally-induced flow maldistribution affects the performance of the heat exchanger, and some possible modifications are investigated to reduce its consequences. Our case study results show that thermally-induced maldistribution decreases the total heat transfer by 10.8%. Heat leakage helps to induce less flow near the leakage region, so it can be managed to overcome the initial thermally-induced flow. Moreover, thermally-induced maldistribution affects a limited region along the heat exchanger height direction. So, thermal performance deterioration decreases with increasing the number of layers for each stream. Nevertheless, increasing the heat exchanger length increases the degraded region in the heat exchanger. Thus, increasing the core length is not a good way to counteract the thermal performance deterioration caused by thermally-induced maldistribution. It is also found that an optimum layer arrangement could help to eliminate the thermally-induced maldistribution in the heat exchanger.

This paper presents an analysis of the combined electro-osmotic and pressure-driven axial flows of viscoelastic fluids in a rectangular microchannel with arbitrary aspect ratios. The rheological behavior of the fluid is described by the complete form of Phan-Thien–Tanner (PTT) model with the Gordon–Schowalter convected derivative which covers the upper convected Maxwell, Johnson–Segalman and FENE-P models. Our numerical simulation is based on the computation of 2D Poisson–Boltzmann, Cauchy momentum and PTT constitutive equations. The solution of these governing nonlinear coupled set of equations is obtained by using the second-order central finite difference method in a non-uniform grid system and is verified against 1D analytical solution of the velocity profile with less than 0.06% relative error. Also, a parametric study is carried out to investigate the effect of channel aspect ratio (width to height), wall zeta potential and the Debye–Huckel parameter on 2D velocity profile, volumetric flow rate and the Poiseuille number in the mixed EO/PD flows of viscoelastic fluids with different Weissenberg numbers. Our results show that, for low channel aspect ratios, the previous 1D analytical models underestimate the velocity profile at the channel half-width centerline in the case of favorable pressure gradients and overestimate it in the case of adverse pressure gradients. The results reveal that the inapplicability of the Debye–Huckel approximation at high zeta potentials is more significant for higher Weissenberg number fluids. Also, it is found that, under the specified values of electrokinetic parameters, there is a threshold for velocity scale ratio in which the Poiseuille number is approximately independent of channel aspect ratio.

Design and fabrication of solar collectors with high performance of energy efficiency to convert solar energy to utility energy is vitally important. This article reports the results obtained from design, construction and investigation of the performance of a Combined Multi-Purpose Vacuum Solar Collector (CMPVSC). This collector consists of three sections: the vacuum section, the liquid section and the air section. In the present collector, it is capable of transferring heat to two flows (liquid and air) simultaneously and separate with the possibility of multipurpose applications. The CMPVSC is compared with the existing individual collectors and the effects of different parameters on the efficiency of this collector are examined. Experimental data indicate that high temperature and high performance with a 43% reduction in cost can be obtained using CMPVSC compared to two individual collectors. To increase the efficiency of the collector, triangular and rectangular channels in the air section have been used. The vacuum part is implemented to reduce heat losses. The effect of water inlet temperature, air flow rate, shape of air channel and vacuum part on the heat delivery by air and water have been investigated. Furthermore, as a matter of comparison of CMPVSC with the individual collector, there is a chance of obtaining highest temperature and efficiency with minimum cost and space requirements.

The performance of an infinitely segmented magnetohydrodynamic generator is analyzed using the second law of thermodynamics entropy generation criterion. The exact analytical solution of the velocity and temperature fields are provided by applying the modified Hartmann flow model, taking into account the occurrence of the Hall effect in the considered generator. Contributions of heat transfer, fluid friction, and ohmic dissipation to the destruction of useful available work are found, and the nature of irreversibilities in the considered generator is determined. In addition, the electrical isotropic efficiency scheme is used to evaluate the generator performance. Finally, the implication of the Hall parameter, Hartmann number, and load factor for the entropy generation and the generator performance are studied and the optimal operating conditions are determined. The results show that the heat transfer has the smallest contribution to the entropy generation compared to that of the friction and ohmic dissipation. The application of the Hall effect on the system showed an appreciable augmentation of entropy generation rate which is along with what the logic implies. A parametric study is conducted and its results provide the generated entropy and also efficiency diagrams which show the influence of the Hall effect on the considered generator.

