Entrance Length Research Articles

Operation and Multi-Objective Design Optimization of a Plate Heat Exchanger with Zigzag Flow Channel Geometry

The performance of a plate heat exchanger (PHE) using water as the working fluid with zigzag flow channels was optimized in the present study. The optimal operating conditions of the PHE are explored experimentally by the Taguchi method, with effectiveness as the objective function. The results are further verified by the analysis of variance (ANOVA). In addition, the zigzag flow channel geometry is optimized by the non-dominated sorting genetic algorithm-II (NSGA-II), in which the effectiveness and pressure drop of the PHE are considered the two objective functions in the multi-objective optimization process. The experimental results show that the ratio of flow rates is the most important factor affecting the effectiveness of the PHE. The optimal operating conditions are the temperatures of 95 °C and 10 °C at the inlets of hot and cold water flows, respectively, with a cold/hot flow rate ratio of 0.25. The resultant effectiveness is 0.945. Three geometric parameters of the zigzag flow channel are considered, including the entrance length, the bending angle, and the fillet radius. The sensitivity analysis of the parameters reveals that a conflict exists between the two objective functions, and multi-objective optimization is necessary for the zigzag flow channel geometry. The numerical simulations successfully obtain the Pareto optimal front for the two objective functions, which benefits the determination of the geometric design for the zigzag flow channel.

Effect of aspect ratio on entrance length in rectangular minichannels with plenum

In the case of a long, straight rectangular channel, hydrodynamic development of flows is influenced by the growth of the boundary layer along the walls of the channel. Though such a geometry is well-studied in the literature, in reality, the flow often happens in channels with plenums on each end and is not studied extensively. This work addresses this gap. There is a sudden contraction from the plenum to the channel which causes the flow to separate at the entrance of the channel. Hence, the flow development is influenced not only by the boundary layer growth but also by recirculation and the presence of a continuous wall along one direction in the case of planar geometries. This causes the centerline velocity in the entrance region to overshoot the value at the fully developed region, which makes the conventional usage of 99% of the fully developed value difficult. Hence, an alternate method of defining entrance length, based on the slowest development across the channel cross section, is proposed. Based on this approach, the entrance length value shows a non-monotonic variation with the aspect ratio (AR)—its value reduces between 0.6 and 1.66; beyond 1.66, it increases up to 20 before becoming flat. The entrance length also shows a weak dependence on the Reynolds number for AR between 2 and 20. A new set of correlations of entrance and recirculation lengths are proposed.

Temperature and Pressure Distribution Analysis on Selected Geothermal Wells at Olkaria Using Completion and Heat Up Test Data

Knowledge of the true temperature and pressure at every location within the formation and their variation across the field has many applications in resource definition, delineation, and power potential and even determines how a resource is exploited. For electricity generation, the rule of thumb is a cut-out temperature of 2300 C. Resources at lower temperatures can be used for power generation from binary plants (below 1800C) or for direct use applications. Temperature and pressure profiles over the wellbore length, particularly those taken after injection and during heating, find use in understanding feed zones in the well and those that are unlikely to be feed zones. Discharge tests directly indicate flow rates, and data from them tend to be more reliable for simulation purposes than data from injection tests. Ultimately complete understanding of a reservoir's temperature at a location was determined after thermal recovery is considered complete. The research uses data from newly drilled adjacent wells in Olkaria 1 and systematic analysis of the database containing pressure and temperature data collected by KenGen staff during completion and heating-up tests. A conceptual model was developed from the formation temperatures and pressure based on this analysis. Temperature and pressure distributions at various depths in each well were correlated with nearby wells to provide a clear understanding of the feed zone locations. The study concluded that the formation temperatures and pressure on geothermal wells were moderate, although slightly above the expected values. The study revealed a significant effect of limited entry length on pressure and temperature behaviours. The study highlighted a strong positive association between entry length and pressure, and moderate positive association between entry length and temperature. The study revealed that injection profile pressures were the highest.

