Local Friction Factor Research Articles

Thermohydraulic performance of microchannel heat sinks with triangular ribs on sidewalls – Part 1: Local fluid flow and heat transfer characteristics

Triangular ribs are mounted on the parallel sidewalls of microchannels in order to reinitialize the thermal boundary layer and improve the mixing of cold and hot fluids. This paper presents a detailed numerical study on local laminar fluid flow and heat transfer characteristics in microchannel heat sinks with tandem triangular ribs for Reynolds number of 443. Three-dimensional conjugate heat transfer models considering entrance effect, viscous heating, as well as temperature-dependent thermophysical properties are employed. Water and silicon are respectively used as fluid and solid for the computational domain. Triangular ribs are attached in microchannels with either aligned or offset arrangement. Four non-dimensional geometry parameters relative to the width, height, converging-diverging ratio and spacing of triangular ribs are proposed to investigate the influence on local fluid flow and heat transfer characteristics. Velocity contour, pressure and temperature distributions are examined to demonstrate the basic fluid flow and heat transfer mechanism. Local pressure and temperature profiles are studied to show the influence of the triangular ribs on fluid flow and heat transfer process. Local friction factor and Nusselt number for different non-dimensional geometry variables are further investigated to comprehensively indicate the impact of triangular ribs. Results shows that the triangular ribs can significantly reduce the temperature rise of the heat sink base and efficiently prevent the drop of local heat transfer coefficient along the flow direction, but also result in higher local friction factor than the straight microchannel. For the studied operation conditions and geometry parameters of flow passage, the heat sink base temperature varies in the range of from 301.90 to 324.31 K, the computed pressure drop and heat transfer coefficient fluctuate from one triangular rib to the next and their amplitude and wavelength significantly depend on the geometry and arrangement of triangular ribs. Compared to the reference straight microchannel heat sink, a superior configuration considered in this paper can yield an improvement of up to 2.15 times higher of average Nusselt number.

MHD mixed convection flow of radiating and chemically reactive Casson nanofluid over a nonlinear permeable stretching sheet with viscous dissipation and heat source

PurposeThe purpose of this paper is to discuss the flow of Casson nanofluid past a nonlinear permeable stretching sheet in the presence of thermal radiation, chemical reaction, viscous dissipation, heat source, and magnetohydrodynamics.Design/methodology/approachAppropriate transformations are used to convert the boundary layer equations into nonlinear ODEs which are then solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique.FindingsSolution of this systems is obtained for velocity, temperature, and concentration profiles. Graphical illustrations are added to discuss the effect of evolving parameters against above-mentioned distributions. Tabular values of local skin friction factor, local Nusselt number, and local Sherwood number are also added and studied accordingly.Originality/valueA good agreement of the present results has been observed by comparing with the existing literature results. It is noted that skin friction coefficient, Nusselt number, and Sherwood number decrease with Casson parameter and increase with suction parameter.

Numerical Study on Heat Transfer and Flow Characteristics for Laminar Flow in a Circular Tube with Swirl Generators

This study investigated the heat transfer and flow characteristics of one kind of swirl generator in a circular heat exchanger tube through a numerical simulation. The swirl flow induced by this type of swirl generator can obtain a high heat transfer rate with minimal pressure drop penalty. The simulations were carried out to understand the physical behavior of this kind of mesoscale heat enhancement component. By visualizing the heat transfer and flow characteristics, it is found that the swirl flow is induced by swirl generator in the circular tube couples with the impinging jet effect. After passing through the swirl generator, the local friction factor of liquid can quickly return to lower level more quickly, while the local Nusselt number maintains higher values for a distance; thus, the evaluation criterion of local performance is improved. Single-factor optimization is used for three geometric parameters, i.e., the angle of swirl generator (25o, 45o, and 60o), the length of swirl generator (0.005, 0.01, and 0.02 m), and the center rod radius (1, 2, and 3 mm). The optimum parameters of the swirl generator for laminar flow of air in a circular tube are obtained, which should be 60o, 0.005 m, and 3 mm, respectively.