We perform a 3D numerical modeling of reaction-diffusion dynamics in a Y-shaped microreactor, considering a fully developed combined electroosmotic and pressure-driven flow. The governing equations, based on a second-order irreversible reaction, are solved invoking a finite-volume approach for a non-uniform grid system. We demonstrate that the reaction is highly position dependent: more production is observed adjacent to the horizontal walls for a favorable pressure gradient, whereas both the wall and centerline are the regions of highest production when a back pressure is applied. We further show that, to achieve the maximum production rate, the EDL should be thick enough, the pressure gradient should be unfavorable, and both the diffusiveties and the inlet concentrations of the reacting components should be identical. Although the same is true for the production efficiency, defined to be the ratio of the average production concentration to the inlet concentration of the limiting component, there is a main difference: when the inlet concentrations are the same the efficiency is minimal. Moreover, the concentration pick is inclined toward the component with either less diffusivity or less inlet concentration; the inclination is magnified when either the Debye length increases or an unfavorable pressure gradient is employed.

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 numbers. Since the same is true for the mean velocity, one may conclude that the roughness effects on the hydrodynamic and thermal features of electroosmotic flow are negative. Further, the Nusselt number is found to be a decreasing function of the Joule heating rate and an increasing function of the dimensionless Debye-Huckel parameter.

Compact heat exchangers are among the vital components used in various industries. In this study, a general framework has been developed with a multi-scale point of view for three-dimensional simulation of multi-stream plate-fin heat exchangers. The most important features in the MSPFHEs simulation, such as phase change phenomena, multi-component mixtures, multiple streams, transversal, lateral and longitudinal conduction, non-uniformity of inlet flow, variable fluid properties, and heat leakage are simultaneously considered in this model. The modular form of the model structure has facilitated layer-by-layer simulation of cross flow heat exchangers as well as parallel flow ones. Our model has been successfully validated with numerical and experimental case studies. Periodic boundary conditions are developed for simulating heat exchangers with a high number of layers to reduce the computational cost. The results for a challenging six-stream test case show that when the number of layers for each stream is more than 15, results converge to the periodic boundary condition case. The total simulation time is decreased by 98.1% for a heat exchanger with 40 repeating unit cells. Liquefied natural gas production has been decreased by 5.8% due to the non-uniformity of natural gas at the entrance of the six-stream test case. Fluid temperature, and vapor quality distributions for a multi-component two-phase cross-flow MSPFHE have been presented. A dead zone is observed in the results of the cross-flow heat exchanger that does not have a significant contribution to the heat exchange. Results show that the total heat exchange between streams has been decreased by 8.5% in comparison to the parallel-flow ones.

Both nonlinear rheology and finite EDL thickness effects on the mixing process in an electroosmotically actuated Y-sensor are being investigated in this paper, utilizing a depthwise averaging method based on the Taylor dispersion theory. The fluid rheological behavior is assumed to obey the power-law viscosity model. Analytical solutions are obtained assuming a large channel width to depth ratio for which a 1-D profile can efficiently describe the velocity distribution. Full numerical simulations are also performed to determine the applicability range of the analytical model, revealing that it is able to provide accurate results for channel aspect ratios of ten and higher and quite acceptable results for smaller aspect ratios down to four. The model is then used for a complete parametric study to determine the effects of the governing parameters on the mixing performance. It is observed that utilizing a fluid with a higher flow behavior index gives rise to a smaller mixing length. Moreover, whereas a larger EDL thickness is accompanied by an improved mixing efficiency, the opposite is true for the channel aspect ratio. The effective diffusivity is also found to be an increasing function of the EDL extent and a decreasing function of the flow behavior index.

A gas turbine shaft is generally exposed to high-temperature gases and may seriously be affected and overheated due to temperature fluctuations in the combustion chamber. Vortex flow in the combustion chamber may increase the heat release rate and combustion efficiency, as well as control the location of energy release. However, this may result in excessive temperature on the combustor equipment and gas turbine shaft. In this study, a new gas turbine combustion chamber implementing a liner around the shaft and the liquid-fuel feeding system is designed and fabricated. The influences of parameters such as the Reynolds number and the equivalence ratio are studied. Experimental results are compared with a numerical simulation using OpenFOAM, which is an open-source computational fluid dynamics software. The results show that the heat transfer to the liner at the head end of the combustion chamber is high enough; and at the outlet of the combustion chamber, it is relatively low. The effects of parameters such...

