Transverse Velocity Profiles Research Articles

Analysis of heat and mass transfer rates in conducting Casson fluid flow over an expanding surface considering Ohmic heating and Darcy dissipation effects

In a recent scenario, the flow of Casson fluid via porous media has practical applications in various engineering processes, such, as the design of cooling systems for electronic devices, oil recovery in porous reservoirs, and polymer extrusion processes, etc. The proposed investigation illustrates the thermal and solutal transfer rates in a conducting Casson fluid flow over an expanding surface. However, the emphasis goes to the behavior of the Ohmic heating and Darcy dissipation when considering the transverse magnetic field and porous matrix. The governing flow phenomena with their dimensional form are altered into a non-dimensional set of equations with the help of suitable similarity rules. Further, an adequate numerical simulation is adopted to solve the transformed equations using the in-house bvp4c function in MATLAB. The physical parameters involved in the flow problem and their behavior on the governing flow phenomena are presented graphically and described briefly. Prior to this investigation, the conformity of the current numerical output obtained for the heat transfer rate was validated with the earlier work with a good correlation. Moreover, the major outcomes are; the non-Newtonian Casson parameter retards the axial and transverse velocity profile and the shear rate also decreases significantly. The Eckert number caused by the inclusion of the dissipative heat encourages the fluid temperature throughout.

An impact of Richardson number on the inclined MHD mixed convective flow with heat and mass transfer

AbstractThe two‐dimensional mixed convective MHD flow with heat and mass transfer is investigated for its behavior with Dufour and Soret mechanisms over the porous sheet. The copper–alumina (Cu–Al2O3) hybrid nanoparticles are used in the base fluid water. The governing system of partial differential equations is converted into a system of ordinary differential equations via similarity transformations, obtaining the solution for velocity, temperature, and concentration fields in exponential form. The problem is demonstrated in the Darcy–Brinkman model, the impact of included parameters such as Richardson number, magnetic field, and Dufour numbers are studied for the obtained solution with the help of graphs. Increasing the magnetic field decreases both transverse and axial velocity profiles. Increasing the magnetic field and Richardson's number decreases the solution (Al2O3–H2O). Increasing the values magnetic field and Richardson's number decreases both transverse and axial velocity profiles. Increasing the values of the Dufour effect increases the axial and transverse velocity boundary layer. The magnetohydrodynamic hybrid nanofluid flow over porous media works efficiently in liquid cooling and, therefore, has significant applications in industrial heating and cooling systems, solar energy, magnetohydrodynamic flow meters and pumps, manufacturing, regenerative heat exchange, thermal energy storage, solar power collectors, geothermal recovery, and chemical catalytic reactors.

Tracking the Nearfield Evolution of an Initially Shallow, Neutrally Buoyant Plane Jet Over a Sloping Bottom Boundary

AbstractUnderstanding coastal plane jets which occur when a body of water discharges into an ocean or a lake through a channel or outlet is important, since they play a significant role in sediment, nutrient, and pollutant exchange. This study investigates the nearfield of initially shallow, neutrally buoyant plane jets, bounded by a free surface and a sloping bottom (Sloping Bottom Jet; SBJ) that issue into a laterally unconfined quiescent ambient both experimentally and numerically, and compares them with a plane jet flowing over a horizontal bottom (Horizontal Bottom Jet; HBJ). Results revealed that, different from the HBJ, the width and centerline velocity of SBJ decrease near the mouth. The SBJ width gradually increases after that as the transverse longitudinal velocity profile progressively transforms from a “top‐hat” into a Gaussian distribution. Once the Gaussian distribution is established, both jets diverge and centerline velocity decreases. Shear layers are generated on the sides of both jets with Kelvin Helmholtz‐type Coherent Structures (KHCS) developing inside. KHCS produce periodic velocity fluctuations with a Strouhal number of ∼0.079 and contribute significantly to momentum exchange and turbulent kinetic energy production. Since the thickness of the SBJ increases longitudinally, the vertical extent of KHCS also increases. When the two shear layers meet and merge at the centerline, they cause a flapping motion of the jet. This location is closer to the jet mouth for SBJs than for the HBJ. These findings demonstrate that a sloping bottom modifies the flow field from quasi‐2D for the HBJ to strongly 3D for SBJs.