Experimental Investigation of Heat Transfer Enhancement in Rectangular Duct with Pentagonal Ribs

ABSTRACTRib turbulators are extensively used in augmentation of convective heat transfer in several applications related to heat exchange and cooling in thermal energy systems. Present experimental investigation examines the local heat transfer and friction factor characteristics of pentagonal ribs mounted on bottom heated wall of a rectangular channel. The emphasis is towards assessing and analysing the potential impact of varying chamfering angle (0 to 20°) and rib pitch to height ratio (6 to 12) on the overall heat transfer enhancement and its distribution on the surface. Experiments are performed at different Reynolds numbers ranging from 9400 to 58850. Liquid crystal thermography is applied to measure surface temperature distribution and finally to demonstrate the local heat transfer coefficient over the ribbed surface. The results depict that the local augmentation Nusselt number distribution is axisymmetric and shows 2-dimensionalty in heat transfer distribution. Pentagonal ribs show a significant improvement for the low heat transfer zones in leeward vicinity of the square rib, specially prominent at higher Reynolds number, and therefore seen as the potential benefit in terms of obviating the hotspots. It is observed that the pentagonal ribs lead to superior heat transfer enhancement in conjunction with significant reduction in pressure penalty as compared to square ribs and thus ensures an enhanced thermo-hydraulic performance.

Flow characteristics of gaseous flow through a microtube discharged into the atmosphere

Flow characteristics for a wide range of Reynolds number up to turbulent gas flow regime, including flow choking were numerically investigated with a microtube discharged into the atmosphere. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The LB1 turbulence model was used in the turbulent flow case. Axis-symmetric compressible momentum and energy equations of an ideal gas are solved to obtain the flow characteristics. In order to calculate the underexpanded (choked) flow at the microtube outlet, the computational domain is extended to the downstream region of the hemisphere from the microtube outlet. The back pressure was given to the outside of the downstream region. The computations were performed for adiabatic microtubes whose diameter ranges from 10 to 500 μm and whose aspect ratio is 100 or 200. The stagnation pressure range is chosen in such a way that the flow becomes a fully underexpanded flow at the microtube outlet. The results in the wide range of Reynolds number and Mach number were obtained including the choked flow. With increasing the stagnation pressure, the flow at the microtube outlet is underexpanded and choked. Although the velocity is limited, the mass flow rate (Reynolds number) increases. In order to further validate the present numerical model, an experiment was also performed for nitrogen gas through a glass microtube with 397 μm in diameter and 120 mm in length. Three pressure tap holes were drilled on the glass microtube wall. The local pressures were measured to determine local values of Mach numbers and friction factors. Local friction factors were numerically and experimentally obtained and were compared with empirical correlations in the literature on Moody’s chart. The numerical results are also in excellent agreement with the experimental ones.

Optimal Configuration of Vortex Generator for Heat Transfer Enhancement in a Plate-Fin Channel

Heat transfer is a naturally occurring phenomenon and its augmentation is a vital research topic for many years. Although, vortex generators (VGs) are widely used to enhance the heat transfer of plate-fin type heat exchangers, few researches deal with its thermal optimization. This work is dedicated to the numerical investigation and optimization of VGs configuration in a plate-fin channel. Three-dimensional (3D) numerical simulations are performed to study the effect of angle of attack and attach angle (angle between VG and wall) and shape of VG on the fluid flow and heat transfer characteristics. The flow is assumed as steady-state, incompressible, and laminar within the range of studied Reynolds numbers (Re = 380–1140). Results are presented in the form average and local Nusselt number and friction factor. The effect of attach angle is highlighted and the results show that the attach angle of 90 deg may not be necessary for enhancing the heat transfer. The flow structure and heat transfer characteristics of certain cases are examined in detail. The parameters of VG are then optimized for maximum heat transfer and minimum pressure drop. The three independent design parameters are considered for the two objective functions. For this purpose, computation fluid dynamics (CFD) data, response surface methodology (RSM) and a multi-objective optimization algorithm (MOA) are combined. The data obtained from numerical simulations are used to train a Bayesian-regularized artificial neural network (BRANN). This in turn is used to drive a MOA to find the optimal parameters of VGs in the form of Pareto front. The optimal values of these parameters are finally presented.