Increasing the efficiency of microreactors utilizing two-phase hydrodynamic focusing

Given the fact that most of the reactions that take place in microreactors occur on the surface, it is crucial to keep the reactants close to the reactive wall. One of the effective techniques that have been proposed in this respect is the single-phase hydrodynamic focusing. This method, however, has the main drawback that the percentage of reactants penetrating the sheath fluid is high. To circumvent this defect, the notion of two-phase hydrodynamic focusing is introduced in the present work. The whole idea is to use a highly viscous sheath fluid to establish a barrier against the penetration of reactants into the sheath flow. To show the effectiveness of the proposed technique, an analytical modeling is performed by considering a parallel-plate microreactor with an irreversible first-order reaction. The sample and sheath fluids are assumed to flow side-by-side and the hydrodynamic entry length is neglected. The results indicate the effectiveness of the two-phase focusing: efficiency, defined to be the number of reactants located in the sample flow divided by the whole reactants, may be kept close to unity and the fully-developed Sherwood number may be increased by one order of magnitude assuming a sheath-to-sample viscosity ratio of 10 under certain conditions.

A comprehensive study of the onset of boundary layer separation in the unbounded flow around a circular cylinder

The onset of boundary layer separation in the unbounded flow around a circular cylinder is determined directly with a numerical experiment with accuracy to the second decimal point of the Reynolds number, Re. The governing equations are the steady state, two dimensional Navier–Stokes equations, which are solved with Galerkin finite elements. A new criterion, the entrance ratio E=D/L with D the diameter of the cylinder and L the entrance length of the domain, is introduced in addition to the traditional blockage ratio; the aim is to establish conditions for unbounded flow in both flow directions. A hypothesis is formulated and verified for the onset of separation leading to the conclusion that this flow undergoes a supercritical pitchfork bifurcation with respect to fixed points on the boundary. Results are presented for various blockage ratios, B, in the range 1.2238·10−8≤B≤0.005 and constant entrance ratio E=2.4472·10−9 until asymptotic behavior is observed for the onset of separation in the Reynolds number, in the angle and the length of the smallest eddy. Onset of separation occurs in the region 6.36≤Re<6.37. The bifurcation diagram of the flow is calculated. Streamlines of the flow domain before and after the bifurcation point are shown, including images of the smallest possible eddies. In addition, coefficients of base suction and total drag are computed and shown in the regime 0.1≤Re≤40. The results are compared with available laboratory and numerical measurements.

Impact of large-scale effects on mass transfer and concentration polarization in Reverse Osmosis membrane systems

We present well-resolved computational fluid dynamics simulations of a large-scale reverse osmosis membrane-spacer configuration (∼ 1 m). Our computational model solves the flow and transport equations with variable solute-dependent properties. We utilize a high resolution computational mesh to resolve all relevant length scales associated with spacer-induced mixing and thin concentration boundary layers. An important contribution of this work is the development of a modified mass-transfer correlation that accounts for the development of the concentration boundary layer along the channel. A set of 2D axisymmetric simulations were performed for a spiral wound module layer with varying cross-flow conditions and spacer diameters which indicate a significant entrance length effect for concentration profile development at lower flow rates while mixing effects dominate at higher flow rates. The mass-transfer correlations at higher flow rates compare well with published correlations while a surrogate model for Sherwood number was obtained that depends on an additional similarity variable that accounted for entrance length effects at lower flow rates. Finally, a large-scale membrane-spacer design relevant to high-pressure reverse osmosis is studied with a non-uniform arrangement of spacers, which indicate a substantial saving in pressure drop (∼ 40%) compared to traditional uniformly spaced pattern with minor variations (∼ 2%) in concentration polarization, product water quality (∼ 1%) and water recovery (∼ 7%) compared to a uniform spacer pattern.

A shape function approach for predicting deteriorated heat transfer to supercritical pressure fluids on account of a thermal entry length phenomenon