Numerical modeling of the two-dimensional free and impinging jets with solid and erosion bed using FLOW-3D

ABSTRACT This study simulates the flow properties of a plane-layered jet in free and impinging jets on a horizontal surface using Flow-3D and validates them with previous research and experimental data. The flow characteristics, such as velocity and shear stress distribution, are compared with theoretical relationships. The simulations vary the outlet velocities for the free jet and the surface types and slip conditions for the impinging jet. The results show that the free jet flow follows the self-similar theory, except for a faster decay of numerical velocities at the end of the jet’s path. The results also reveal a virtual origin (λ) before the nozzle outlet, ranging from 7.6 to 8.4 mm. The impinging jet results match the experimental wall shear stress distribution diagram, with the peak at y/H = 0.14. The transverse velocity profiles and the wall shear stress distribution of the impinging jet are influenced by the slip condition and the surface type, but the difference between smooth and granular surfaces is less than 3%. This study offers valuable insights into the behaviour of free and impinging jets on a horizontal surface and shows the effectiveness of the Flow-3D numerical model.

Finite element analysis of MHD naturally convective flow past an exponentially accelerated plate with viscous dissipation

The MHD finite element analysis naturally convective flow across an exponentially accelerating plate with viscous dissipation is investigated numerically. In this process dimensional partial differential equations are changed to dimensional less form. The Galerkin finite element method is emerged to solve non-dimensional partial differential equations. Obtained results are effectively depicted through the utilization of graphs, allowing for a comprehensive understanding of the impact that different physical parameters on primary velocity, transverse velocity, temperature, and concentration profiles. The study effectively differentiated between the present and prior findings, ultimately demonstrating a strong consensus of excellent agreement between the results. The key findings of this study are: The primary velocity increases on growing the values of Thermal Grashof number, Solutal Grashof number, Eckert number, and Dufour number and decreases on climb up the values of Magnetic parameter, Prandtl number, Schmidt number, and Hall parameter. The secondary velocity increases on raising the values of Thermal Grashof number and Solutal Grashof number and diminishes on enhancing the value of Hall parameter. The temperature increases on increasing the values Eckert number and Dufour number and decreases on improving the value of Prandtl number. The concentration decreases on increasing the value of Schmidt number.

Estimation of transverse velocity and concentration profile using Kumaraswamy distribution

Estimation of transverse velocity and concentration profile using Kumaraswamy distribution

Transverse energy loss slope in meandering channels

Limited research has been conducted on transverse energy loss in meandering channels. Previous studies made assumptions regarding a linear vertical profile of transverse velocity and rectangular cross sections with horizontal transverse beds, neglecting the effects of nonlinear transverse velocity profiles and transverse bed slopes that contribute to topographic steering. In this study, a novel expression for the transverse energy loss slope is derived analytically. This expression incorporates a nonlinear vertical distribution for transverse velocity and considers non-rectangular cross sections, thereby improving the computation of roughness coefficients in curved channels. A topographic steering number is introduced, which indicates the presence of topographic steering when it exceeds unity. The developed equation rectifies the previous underestimation of sinuosity in natural rivers when compared to existing equations. Additionally, an expression for superelevation is derived, accounting for channel roughness and transverse bed slope, unlike previous equations. The study reveals that roughness can significantly affect the height difference between outer and inner banks. Under higher roughness conditions, the height difference can exceed predictions from existing formulas by up to 50%. This emphasizes the importance of considering roughness effects in accurately estimating superelevation. The developed equations are validated through comparisons with available field, laboratory, and numerical data.