Numerical solution of MHD slip flow of a nanofluid past a radiating plate with Newtonian heating: A Lie group approach

In this paper, we have examined the magnetohydrodynamic flow of a nanofluid past a radiating sheet. The Navier velocity slip, Newtonian heating and passively controlled wall boundary conditions are considered. The governing equations are reduced into similarity equations with the help of Lie group. A collocation method is used for simulation. The influence of emerging parameters on velocity, temperature, nanoparticle volumetric fraction profiles, as well as on local skin friction factor and local Nusselt number is illustrated in detail. It is found that the friction (heat transfer rate) is lower (higher) for passively controlled boundary conditions as compared to the case of an actively controlled boundary condition. The magnetic field effects decrease both the skin friction and the rate of heat transfer. The findings are validated with existing results and found an excellent agreement. The model explores new applications in solar collectors with direct solar radiative input using magnetic nanofluids.

Effect of nonlinear thermal radiation on double-diffusive mixed convection boundary layer flow of viscoelastic nanofluid over a stretching sheet

BackgroundThe present exploration deliberates the effect of nonlinear thermal radiation on double diffusive free convective boundary layer flow of a viscoelastic nanofluid over a stretching sheet. Fluid is assumed to be electrically conducting in the presence of applied magnetic field. In this model, the Brownian motion and thermophoresis are classified as the main mechanisms which are responsible for the enhancement of convection features of the nanofluid. Entire different concept of nonlinear thermal radiation is utilized in the heat transfer process.MethodsAppropriate similarity transformations reduce the nonlinear partial differential system to ordinary differential system which is then solved numerically by using the Runge–Kutta–Fehlberg method with the help of shooting technique. Validation of the current method is proved by having compared with the preexisting results with limiting solution.ResultsThe effect of pertinent parameters on the velocity, temperature, solute concentration and nano particles concentration profiles are depicted graphically with some relevant discussion and tabulated result.ConclusionsIt is found that the effect of nanoparticle volume fraction and nonlinear thermal radiation stabilizes the thermal boundary layer growth. Also it was found that as the Brownian motion parameter increases, the local Nusselt number decreases, while the local friction factor coefficient and local Sherwood number increase.

Boundary layer analysis of an incessant moving needle in MHD radiative nanofluid with joule heating

The boundary layer analysis of a 2D forced convection flow along an incessant moving horizontal needle in magnetohydrodynamic radiative nanofluid is investigated. The energy equation is incorporated with the joule heating, non-constant heat source/sink, and viscid dissipation effects. To check the variation in the boundary layer nature, we considered the two nanofluids namely, Ag–water and Ag–Kerosene. The reduced system of governing PDEs is solved by employing the Runge–Kutta Fehlberg integration scheme. Computational results of the local Nusselt number and friction factor are tabulated and discussed. Velocity and temperature fields are discussed with the help of graphical illustrations. Increasing the needle size significantly reduces the flow and energy boundary layers of both nanofluids. In particular, thermal and velocity fields of Ag–kerosene nanofluids are highly dissed when equated with the Ag–water nanofluid.