Consideration is given to the buoyancy effects on fully developed gaseous slip flow in vertical microducts of constant but arbitrary geometry. The thermal boundary condition is assumed to be the constant wall heat flux of the first kind, H1. The rarefaction effects are treated using the first-order slip velocity and temperature jump boundary conditions. The method of solution being considered, in which the governing equations in cylindrical coordinates and three of the boundary conditions are exactly satisfied, is mainly analytical. The remaining slip boundary conditions on the duct wall are applied to the solution through the least-squares matching method. As an application of the method, the hydrodynamic and thermal features are obtained for five duct geometries including a trapezoid, double trapezoid, isosceles triangle, rhombus, and ellipse. A complete parametric study indicates that both Poiseuille and Nusselt numbers are decreasing functions of Knudsen number and increasing functions of the mixed co...

In this paper, the fully developed electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient is analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. A complete parametric study reveals that the pressure effects are more pronounced at higher values of the channel aspect ratio and smaller values of the flow behavior index. The Poiseuille number is found to be an increasing function of the channel aspect ratio for pressure assisted flow and a decreasing function of this parameter for pressure opposed flow. It is also observed that the Poiseuille number is increased by increasing the zeta potential. Furthermore, the results show that an increase in the flow behavior index results in a lower flow rate ratio, defined to be the ratio of the flow rate to that of a Newtonian fluid at the same conditions. Moreover, whereas the flow rate ratio in the presence of an opposed pressure gradient is smaller than that of a favorable pressure force for shear thinnings, the opposite is true for shear-thickening fluids.

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 observed that decreasing the channel aspect ratio causes the energy generated due to the viscous heating to become more significant. Furthermore, the viscous dissipation is higher for shear-thickening fluids. The Nusselt number is ascertained to be an increasing function of the channel aspect ratio regardless of the flow behavior index and pressure gradient. Moreover, the results suggest that increasing the flow behavior index can either increase or decrease the Nusselt number, depending on the thermal conditions of the flow.

The present research proposes an effective method to enhance the heat transport capability of conventional electronic coolers and improve their thermal management. Pulsating heat pipes (PHPs) are outstanding heat transfer devices in the field of electronic cooling. In the present study, two sets of open-loop pulsating heat pipes (OLPHPs) for two different magnetic nanofluids (with and without surfactant) were fabricated and their thermal performance was experimentally investigated. Effects of working fluid (water and two types of magnetic nanofluids), heating power, charging ratio, nanofluid concentration, inclination angle, application of a magnetic field, and magnet location are described. Experimental results showed that magnetic nanofluids can improve the thermal performance of OLPHPs. Application of a magnetic field reduces the thermal resistance of OLPHPs charged with magnetic nanofluids. The optimum charging ratio and nanofluid concentration are reported. The best thermal performance of OLPHPs was ...

The fully developed longitudinal slip-flow mixed convection between a periodic bunch of vertical microcylinders arranged in regular arrays is investigated in the present work. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The rarefaction effects are taken into consideration using first-order slip velocity and temperature jump boundary conditions. The method considered is mainly analytical, in that the governing equations and three of the boundary conditions are exactly satisfied. The remaining symmetry condition on the right-hand boundary of the typical element is applied to the solution through the point-matching technique. The results indicate that both the pressure drop and Nusselt number are not dependent on the type of the boundary conditions at small and moderate blockage ratios. At higher blockage ratios, the pressure drop is higher for the H2 case, whereas the opposite true for the Nusselt number. Furthermore, the pressure drop is an increasing...

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-Huckel 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-Huckel 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 scale ratio. In addition, unless a sufficiently high opposed pressure is present, a higher Joule heating rate is generally accompanied by a lower Nusselt number. Moreover, increasing the dimensionless Debye-Huckel parameter gives rise to a higher Nusselt number, unless a high value of the channel aspect ratio with surfa...

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 associated with the solution of the thermal field, an approximate solution methodology based on the variational calculus is employed. An analytical solution is also presented by considering thin electrical double layer limits. The results reveal non-monotonic behaviors of the Nusselt number such as the occurrence of singularities in the local Nusselt number values when the fluid is being heated from the wall. Moreover, the effect of increasing the channel aspect ratio is found to be increasing both the temperature difference between the wall and the bulk flow and the Nusselt number. In addition, higher wall heat fluxes are obtained in the entrance region by increasing the Peclet number.