Ultrahigh‐Pressure Acoustic Velocities of Aluminous Silicate Glass up to 155 GPa With Implications for the Structure and Dynamics of the Deep Terrestrial Magma Ocean

AbstractWe have carried out in situ high‐pressure acoustic velocity measurements of (Fe2+, Al)‐bearing MgSiO3 glass up to pressures of 155 GPa, which confirmed a distinct pressure‐induced trend change in the transverse acoustic velocity (VS) profile around 98 GPa, likely caused by the Si‐O coordination number (CN) change from 6 to 6+. Although it has been reported that the substitution of Fe2+ in MgSiO3 glass induces almost linear velocity reduction up to ∼160 GPa, we revealed that the VS profile of (Fe2+, Al)‐bearing MgSiO3 becomes anomalously steeper above ∼100 GPa and eventually came to be equivalent to MgSiO3 glass above ∼125 GPa. This implies the incorporation of Al into Fe‐bearing MgSiO3 glass significantly facilitates making it far elastically stiffer and thus the densification under pressures well within the Earth's lower mantle. Our results indicate the possible presence of stiff and highly dense silicate melts in deep MOs in the rocky terrestrial planets.

Impact of inertial drag on the entropy generation for water-based hybrid nanofluid through a permeable medium with heat generation/absorption

The consequence of thermal radiation vis-a-vis external heat generation/absorption on the inertial drag force of a hybrid nanoliquid flow in three-dimensional geometry is investigated. It is proposed that with the symmetric or non-symmetric particle shape, the velocity differs because of the direction of the drag. Furthermore, the conducting fluid for the interaction of the magnetic field through a permeable medium past an expanding surface influences the flow phenomenon. The present analysis is useful for the dialysis of blood in the artificial kidneys, the flow of blood in capillaries as well as the design of filters in engineering problems. However, the formulated problem is transformed into its non-dimensional form for the implementation of particular similarity rules. The set of nonlinear governing equations with specific contributing parameter values is subjected to handle by employing shooting-based Runge–Kutta fourth-order technique. Because of the system’s irreversibility, the simulation of entropy and the Bejan value is the main draw. For each profile, the graphical results of specific parameters such as momentum, temperature, entropy, and the Bejan number are shown. Further, the important outcomes are the axial and the transverse velocity profiles are restricted by the inclusion of volume concentration in association with magnetic field and the enhanced Brinkman number augments the entropy generation significantly. However, the numerical validation shows a good correlation between the earlier investigations in particular cases.

Mapping non-axisymmetric velocity fields of external galaxies

ABSTRACT Disc galaxies are typically in a stable configuration where matter moves in almost closed circular orbits. However, non-circular motions caused by distortions, warps, lopsidedness, or satellite interactions are common and leave distinct signatures on galaxy velocity maps. We develop an algorithm that uses an ordinary least squares method for fitting a non-axisymmetric model to the observed two-dimensional line-of-sight velocity map of an external galaxy, which allows for anisotropic non-circular motions. The method approximates a galaxy as a flat disc, which is an appropriate assumption for spiral galaxies within the optical radius where warps are rare. In the outer parts of H i distributions, which may extend well into the warp region, we use this method in combination with a standard rotating tilted ring model to constrain the range of radii where the flat disc assumption can be conservatively considered valid. Within this range, the transversal and radial velocity profiles, averaged in rings, can be directly reconstructed from the velocity map. The novelty of the algorithm consists in using arc segments in addition to rings; in this way, spatial velocity anisotropies can be measured in both components, allowing for the reconstruction of angularly resolved coarse-grained two-dimensional velocity maps. We applied this algorithm to 25 disc galaxies from the THINGS sample, for which we can provide 2D maps of both velocity components.

Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditions

We present a model for thermo- and pressure-driven membrane processes accompanied by transmembrane water and heat fluxes combined in a single unit. High-pressure channel (high-pressure control volume) is characterized by low operating temperature and vice versa. A symmetric plate-and-frame membrane channel was considered in this study. An elementary parallelepiped was selected as a control volume. Balance equations were written over the control volume. A membrane element was represented as a set of conjugate semipermeable volumes. The model is based on the following assumptions: (1) incompressible fluid under steady-state conditions; (2) trans-membrane water flux is opposed to transmembrane heat flux. Transverse velocity profile is approximated by Berman distribution; (3) the mechanisms of transverse transport include: convection resulting from pressure differences and conduction resulting from temperature gradients; (4) the thickness of thermal layer is equal to half height of the channel (δt=H). The temperature polarization (TP) module reveals high sensitivity to thermo-physical properties and hydrodynamics such as to the coefficient of thermal diffusivity a=λ/cρ and to the transverse velocity, V(z). We find that (a) variation of the coefficient of thermal diffusivity in liquid phase from a= 2.0 10−7 m2/s to a= 1.0 10−7 m2/s will reduce TP module from 0.96 to 0.91; (b) variation of transverse velocity at the membrane surface from 5.5 10−5 to 1.5 10−5 m/s can decrease of TP module from 0.95 to 0.79. The developed solution can be used as a sub-model for quantitative estimation of TP phenomena in thermo-driven membrane operations. It can be applied for analysis of pressure-driven processes at non-isothermal conditions and be used as a mathematical algorithm for process analysis and optimization.

Numerical investigations of flow in nuclear fuel assembly with spacer grid and OpenFOAM validation

Abstract Spacer grids with mixing vanes have complex geometry and are used to support the fuel rods in nuclear fuel assemblies as well as to improve heat transfer by generating turbulence downstream of the spacer grid in the cores of the pressurized water reactors. To validate the CFD code OpenFOAM for relevant spacer grid geometries, numerical analyses on the OECD/NEA MATiS-H benchmark were performed. The flow behind two different types of spacer grid designs was analysed: split- and swirl-type. Initially, an appropriate inlet velocity profile was generated. In a next step, Computer-Aided Design models of the spacer grids were prepared and then meshed using ANSYS Mesher 19.2. Transient URANS simulations were performed with the k-ω-SST turbulence model and the results were compared with data. Good agreement was obtained for the mean velocity profile and the vorticity in the swirl-type configuration, while the numerical results slightly overestimated the transverse velocity profile at some measurements locations of the split-type configuration. The content of this article was initially presented at the 33rd German CFD Network of Competence Meeting, held on March 22–23 at GRS in Garching, Germany.

Mathematical Analysis of Transverse Wall-Shearing Motion via Cross Flow of Nanofluid

The investigation of nanofluid’s cross flow, which is caused by a nonlinear stretching sheet within the boundary layer, is presented. The proper mathematical detail is provided for three distinct cross flow instances with the streamwise flow. A uniform transverse stream located far above the stretched plate, in one instance, creates the cross flow. Two further situations deal with cross flows caused by surface transverse shearing motions. Weidman’s work was used to find a similarity solution by making the necessary changes. It has been found that two parameters, namely nanoparticle volume frictions ϕ and a nonlinear stretching parameter β, have a significant impact on the flow of fluids in cross flow scenarios. Graphical representations of transverse and streamwise shear stresses and velocity profiles are provided. From this study, we found that nanoparticle volume fraction ϕ reduces the momentum boundary layer in both streamwise and cross flow scenarios while increasing the temperature of the fluid and, hence, increasing thermal boundary layer thickness. The same is observed for the nonlinear stretching parameter β.

Numerical study on transverse mixing characteristics of flow sweeping in helical cruciform rod bundle