Variation of Local Friction Factor in an Open Channel Flow

Objectives: This present paper investigated experimentally on the variation of local friction factor over the cross section in channels of different geometries. The dependency of the variation of friction factor with aspect ratio has been well compared with the results of other researchers and natural river data. Methods/Analysis: Experiments have been conducted on trapezoidal and rectangular open channel for different geometry, hydraulic and roughness conditions. The local friction factors along every vertical interface have been carried out. The actual prediction of boundary shear stress and depth averaged velocity distribution have been calculated by finding the changes of these indispensible parameters, from wide range of data collected from previous literatures. Also the experimental depth averaged velocity and boundary shear stress have been carried out for assessing the friction factor. Findings: The global friction factor f g and local friction factors f l were calculated based on the measured depth-averaged velocity and boundary shear stress. The local friction factor does not remain constant across the channel as it depends upon the geometry and roughness parameter. The paper describes the variation of friction factor for both smooth and rough channels under different flow condition. Local boundary shear stress around the wetted perimeter τ b , and depth averaged velocity, U d , data are used to evaluate local friction factor, f l . Applications/Improvement: Local friction factor variation analysis is a very rare factor that few researchers are taken into consideration. But it has a more importance for flow characteristics which is studied in this paper.

Bypass Flow Resistance in Prismatic Gas-Cooled Nuclear Reactors

Available computational fluid dynamics (CFD) predictions of pressure distributions in the vertical bypass flow between blocks in a prismatic gas-cooled reactor (GCR) have been analyzed to deduce apparent friction factors and loss coefficients for nuclear engineering systems and network codes. Calculations were performed for vertical gap spacings “s” of 2, 6, and 10 mm — representing 1, 3, and 5 mm in a GCR design, horizontal gaps between the blocks of 2 mm and two flow rates, giving a range of vertical gap Reynolds numbers ReDh of about 40–5300. The present focus is on the examination of the flow in the vertical gaps. Horizontal gaps are treated in CFD calculations but their flows are not examined. Laminar predictions of the fully developed friction factor ffd were about 3–10% lower than the classical infinitely wide channel. In the entry region, the local apparent friction factor was slightly higher than the classic idealized case, but the hydraulic entry length Lhy was approximately the same. The per cent reduction in flow resistance was greater than the per cent increase in flow area at the vertical corners of the blocks. The standard k–ϵ turbulence model was employed for flows expected to be turbulent. Its predictions of ffd and flow resistance were significantly higher than direct numerical simulations (DNS) for the classic case; the value of Lhy was about 30 gap spacings. Initial quantitative information for entry coefficients and loss coefficients for the expansion–contraction junctions between blocks is also presented. The present study demonstrates how CFD predictions can be employed to provide integral quantities needed in systems and network codes.

Local convective heat transfer coefficient and friction factor of CuO/water nanofluid in a microchannel heat sink

Forced convective heat transfer in a microchannel heat sink (MCHS) using CuO/water nanofluids with 0.1 and 0.2 vol% as coolant was investigated. The experiments were focused on the heat transfer enhancement in the channel entrance region at Re < 1800. Hydraulic performance of the MCHS was also estimated by measuring friction factor and pressure drop. Results showed that higher convective heat transfer coefficient was obtained at the microchannel entrance. Maximum enhancement of the average heat transfer coefficient compared with deionized water was about 40 % for 0.2 vol% nanofluid at Re = 1150. Enhancement of the convective heat transfer coefficient of nanofluid decreased with further increasing of Reynolds number.

Heat transfer and fluid flow characteristics in air duct with various V-pattern rib roughness on the heated plate: A comparative study

This article presents three dimensional CFD (computational fluid dynamics) investigation of local Nusselt number and local friction factor ratios in an air channel with various V-pattern ribs as roughness elements employed on one wall. The various ribs such as, V-pattern rib, protrusion rib in V-pattern, dimpled rib in V-pattern, and V-pattern rib combined with groove have been considered in the study. The CFD analysis on heat transfer and fluid flow characteristics is conducted to investigate the overall effects of the various V-pattern rib shapes on the thermal hydraulic performance. The results found that V-pattern rib with a combination of groove roughness shapes provides better thermal hydraulic performance than other comparable V-pattern rib roughness shapes.