Consideration is given to the buoyancy effects on the fully developed gaseous slip flow in a vertical rectangular microduct. Two different cases of the thermal boundary conditions are considered, namely uniform temperature at two facing duct walls with different temperatures and adiabatic other walls (case A) and uniform heat flux at two walls and uniform temperature at other walls (case B). The rarefaction effects are treated using the first-order slip boundary conditions. By means of finite Fourier transform method, analytical solutions are obtained for the velocity and temperature distributions as well as the Poiseuille number. Furthermore, the threshold value of the mixed convection parameter to start the flow reversal is evaluated. The results show that the Poiseuille number of case A is an increasing function of the mixed convection parameter and a decreasing function of the channel aspect ratio, whereas its functionality on the Knudsen number is not monotonic. For case B, the Poiseuille number is decreased by increasing each of the mixed convection parameter, the Knudsen number, and the channel aspect ratio.

Pulsating heat pipes (PHPs) are simple, cheap, and efficient heat transfer devices. They have applications in electronic cooling. In the present research, an experimental investigation is conducted on startup and steady thermal performances of open loop pulsating heat pipes (OLPHPs). Effects of working fluid, heat input, non-condensable gases (NCGs), ferrofluid concentration, magnets location, and inclination angle on the thermal performance of OLPHPs have been considered. Obtained results show that using ferrofluid can improve the thermal performance in steady state condition. Furthermore, applying a magnetic field enhances the heat transfer characteristics of ferrofluidic OLPHPs in both startup and steady state conditions. At 20 W heating power and startup condition, higher NCGs have the best performance in the presence of magnetic field. However, in the absence of magnetic field opposite trend is observable. In the case of steady thermal performance in both presence and absence of magnetic field, lower amounts of NCGs lead to better thermal performance. Best heat transfer capability is achieved at around 67.5° inclination angle relative to the horizontal axis for all of the working fluids. With the application of magnetic field in different locations of the OLPHPs, one can adjust their thermal performance to the desired value.

The secondary flow of PTT fluids in rectangular cross-sectional plane of microchannels under combined effects of electroosmotic and pressure driving forces is the subject of the present study. Employing second-order central finite difference method in a very refined grid network, we investigate the effect of electrokinetic and geometric parameters on the pattern, strength and the average of the secondary flow. In this regard, we try to illustrate the deformations of recirculating vortices due to change in the dimensionless Debye–Huckel and zeta potential parameters as well as channel aspect ratio. We demonstrate that, in the presence of thick electric double layers, significant alteration occurs in the secondary flow pattern by transition from favorable to adverse pressure gradients. Moreover, it is found that for polymer-electrolyte solutions with large Debye lengths, the secondary flow pattern and the shape of vortices are generally dependent upon the width-to-height ratio of the channel cross section. Also, the inspections of strength and average of secondary flow reveal that the sensitivity of these quantities with respect to the electrokinetic, geometric and rheological parameters increases by increasing the absolute value of velocity scale ratio. In this regard, utilizing the curve fitting of the results, several empirical expressions are presented for the strength and average of the secondary flow under various parametric conditions. The obtained relations with the other predictions for secondary flow are of high practical importance when dealing with the design of microfluidic devices that manipulate viscoelastic fluids.

This is a theoretical study dealing with longitudinal gaseous slip flow forced convection between a periodic bunch of microcylinders arranged in regular array. The selected geometry has applications in microscale pin fin heat sinks used for cooling of microchips. The flow is considered to be hydrodynamically and thermally fully developed. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first order slip boundary conditions. The method considered is mainly analytical in which the governing equations and three of the boundary conditions are exactly satisfied. The remaining symmetry condition on the right-hand boundary of the typical element is applied to the solution through the point matching technique. The results show that both the Poiseuille number and the Nusselt number are decreasing functions of the degree of rarefaction characterized by the Knudsen number. While an increase in the blockage ratio leads to a higher Poiseuille number, the functionality of the Nusselt number on this parameter is not monotonic. At small and moderate values of the blockage ratio, the Nusselt number is higher for a higher blockage ratio, whereas the opposite may be right for higher values of this parameter. It is also observed that the angular variations of the parameters are reduced at smaller blockage ratios. Accordingly, the H1 and H2 Nusselt numbers are the same for small and moderate blockage ratios.