The paper addresses the problem of predicting deteriorated heat transfer to supercritical pressure fluids, trying a novel approach whose main features are obtained by consideration of the experimental trends of a meaningful series of experimental data. This approach takes into consideration the modifications that the axial velocity profile undergoes at the entrance of a bare tube, when a supercritical pressure fluid is heated at the wall and decreases its density owing to thermal expansion, giving rise to buoyancy effects. Combining the observation of measured wall temperature trends with their successful predictions by CFD RANS models, the effects giving rise to flow laminarization are firstly interpreted as a very peculiar form of the entry length problem applicable to supercritical pressure fluids. Then, their quantitative prediction is addressed by the use of an iterative procedure based on shape functions tailored on the observed trends of the Nusselt number and of the consequent wall temperature trends. In this frame, the results of a recently developed fluid-to-fluid similarity theory for heat transfer at supercritical pressures provide indication about the relevant dimensionless numbers to be involved in determining the shape functions. Being based at the moment on a series of water experimental data collected at 25 MPa for vertical upward flow, the methodology may suggest a way for predicting heat transfer deterioration in the proposed supercritical water nuclear reactor conditions, providing an additional means to tackle this critical problem by a different approach that may result useful as a practical means to bound expected wall temperature trends.

A simplified model of low Re, immiscible, gas–liquid flow, and heat transfer in porous media numerical solution with experimental validation

ABSTRACT This study investigates the thermohydraulic characteristics of immiscible two-phase downward flow and heat transfer through porous media in a vertical, cylindrical, and homogeneous porous medium numerically and experimentally. The test section is exposed to a constant wall temperature after filled with spherical beads. Numerical solution of the model is achieved by the finite volume method and applied to a single-phase flow model. The numerical results are experimentally validated according to air/water downward flow, spherical beads, a ratio of particle diameter to pipe radius is 0.412, 0.396 porosity, 0.01 ≤ Re ≤ 500, water to air volume ratio range from 0 to ∞, and saturation ratio from 0 to 1. The results show that the average Nu is nearly constant up to Re = 40. At Re > 100, it is recommended to take inertia and friction effects into account by means of Forchheimer–Brinkman’s equation. For single-phase flow (water or air) and two-phase flow mixtures, the local Nu has higher values at the entrance section and decreases as the axial distance increases until it reaches its fully developed value of 4.37 at the end of the thermal entrance length. The comparison between numerical, experimental, and other available previous results shows good agreement and validates the numerical model.

Numerical investigations on the difference between aiding and opposing flows in the developing regime of laminar mixed convection in vertical tubes

The present article discusses the numerical simulation results of laminar mixed convection flow in vertical tubes. A comparative analysis of the thermal and hydrodynamic features of both buoyancy-assisted and opposed flows was performed for Reynolds number (), Grashof number () and Richardson number () with uniform heat flux boundary condition. 2-D axisymmetric steady state simulations were carried out for a length-to-diameter () ratio of with water as the working fluid. Numerical simulations were performed by employing SIMPLE scheme for pressure–velocity coupling in momentum equations and second order UPWIND scheme for solving energy equations. In case of assisting flow (), at fully developed state the centerline velocity decreases, and velocity is increased near the tube wall due to heat flux induced free convection. With increasing heat flux, the decrement in centerline velocity compared to the no-heat flux condition increases. Further, with increasing heat flux, the increase in friction factor and Nusselt number was observed. Therefore, at the same the variation of heat flux led to unique velocity profiles and temperature gradients. The variation of centerline velocity and temperature in developing region was also studied. While centerline temperature was monotonically increasing with length, the centerline velocity increased up to a maximum in the developing region and then attained the steady state at a lower value in the fully developed state. Subsequently we studied the dependence of on the hydrodynamic and thermal features. For constant friction factor and Nusselt number was observed to increase with increase in from 0.1 to 1.5 range. At fixed variation of heat flux leads to variation of or Hence, the buoyancy effect has a significant role in the entrance length development. The hydrodynamic entry length after an initial increase, attained an almost constant value with increasing On the other hand, the thermal entry length exhibited a decreasing trend with increasing Similarly, at constant Nusselt number increased with increasing for a range of 100–1000. It was evident that for a given and the heat transfer in the developing flow is always higher as that of the fully developed flow. Contrasting observations were observed for buoyancy-opposed flow. Velocity is accelerated at the center as compared to the tube wall in case of opposing flow for same and For a fixed the friction factor and Nusselt number decreased with increasing the Both the hydrodynamic and thermal entry length increases for opposing flows. Finally, we have developed correlations for fully developed friction factor () with as well as and Nusselt number () with for buoyancy-assisting and buoyancy-opposing flows. Two independent correlations are also produced for with Graetz number () for developing and fully developed regimes in both assisting as well as opposing flows.