Parametric study on thermal and hydraulic characteristics of laminar flow in microchannel heat sink with fan-shaped ribs on sidewalls – Part 2: Pressure drop

This second part of a three-part study concerns pressure drop of laminar flow in microchannel heat sinks with water and silicon used as fluid and solid for the computational domain. In the rectangular microchannel with width of 0.1mm and depth of 0.2mm, the repeating aligned or offset fan-shaped ribs are mounted to the channel sidewalls. To examine the influence of fan-shaped rib’s geometry on thermal and hydraulic characteristics of laminar flow, three non-dimensional variables, representing the width (0.05–0.4mm), height (0.005–0.025mm) and spacing (0.2–5mm) of fan-shaped ribs are designed. The present study firstly presents the pressure distributions in microchannels to analyze the local hydraulic characteristics, and then examines the local pressure and friction factor along the flow direction for different geometry of fan-shaped ribs. Results show that the fan-shaped ribs can lead to large increase of local pressure in comparison with the smooth microchannel, especially for the aligned fan-shaped ribs. Further, the effect of fan-shaped ribs’ geometry on the average friction factor has been investigated. Results show that with the increase of fan-shaped ribs’ width, the friction factor ratio of the studied microchannels to the smooth one firstly decreases and then increases. The increase of fan-shaped ribs’ height and decrease of ribs’ spacing can lead to the extreme increase of average friction factor, especially for the microchannels with aligned fan-shaped ribs. For Reynolds number ranging from 187 to 715, the microchannels with aligned fan-shaped ribs show the average friction factor 1.1–8.28 times larger than the smooth one, while those with offset fan-shaped ribs show 1.22–6.27 times higher. New pressure drop correlations for such microchannel heat sinks are developed, which fit the present data with a mean absolute error of 13.2% for the ones with aligned fan-shaped ribs and 13.5% for the ones with offset fan-shaped ribs.

Tube Dynamics Works for Randomly Entangled Rings.

The tube model is the cornerstone of molecular theory for polymer rheology. We test its microscopic assumptions by simulating topologically equilibrated ring polymers, whose dynamics is free from end segment relaxation. We show that a closed-form expression derived from the tube model adapted to ring polymers quantitatively predicts the segmental mean squared displacements over the entire range of time scales from local motion to complete equilibration, with a time-independent local friction factor.

Estimating tsunami run-up

Tsunami risk reduction activities rely on a sound knowledge of the hazard characteristics. Our understanding of these characteristics is derived from empirical measurements, numerical models or established rules. Conventional methods used to delineate areas vulnerable to tsunami inundation are often calculated from estimated maximum wave height at the coast and “rules-of-thumb”. Applying such rules may give unreliable results for decision-makers. Using basic hydraulic principles and assumptions, this paper improves on the existing rules by developing and testing new equations for predicting tsunami maximum depth profiles and inundation distances. The proposed equations require knowledge of shoreline wave-crest level, the onshore ground profile and an index for onshore roughness (a ratio of distance between protrusions to a local friction factor). As a tsunami wave moves inland, the equations demonstrate that there will usually be an exponential decline in peak water depth. The equations also confirm that a smaller spacing between onshore roughness elements, such as trees or houses, will give a steeper decline in peak depth due to increased friction as a wave moves inland. Furthermore, where ground level is rising faster than friction head is being lost, it is predicted that the water level of a tsunami will rise above the shoreline wave-crest level. The ground slope at which run-up starts to exceed shoreline wave-crest level can be predicted from the shoreline wave-crest level and roughness spacing. Results predicted by the new equations are verified by comparison with tsunami run-up measurements made in Samoa and Java.

Numerical simulation of Al2O3–water nanofluid mixed convection in an inclined annulus

Laminar mixed convection of Aluminium oxide (Al2O3)–water nanofluid flow in an inclined annulus using a single-phase approach was numerically studied. Constant heat flux boundary conditions were applied on the inner and outer walls. All the thermophysical properties of nanofluid, such as, viscosity, heat capacity, thermal conductivity, and thermal expansion coefficient, except density in the body force term were assumed to be constant. Based on Boussinesq’s hypothesis, density was assumed to be a linear function of temperature. The nanofluid properties were calculated in terms of constant properties of nanoparticles and the base fluid. Using the finite volume method the continuity, momentum, and energy equations were numerically solved. Numerical simulations were conducted for the nanoparticle concentrations of 0, 2, and 5% and five different inclination angles including -30o, -15o ,0 , +15o, and+30o. Results showed that a variation in the inclination angle affected the Nusselt number on the inner wall more than the outer one. The Nusselt number in negative angles was higher than in the positive ones, so that at a volume fraction of 5%, the average Nusselt number at the inner wall decreased almost 2% when changing the angle from -30o to+30o. The local Friction factor in the positive angles was higher than in the negative ones.