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 heat fluxes, whereas the opposite is true for the flow behavior index. Furthermore, based on the value of the dimensionless Joule heating parameter, the Nusselt number may be either an increasing or a decreasing function of the axial coordinate or even both of them in the presence of a singularity point. The viscous heating effects are also found to be negligible.

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–Huckel 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 temperature dependent effects result in reduction of viscosity and the electrical resistivity over the majority of the channel cross section. It is also found that the shear-thinning fluids are more sensitive to fluid properties variation with temperature compared with Newtonian and shear-thickening fluids.

Double-inlet pulse tube refrigerators are one of the most common types of cryocoolers. There are several advantages of double-inlet pulse tube refrigerators, such as not having moving parts, reliability, and long life. Double-inlet pulse tube refrigerators have been used in several applications such as cooling the semiconductors, infrared sensors, and astronomical detectors. In the recent decade, several research efforts have been performed to investigate double-inlet pulse tube refrigerators. Generally, most of them are experimental or numerical, and the recent literature survey shows there is not an analytical solution for the complete system of a double-inlet pulse tube refrigerator, simultaneously. In the present work, an analytical solution of the complete system of double-inlet pulse tuberefrigeratorshasbeenpresented.Oneoftheobjectivesistodecoupletheequationoftemperatureforapressure wave generator from other equations such that the governing equations become simplified significantly. Applying perturbation theory inspired by physics of the double-inlet pulse tube refrigerator, the governing equations will be quite easily solved. High accuracy and simplicity of solution are some of the most important benefits of this method. The solution has been validated with the experimental data.

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 diminishes at higher values of the dimensionless Debye-Huckel parameter. It is also found that the zeta potential, whose value is dependent on the channel wall and the electrolyte solution characteristics, can highly affect the thermal behaviors of the flow, especially at smaller values of the dimensionless Debye-Huckel parameter.

In automobile painting industries, new automobile body products frequently should be tested in order to determine the actual thermal behavior of a paint curing process before starting mass production. During the hardening processes of dipped paint coating, applied in the electrophoretic enameling process, or top paint coating, applied in the final coating process, the automobile body must be warmed up according to the specific paint manufacturer curve. Consequently, prediction of car body temperature during the curing process may be vital in the design and performance analysis of the paint ovens. Numerical simulation of these processes may reduce expensive and time-consuming experimental procedures. In this research, a novel semi-analytical approach has been developed to predict the car body temperature during the curing process. Considering energy balance for each part of the body, a set of nonlinear differential equations has been extracted, which are related to the oven type and the heating zone. These...

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–Huckel 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–Huckel 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–Huckel 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.

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 number. Two different behaviors are observed for the Nusselt number variations due to increasing ϵgeWe2 which are an increasing trend for positive wall heat flux and a decreasing one for negative wall heat flux. However, the influence of ϵgeWe2 on Nusselt number vanishes at higher values of the dimensionless Debye–Huckel parameter. It is also realized that the effect of viscous heating is more important at small values of both ϵgeWe2 and the dimensionless Debye–Huckel parameter. Furthermore, the results show a singularity in Nusselt number at higher negative values of the dimensionless Joule heating parameter.

Because of technological restrictions, it is actually impossible to fabricate smooth microchannels. Therefore, exploring the roughness effects on the flow characteristics at microscale is of great importance for scientific communities. The present investigation deals with the effects of corrugated roughness on the fully developed slip flow forced convection in micropipes. The governing equations subject to first-order slip boundary conditions are solved by means of the straightforward perturbation method. Closed-form expressions are obtained for the dimensionless velocity and temperature distributions, for the friction coefficient and pressure drop, and finally for the Nusselt number. The results demonstrate that the corrugated roughness increases both the pressure drop and the heat transfer rate, with the amount of the increase in the pressure drop being a little more. Despite increasing the heat transfer rate, the effect of roughness is found to be unfavorable as it leads to smaller values of the channel performance, defined as the ratio of the heat transfer rate to the pressure drop. In other words, for a given heat transfer rate some increase in pumping power requirements is incurred.