Study on Convective Heat Transfer Characteristics of Supercritical Liquid Hydrogen in a U-Type Tube inside a Moderator

The flow and heat transfer characteristics of supercritical fluid in a U-tube have an important influence on the safe operation of a moderator, and the variation of gravity direction is suitable for special working conditions of the moderator. In this study, the three-dimensional turbulence flow and heat transfers of supercritical liquid hydrogen in a U-tube were investigated at an Re number ranging from 16,425 to 54,750 under constant heat flux (q = 80 kW/m2). The total length of the U-tube was 1725 mm, which had an entrance length L/D of 23, with the inner diameter and wall thickness of D × δ = 10 × 2 mm. The finite volume method was adopted, and the grid independence was verified by the grid convergence index (GCI). The calculation results of three turbulence models (SST k-w, RNG k-ε, Standard k-ε) were compared with the corresponding experimental data to obtain the turbulence model with the smallest error. The convective heat transfer characteristics with different values of heat flux (q = 30 kW/m2~100 kW/m2), mass flow (G = 3 g/s~10 g/s), and gravity (gx, gy, gz) were compared. Meanwhile, the heat transfer characteristics of supercritical liquid and conventional liquid hydrogen were compared. The results show that Nu increased from 5 g/s to 10 g/s by 56.6%, and mass flow rate had a greater impact on the variation of Nu; when gravity direction was consistent with the flow direction of liquid hydrogen (gx direction), the Nu number inside the channel was 4.21% and 5.56% higher than that in gy and gz direction, respectively. Supercritical liquid hydrogen has a stronger heat transfer ability than conventional liquid hydrogen, of which the Nu number is 16.7% higher. This study can provide useful guidance for the design of flow and heat transfer of supercritical liquid hydrogen in a U-tube and its application in moderators. Furthermore, it provides reference technical values for thermal safety and thermal management of the target station to ensure its safe and stable operation.

Numerical investigation of TiO2 and MWCNTs turbine meter oil nanofluids: Flow and hydrodynamic properties

The main aim of the present study is to evaluate the influence of multi-walled carbon nanotubes (MWCNTs) and TiO2 nanoparticles (NPs) on lubricant and fluid flow within natural gas turbine meters. In light of this purpose, disparate concentration of TiO2 NPs (0.1, 0.2, and 0.3 wt%), various volume flow rates 0.14, 0.35, and 0.12 cm3S were employed for experimental analyses. In the facet of simulation, Gambit software version 2. 4. 6 to mesh oil pathway and Fluent software version for solving the equations were utilized. It was revealed that the pressure drop in the presence of nanoparticles was increased. Moreover, there was an increase in pressure drop value with raising the NPs concentration; for instance, the pressure drop value of MWCNTs-containing nanofluids at the volume flow rate of 0.35 cm enhanced from 92.72 Pa to 94.64 Pa as the NPs concentration raised from 0.1 to 0.3. Furthermore, modeling outcomes corroborated the uptrend in pressure drop value by increasing the volume flow rate and reported the maximum pressure drop value of 0.12 cm3S. On the other hand, the numerical results revealed that the friction coefficient is directly and inversely proportional to NPs concentration and the volume flow rates, sequentially. Additionally, with increasing the volume flow rate, the entrance length increased, and reaching the developed state was delayed. It is worth noting as the final finding of this study that increasing the NPs concentration resulted in decreasing the entrance length and the fast reaching of the developed state.

Stability of gravity-driven particle-laden flows – roles of shear-induced migration and normal stresses