Fluoride salt serves as a coolant in the fluoride-salt-cooled high-temperature reactor and flows through the reactor core to remove heat produced by the nuclear fuel. To enhance the flow heat transfer performance of coolant in the fuel assembly, helical cruciform fuel rods are designed as a foundation fuel element. In the present study, the numerical method in helical cruciform rod bundle is used to analyze the transverse mixing characteristics of flow sweeping. A heat transfer fluid (Dowtherm A) flows and transfers heat by convection along the heated wall of helical cruciform rod. The fluid in the helical cruciform rod bundle exhibits a substantial flow sweeping crossflow phenomena as a result of the impact of the helical structure. The transverse mixing velocity and temperature profiles are analyzed. The subchannel conservation equation is optimized, and the correlation between flow sweeping mixing parameters and dimensionless local gap distance in various Reynolds number ranges is determined by fitting. Furthermore, the maximum of flow sweeping mixing parameter of the helical cruciform rod bundle is more than seventy times greater than the turbulent mixing parameter's maximum of the cylindrical rod bundle under an identical Reynolds number. It can be concluded that the helical cruciform rod bundle has considerable transverse mixing, which enhances the flow heat transfer performance of the reactor core. This study provides a guide for the numerical study of flow heat transfer in helical structures, and a foundation for the development of the subchannel mixing model.

Evaluations of Lagrangian egg drift models: From a laboratory flume to large channelized rivers

To help better interpret computational models in predicting drift of carp eggs in rivers, we present a series of model assessments for the longitudinal egg dispersion. Two three-dimensional Lagrangian particle tracking models, SDrift and FluEgg, are evaluated in a series of channels with increasing complexity. The model evaluation demonstrates that both models are able to accommodate channel complexity and provide a wide range of dispersion coefficients: Kl=O(1−100)Hu∗ with H being water depth and u∗ being shear velocity. In a straight channel with Kl=O(1)Hu∗, SDrift predicts weaker longitudinal dispersion than FluEgg in the early stage as a result of weak vertical mixing associated with smooth wall turbulence. With sufficient time, SDrift and FluEgg predict similar egg dispersion, accounting for the differential advection due to the vertical velocity profile. In an idealized curved channel with Kl=O(10)Hu∗, dispersion is driven by both vertical and transverse velocity profiles. SDrift yields slightly larger dispersion coefficients than FluEgg. In a real river with channel-training structures and having Kl=O(100)Hu∗, SDrift predicts a stronger longitudinal dispersion than FluEgg due to substantial local turbulent eddies and velocity gradients. To summarize, FluEgg shows good performance in capturing dispersion due to vertical velocity profiles and cross-channel velocity gradients. SDrift shows excellent model capabilities of revealing various dispersion mechanisms in addition to the vertical and cross-channel velocity variations. They include the initial turbulent diffusion stage with growing dispersion coefficients and strong dispersion due to in-stream hydraulic structures and localized turbulence.

Electronic viscous boundary layer in gated graphene

We investigate the boundary layer problem in viscous electronic flows in gated graphene. Recent experiments on graphene hydrodynamics indicate the emergence of non-Poiseuille behavior, a feature that we reproduce with direct numerical simulations of gated graphene electrons. In fact, the velocity profile displays a maximum value close to the boundary and then decreases as it approaches the bulk. By taking into account the compressibility of the electron fluid, that arises from the dependence of effective hydrodynamic mass on the number density, we derive a generalized Blasius equation governing the transverse velocity profile, in excellent agreement with the simulation results. Evidence of a non-monotonic profile and further deviations with respect to incompressible (classical) hydrodynamics may shed some light on the subject of non-topological edge currents in graphene.

Irreversibility analysis on the radiative buoyancy flow toward stagnation point through water conveying three kinds of nanoparticles past a heated vertical flat plate with the ramification of Hall effects

Recent advancements in nanotechnology have created a tremendous platform for the development of the improved performance of ultrahigh coolants known as nanofluids for several industrial and engineering technologies. The present research peruses an inspection of irreversibility analysis of mixed convective flow near a stagnation point provoked by ternary hybrid nanoparticles through a vertical heated flat plate with the Hall effects. Water conveying alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) nanoparticles experiencing convectively heated as appropriate in the engineering or industry are investigated. The leading equations are non-dimensionalized using relevant similarity variables and then numerically cracked via utilizing the bvp4c solver. The impressions of different pertinent parameters on the axial velocity, transverse velocity and temperature profile along with heat transfer and drag force are discussed carefully. Double solutions are observed in the opposing flow; however, a single solution is obtained for the assisting flow. Also, the results indicate that due to nanofluid, the velocity boundary layer thicknesses decrease and the thermal boundary layer width upsurges. Further, the flow and the characteristics of heat transfer can be controlled using a magnetic field.