In the present work, the second law of thermodynamics analysis has been carried out for steady-state fully developed laminar gas flow in a parallel plate microchannel with asymmetrically heated walls. The rarefaction effects as well as viscous heating effects are taken into consideration. Closed-form expressions are obtained for velocity and temperature distributions and entropy generation rates. The results demonstrate that increasing values of the wall heat fluxes ratio result in greater entropy generation for positive Brinkman numbers, whereas the opposite is true for negative values of Brinkman. However, the effect of the wall heat fluxes ratio on entropy generation becomes insignificant at high values of the group parameter and Peclet number. The entropy generation decreases as Knudsen and Peclet numbers increase; however, the effect of increasing values of Brinkman number and the group parameter is to increase entropy generation. Also, it is realized that the influences of rarefaction on entropy gen...

The present investigation is devoted to the second law of thermodynamics analysis of steady-state hydrodynamically and thermally fully developed laminar gas flow in a microannulus with constant but different wall heat fluxes. Slip velocity and temperature jump boundary conditions are used to describe rarefaction effects. Viscous heating is also included for both the wall cooling and heating cases. Using already available velocity profile, closed-form expressions are obtained for the transverse distribution of temperature and entropy generation rates. The results demonstrate that the effect of the wall heat fluxes ratio on entropy generation is negligible at large values of the group parameter and Peclet number, while the effect of increasing values of the annulus geometrical aspect ratio is to severely increase entropy generation. The entropy generation decreases as Knudsen and Peclet numbers increase, however, the effect of increasing Brinkman number and the group parameter is to increase entropy generation. Furthermore, it is realized that the influences of rarefaction on entropy generation are slighter for low Peclet number flows.

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.

The rates of total and radiative heat transfers are measured experimentally, and the convective cooling is calculated from the difference between the two above mentioned quantities. It was observed that the radiation heat transfer is the dominant mode of heat transfer in a vortex engine which causes a rise in the temperature of the chamber wall; however, convective cooling provided by an outer cooled vortex decreases the wall temperature

Recent developments of superconductive industries require cryocoolers with cooling power higher than 1 W in the 70–80 K temperature range. High capacity pulse tube cryocoolers assure the cooling power required for operation of superconducting devices. This paper presents numerical simulation of a high capacity pulse tube cryocooler, intended to provide more than 200 W cooling power at 80 K. In this respect the behavior of the cryocooler is explained by applying the mass and energy balance equations to different components of the cryocooler. Nodal analysis technique is employed to simulate the tube section behavior numerically. To perform the system optimization the influence of key operating parameters on cryocooler cooling capacity and coefficient of performance is studied. The proposed model reports the optimum cooling capacity of 244 W at 80 K cold end temperature at frequency of 50 Hz with 3.5 kW net power delivered to the gas.

The performance of an MHD generator utilizing plasma as working fluid has been assessed from the viewpoint of the second law of thermodynamics. The plasma flow in the generator linear duct has been solved by dividing the channel cross-section to an inviscid core region and the viscous boundary layers in the vicinity of the walls. The Hall effect has been taken into account and equilibrium ionization has been assumed. The dependence of the plasma properties such as Hall parameter, the coefficients of thermal and electrical conductivity, and viscosity on the plasma state has also been considered. Using the information obtained on the plasma behaviour in the generator, the entropy generation minimization approach is applied to improve the conversion efficiency. In addition to seeking the optimal working conditions, the nature of the irreversibilities occurring in the generator has been inspected and the relative importance of the phenomena of fluid friction, heat transfer and Ohmic dissipation and their contribution to the rate of destruction of useful available work has been compared. These studies reveal notable contrasts between the nature of irreversibilities in the liquid metal generators considered earlier and the more common plasma generators studied in the present work.

Turbulent swirling decay pipe flow has been investigated numerically in a vertical straight fixed pipe. The swirling flow is created by means of a rotating honeycomb which produces the solid body rotation at the inlet of the fixed pipe. Since there are no experimental data at the inlet of the fixed pipe; different axi-symmetric approaches may be considered to model the honeycomb effects at the downstream flow. Considering the appropriate approach and using the resulting flow field properties from the exit of the modeled swirl generator which are applied as the inlet boundary condition for the fixed pipe, several high Reynolds turbulence models are used to predict this type of the swirling flow. For wall treatments, both the standard wall function and the two-layer zone model are used. The comparison between the numerical and the existing experimental results shows that the RSM with two-layer zone model is generally more powerful than the others. Results show that the two-equation models with different near wall approaches are fairly well to predict the swirling flow in solid body rotation regions, but they fail to predict the pressure distribution along the pipe wall. Regarding the swirl intensity decay rate, irrespective of the inlet swirl type, the obtained decay rates from computations are in good agreement with the existing experimental results.