In this paper, we study the role of shear-induced migration and particle-induced normal stresses in the formation and stability of a particle-laden, gravity-driven shallow flow. We first examine the modification of the base-state Nusselt flow due to the underlying microstructure, how shear-induced migration leads to viscosity stratification. We inspect the development of the base state via the boundary layer formation in the ‘shallow’ limit and find a reduction in entrance length with increasing bulk particle concentration and an increase in entrance length with increasing Péclet number ($Pe_p = \dot {\gamma } a^2 / D_0$, where $\dot{\gamma}$ is the average shear rate, a is the particle size and $D_0$ is the single particle diffusivity). A linear stability analysis is then performed on the fully developed state to identify two modes of instability typically found in gravity-driven falling films – the long-wave surface and the short-wave shear modes. We find that when the associated Péclet number is $Pe_p \ll 1$, increasing bulk particle volume fraction delays the onset of instability for both the surface mode and shear mode. However, with $Pe_p = {O}(1)$, we find an enhancement in both modes of instability. We also find that, beyond a critical Péclet number, for a fixed particle volume fraction, the surface mode is unstable even in the absence of fluid inertia. The enhanced destabilisation is attributed to the combined effects of base-state viscosity stratification and momentum forcing via particle concentration perturbations. We also show that the physics behind the enhancement of instability is independent of the choice of the constitutive model used to describe the dynamics of the particle phase, provided the chosen model has elements of shear-induced migration.

Comprehensive analysis of pedicle screw implantation in the C7 vertebra using computed tomography-based three-dimensional models

BackgroundFrom a biomechanical point of view, pedicle screws (PS) are better than other kinds of screws for implantation in the seventh cervical vertebra (C7). However, the application of PS is limited because of the high risk of severe complications. It is essential to define the optimal entry point and trajectory. The aim of this study was to comprehensively analyze the starting point and trajectory for C7 PS insertion using three dimensional (3D) models.MethodsOverall, 60 subjects aged 18 to 67 years old were included. All CT images were used to construct 3D computer models of the C7 vertebrae. A new coordinate system was established for the next evaluation. The pedicle axis was calculated with respect to the entire pedicle; then, the ideal entry point, screw diameter and length, sagittal angle and lateral angle were assessed.ResultsAll the ideal entry points were located at the medial superior to lateral notch (LN), and the mean distance between the entry point and LN was 5.86 ± 1.67 mm in the horizontal direction and 3.47 ± 1.57 mm in the vertical direction. The mean distance between the entry point and the middle point of the inferior edge of the C6 articular process (MP) was 0.74 ± 1.83 mm in the horizontal direction. The mean sagittal angle of the pedicle axis was 90.42°, and the mean pedicle transverse angle was 30.70°. The average diameter and length of the PS were 6.51 ± 0.76 mm and 31.58 ± 4.40 mm, respectively.ConclusionsThis study provided a novel method to calculate the ideal starting point and trajectory for C7 PS insertion. These measurements may be helpful for preoperative planning. It is recommended that 3D CT imaging is used preoperatively to carefully evaluate the anatomy of each individual.

Mixed convective heat transfer of medium-Prandtl-number fluids in horizontal circular tubes

Studies on mixed convective heat transfer or mixed convection of laminar flows in horizontal circular tubes are normally restricted to fluids of low or high Prandtl numbers, such as air or oil, while few of them focus on fluids of medium Prandtl numbers, such as molten salts for liquid-fuel and solid-fuel Molten Salt Reactors (MSRs). Therefore, this paper attempts to investigate mixed convection of medium-Prandtl-number fluids. A three-dimensional model is built in STAR-CCM+ for a molten salt, LiF-BeF2-ThF4-UF4 (67.5–20.0–12.0–0.5 mol%), flowing in horizontal circular tubes uniformly cooled. Correlations are developed to predict the entrance length for laminar mixed convection with ± 20% uncertainties. In addition, the Nusselt number predicted by STAR-CCM+ deviates significantly from conventional correlation results by up to 85%. An accurate mixed convective heat transfer correlation is therefore developed with ± 15% uncertainties and recommended for medium-Prandtl-number fluids in horizontal circular tubes, which is applicable for Re¯=2.0×102to1.8×103, Gr¯=9.2×101to1.3×105 (or Gr*¯=1.7×103to1.8×106), Pr¯=3.9to3.2×101, and L/Di=2.0×102to1.0×103. The proposed correlation is also applicable for Pr¯=7.0×10−1to1.8×104 with ± 40% uncertainties by comparing with the experimental data. Furthermore, flow regime maps are proposed for forced and mixed convection by presenting Nu¯m/Nu¯f in a plot with the ordinate of Gz¯ (=Re¯Pr¯Di/L) and abscissa of Gr¯Pr¯Di/L or Gr*¯Pr¯Di/L, which help visibly identify under what conditions it is necessary to consider the buoyancy effect. A correlation is also developed with ± 15% uncertainties to quantitatively evaluate the buoyancy effect in laminar mixed convection of medium-Prandtl-number fluids in horizontal circular tubes.