Study on local thermal–hydraulic performance and optimization of zigzag-type printed circuit heat exchanger at high temperature

High temperature heat exchanger is one of the most important components to transfer heat from the first loop to the second loop in the very high temperature reactor in nuclear energy application. In order to enhance the heat transfer performance, a mini-channel heat exchanger called printed circuit heat exchanger has attracted more attention in recent years. In this paper, the thermal–hydraulic performance of zigzag-type printed circuit heat exchanger with helium as the working fluid operating at the typical temperature of 900°C in the very high temperature reactor is studied. It is found that the flow and temperature at high temperature cannot achieve a fully-developed condition due to the significant variation of thermal physical properties arisen from the large temperature difference. However, the non-dimensional velocity and temperature can become steady after the second pitch and is similar to the fluid flow behaviors at low temperature. Therefore the local Nusselt number and friction factor at high temperature can match well with those at low temperature when the Reynolds number is bigger than 900. With the increase of inclined angle, the heat transfer and pressure drop increase. It is recommended to put the channel with a larger inclined angle to the cold region when using the hybrid channels. The heat transfer enhancement method with inclined angles completely depends on the operating conditions.

Numerical Study on Mixed Convection Heat Transfer in Inclined Triangular Cavities

This article presents a parametric study on flow behavior and heat transfer in an inclined triangular cavity subjected to a moving lid and temperature differential. The systematic study considers three physical parameters (inclination angle, Reynolds number, and Grashof number) and explores the influence of these parameters on flow pattern and heat transfer characteristics. A series of computations were performed for the inclination angle (θ) ranging from 0° to 360° (in increments of 45°), Reynolds number (Re) from 100 to 1,500, and Grashof number (Gr) from 105 to 107. The numerical results show that there are three kinds of flow regime in a triangular cavity inclined from 0° to 360°: buoyancy-dominant, inertia-dominant, and intermediate transition (mixed convection flow). It is interesting that the case with Re = 100, Gr = 107, and θ = 0° exhibits five circulation cells and induces excellent thermal performance, corresponding to wavy profiles in local Nusselt number and local friction factor. The study also reveals that the good thermal performance within a local region can generate higher friction force on the neighboring boundary and this friction force may reduce the strength of the vortex.

A CFD study of the hydrodynamics in a desalination membrane filled with spacers

Reverse osmosis (RO) is by far the most widely used membrane desalination process worldwide. The RO process depends on the properties of semi-permeable membranes which allow the separation of water from a salt solution by applying external pressure higher than the osmotic pressure on the seawater. The main problem in membrane separation process is the fouling of the membrane walls, which decreases the permeate flux. Having spacer filaments in the feed channel has been proven to dynamically change the concentration boundary layer and preventing fouling. In this study, computational fluid dynamics (CFD) techniques were used to study the hydrodynamics of feed channels of a desalination membrane filled with spacers in zigzag arrangements and transverse in relation to the flow. Numerical solutions were obtained with FLUENT software for laminar flows. A fully developed laminar flow, quasi-periodically repeating in successive inter-filament regions, was used. Four types of settings were tested with different inter-filament distances in the range of Reynolds numbers between 10 and 300. The results show the effect of the distance between elliptical filaments in the velocity field, streamlines, local and average friction factors, pressure drop and on the shear stress developed in the membrane walls. Further, the decrease in distance between filaments may lead to more active recirculation patterns that may promote mass transfer on the membrane surfaces, despite the decrease in their usable area.