The objective of this paper is to provide optimization of falling film LiBr solution on a horizontal single tube based on minimization of entropy generation. Flow regime is considered to be laminar. The effect of boiling has been ignored and wall temperature is constant. Velocity, temperature and concentration distributions are numerically determined and dimensionless correlations are obtained to predict the average heat transfer coefficient and average evaporation factor on the horizontal tube. Thermodynamic imperfection due to passing lithium bromide solution is attributed to nonisothermal heat transfer; fluid flow friction and mass transfer irreversibility. Scale analysis shows that the momentum and mass transfer irreversibilities can be ignored at the expense of heat transfer irreversibility. In the process of optimization, for a specified evaporation heat flux, the entropy generation accompanying the developed dimensionless heat and mass transfer correlations has been minimized and the optimal geometry and the optimum thermal hydraulic parameters are revealed. The investigation cited here indicates the promise of entropy generation minimization as an efficient design and optimization tool.

Electrohydrodynamic (EHD) is introduced as a promising phenomenon for heat transfer enhancement mechanisms. In order to investigate exergy analysis through formation of bubble embryo, a qualitative point of view is used in the present study. Nucleate boiling is considered to be affected by a uniform electric field. Bubble dynamic investigation is a means to evaluate heat transfer. This study investigates bubble formation, including homogeneous nucleation, from a thermodynamic point of view under electric field effect. Change in availability due to bubble embryo nucleation is discussed and results are compared to available experimental studies

Semi-analytical solutions are obtained for the electrical potential, electroosmotic velocity, ionic conductance, and surface physicochemical properties associated with long pH-regulated nanochannels of arbitrary but constant cross-sectional area. The effects of electric double layer overlap, multiple ionic species, and surface association/dissociation reactions are all taken into account, assuming low surface potentials. The method of analysis includes series solutions which the pertinent coefficients are obtained by applying the wall boundary conditions using either of the least-squares or point matching techniques. Although the procedure is general enough to be applied to almost any arbitrary cross section, nine nanogeometries including polygonal, trapezoidal, double-trapezoidal, rectangular, elliptical, semi-elliptical, isosceles triangular, rhombic, and isotropically etched profiles are selected for presentation. For the special case of an elliptic cross section, full analytical solutions are also obt...

Infinite series solutions are obtained for electrical potential, electroosmotic velocity, ionic conductance, and surface physicochemical properties of long pH-regulated rectangular nanochannels of low surface potential utilizing the double finite Fourier transform method. Closed form expressions are also obtained for channels of large height to width ratio for which the depthwise variations vanish. Neglecting the Stern layer impact, the effects of EDL (Electric Double Layer) overlap, multiple ionic species, and association/dissociation reactions on the surface are all taken into account. Moreover, finite-element-based numerical simulations are conducted to account for the end effects as well as to validate the analytical solutions. We show that, with the exception of the migratory ionic conductivity, all the physicochemical parameters are strong functions of the channel aspect ratio. Accordingly, a slit geometry is not a good representative of a rectangular channel when the width is comparable to the heig...

The present investigation is devoted to the fully developed slip flow mixed convection in vertical microducts of two different cross sections, namely, polygon, with circle as a limiting case, and rectangle. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first-order slip boundary conditions. The method considered is mainly analytical in which the governing equations in cylindrical coordinates along with the symmetry conditions and finiteness of the flow parameter at the origin are exactly satisfied. The first-order slip boundary conditions are then applied to the solution using the point matching technique. The results show that both the Nusselt number and the pressure drop parameter are increasing functions of the Grashof to Reynolds ratio. It is also found that, with the exception of the H2 Nusselt number of the triangular duct, which shows an opposite trend, both the Nusselt number and the pressure drop are decreased by increasing the Knudsen number. Furthermore, the pressure drop of the H2 case is found to be higher than that obtained by assuming an H1 thermal boundary condition.