Reduction of skin friction and two-phase flow structure beneath wall in horizontal rectangular channel

From the viewpoint of the improvement of the air lubrication method for the ship's hull resistance reduction, an experimental study was conducted for two-phase flow in a horizontal rectangular channel with a length of 3.0 m, a gap of 0.05 m, and a width of 0.2 m, which simulates the external two-phase flow. The database on frictional drag and local two-phase flow parameters, including void fraction profile and gas chord length, was collected using a shear stress sensor and a double sensor probe. Measurement of two-phase flow structure was performed at three axial positions of z = 0.930, 1.43, and 1.93 m from the bubble injection port. The wall shear stress was obtained at z = 1.93 m. A total of 72 datasets are acquired a room temperature and at flow conditions of superficial liquid velocity <jf> ranging from 0.832 to 3.00 m/s and superficial gas velocity <jg> ranging from 0.0232 to 0.714 m/s. The effects of entry length, liquid and gas flow rates on the phase distribution characteristics beneath the wall were discussed. The bubble layer thickness was newly defined as the length scale. The bubble layer thickness was not so sensitive to the changes in the liquid flow rates and the entry length, and highly dependent on the gas flow rates in the present experimental conditions. The mean void fraction in the bubble layer was highly reliant on the liquid flow rate and decreased with the superficial liquid velocity. In contrast, the insignificant effect of gas flow rate on the mean void fraction was confirmed. A strong correlation between the drag reduction effect due to the air lubrication and the mean void fraction in the bubble layer was confirmed. The obtained data are expected to be used for the modeling of the interfacial area transport terms, development of the constitutive equations of the drift flux model, modeling of the drag reduction for the external two-phase flow and the benchmark tests of various CFD codes in the future study.

Finite element simulation of a viscoelastic cell entering a cylindrical channel: Effects of frictional contact

Finite element method has been extensively used to simulate the process of single cells entering a narrow channel under a prescribed pressure. Yet an in-depth understanding on the effects of the frictional boundary condition in such simulations is lacking. The main challenge lies in the continuously evolving contact region between the deformed cell and the channel wall during the entry process, which makes it difficult to apply proper boundary conditions for the friction and pressure. In this work, we present an approach to continuously update the boundary condition according to the contact status during entry. Using this approach and modeling the cell as a visco-hyperelastic sphere, we study how the pressure boundary conditions and the friction coefficient affect the simulated cell entry process. Specifically, we compare two special cases of pressure boundary conditions: positive pressure at the trailing edge of the cell or negative pressure at the leading edge. It is found that the two cases produce the same result in terms of the cell entry length under frictionless contact, but give considerably different results under frictional contact. Effects of whether the pressure boundary is updated are then studied by considering more special cases. All these results are well explained by the pressure superposition principle, and further insights into the effects of pressure boundary condition and boundary update are also acquired. Finally, focusing on the case of positive pressure with boundary updates, we obtain simulation results revealing how the entry length depends on the pressure, time and friction coefficient. In particular, a larger friction coefficient can significantly reduce the entry length under a prescribed pressure or a certain entry time. Our results suggest that it is necessary to implement accurate pressure boundary conditions (e.g., pressure magnitudes at the two edges of cell and continuously updated pressure boundary regions) in order to faithfully capture the frictional contact between the cell and the channel wall. In addition, the simulation approach can be useful in modeling the general process of a viscoelastic sphere entering a cylindrical channel involving frictional contact.

Analytical Modeling of Laminar Developing Flow Between Hydrophobic Surfaces With Different Slip-Velocities

Abstract Theoretical analysis of the entrance hydrodynamics of microchannels is an important design aspect in connection with the development of microfluidic devices. In this paper, pressure-driven fluid flow in the entrance region of two infinite hydrophobic parallel plates with dissimilar slip-velocities is analytically modeled. The linearized momentum equation is solved by applying the Navier-slip model at the boundaries to achieve the most generalized two-dimensional form. The velocity profile is obtained by combining the developed and developing velocities, which is estimated by invoking the separation of variable method. It is observed that the velocity profile is asymmetric, and the shear-free region can be shifted from the geometrical central line by altering the wall hydrophobicity. Moreover, the zero shear zone is transferred more toward the surface having high hydrophobicity. The expression for wall shear stress is obtained analytically using Newton's law of viscosity. Moreover, the boundary layer growth from the upper and lower walls is found to be entirely different, and they merge at the entrance length and are noticed to be offsetted from the geometric centerline. The effect of slip-length on the entrance length is analyzed, and an empirical correlation is deduced.

Thermal creep effects on fluid flow and heat transfer in a microchannel gas cooling

This work presents a numerical analysis of the effect of thermal creep on gas flow and heat transfer in a microchannel under gas cooling conditions. The hydrodynamic equations in vorticity-stream function form are solved together with the energy equation using a finite difference scheme. Axial conduction, pressure work, and viscous dissipation effects are included in the analysis. Solutions are obtained with and without thermal creep effects to illustrate the thermal creep effect on gas cooling. The results show that thermal creep becomes more pronounced as the wall temperature decreases relative to the inlet gas temperature. The results also show that the thermal creep effect on gas cooling becomes more significant as Reynolds number decreases. Furthermore, increasing Knudsen number has caused thermal creep effects to extend further into the channel. Additionally, the work has concluded that thermal creep causes an increase in the hydrodynamic entrance length. Moreover, the work also showed that for low enough wall temperature, Knudsen number, and Reynolds number, the slip velocity can reach negative values resulting in a significant change in the wall velocity allowing vortices to form. The work has also concluded that, at least for most practical purposes, thermal creep has no tangible effects on the thermal part of the problem, where the solution with and without thermal creep effect, is producing almost the same results for temperature field, total heat transfer, and thermal entrance length.

Numerical study of thermally developing turbulent internal flows

The effect of fluid Prandtl number on the thermal characteristics of the flow at the thermal-entry region of a hydrodynamically fully developed turbulent channel flow at a friction Reynolds number of Reτ=180 is investigated using direct numerical simulation. Four test cases with molecular Prandtl numbers of Pr = 0.71, 1, 3, 7 are considered. The numerical results confirm that in contrast to laminar flows, where the thermal entry length increases with the increase of the Prandtl number, for turbulent flows the increase of the Prandtl number accelerates the thermal development of the flow toward its asymptotic fully developed state. The variations of the Nusselt number, and the mean and rms temperature profiles are reported in the streamwise direction. It is shown that at highest Prandtl number considered in this study (Pr =7 ), while the mean temperature profile in the logarithmic region is still developing, the temperature profile in the conductive sublayer and the Nusselt number approach their fully developed values, confirming the dependence of the Nusselt number of turbulent flows to the development of the conductive sublayer. The development of the rms temperature profiles in the streamwise direction is also shown to be a good indicator for the flow reaching its thermally fully developed condition. The temperature-velocity correlations, temperature variance budgets, and contours of temperature are also reported at different streamwise locations for different Prandtl numbers.

Counterflow HE analysis of Cu and SiO2 nanofluids in the developing flow region

AbstractThree concentrations of 0.2, 0.6, and 1.0 vol.% Copper/25 nm and silica/22 nm nanofluids are prepared in a base liquid glycerol–water mixture of 30:70 ratio by volume (GW70). The thermophysical properties of Cu and SiO2 nanofluids are determined with a TPS500S hot disc thermal analyzer and Brookfield viscometer in the temperature range of 20–80°C. The maximum enhancement in Cu and SiO2 nanofluid viscosity (63.4%, 35.7%), thermal conductivity (100.4%, 71.3%), and density (7.5%, 1.5%) while specific heat (7.8%, 2.3%) determined for 1.0% concentration at 80°C compared to base liquid GW70. Heat transfer experiments are conducted in a short‐length double pipe heat exchanger. The flow rates resulted in the lamifnar entry length region. A maximum enhancement in the overall heat transfer coefficient (HTC; 25.0%, 19.7%) and convective HTC (46.2%, 34.8%), respectively for Cu and SiO2 nanofluids is estimated at 1.0% concentration compared to base liquid at a bulk temperature of 35°C.