Semi-numerical treatment of MHD Maxwell nanofluid rotating flow on a stretching sheet with the presence of mass transpiration, heat source/sink, and chemical reaction

ABSTRACT The study of the flow of heat and mass transfer in the presence of suction and injection has many scientific and engineering applications such as in aerodynamics and space sciences. A significant role of suction/injection is observed in controlling fluid flow along a boundary layer surface and it is also affecting the heat transfer rate in the mass transfer cooling process. In the present study, we investigate suction/injection effects and heat transfer features of Maxwell nanofluid along a stretched sheet in addition to a chemical reaction, magnetohydrodynamics, and heat source/sink. The partial differential equations describing the physical phenomena of the problem under consideration are converted into non-dimensional ordinary differential equations (ODEs) through an appropriate set of similarity transformations. Transformed ODEs solution is obtained with a semi-optimal homotopy analysis method (OHAM). The influencing behavior of suction and injection, as well as of other parameters, on the velocity, temperature, and concentration fields are shown through graphs and tables. The horizontal velocity and temperature field show a decreasing behavior for both suction and injection while opposite trends are noticed in transverse velocity and concentration profile.

Hydraulics of flow over full-cycle cosine and rectangular sharp-crested weirs

Laboratory experiments were carried out to investigate the hydraulic characteristics of full-cycle cosine and rectangular sharp-crested weirs in free flow condition. The head–discharge relationships of full-cycle cosine weirs were determined theoretically and the discharge coefficients were correlated with weir geometry for both rigid and erodible bed conditions. The proposed model showed higher discharge coefficients in full-cycle cosine weirs in comparison with rectangular sharp-crested weirs. The three-dimensional velocity profiles of full-cycle cosine and rectangular weirs were measured by an acoustic Doppler velocimeter probe. The effects of weir geometry on mean flow and local erosion upstream of the weirs were studied for two sediment sizes of 0.7 mm and 1.2 mm. The time-averaged velocity profiles exhibited strong three-dimensional flow in full-cycle cosine weirs. The strength of the upper eddy in the crest location of full-cycle cosine weirs decreased by increasing the weir gap opening and the jet stream deflected upward due to uneven eddy sizes. The maximum streamwise velocity of cosine weirs increased by four times the average velocity at the crest level of the weir and the transverse velocity profiles captured strong vortices in the vertical plane closest to the weir. The effect of weir gap opening of full-cycle cosine weirs on the total scour volume was studied for two sediment sizes. It was found that the scour volume in the upstream region of cosine weirs was higher than the scour volume formed upstream of a rectangular weir with the same opening.

Flow visualization by Matlab® based image analysis of high-speed polymer melt extrusion film casting process for determining necking defect and quantifying surface velocity profiles

Abstract The primary objective of this research paper is to detect and quantify the necking defect and surface velocity profiles in high-speed polymer melt extrusion film casting (EFC) process using Matlab® based image processing techniques. Extrusion film casting is an industrially important manufacturing process and is used on an industrial scale to produce thousands of kilograms of polymer films/sheets and coated products. In this research, the necking defect in an EFC process has been studied experimentally and the effects of macromolecular architecture such as long chain branching (LCB) on the extent of necking have been determined using image processing methodology. The methodology is based on the analysis of a sequence of image frames taken with the help of a commercial CCD camera over a specific target area of the EFC process. The image sequence is then analyzed using Matlab® based image processing toolbox wherein a customized algorithm is written and executed to determine the edges of the extruded molten polymeric film to quantify the necking defect. Alongwith the necking defect, particle tracking velocimetry (PTV) technique is also used in conjunction with the Matlab® software to determine the centerline and transverse velocity profiles in the extruded molten film. It is concluded from this study that image processing techniques provide valuable insights into quantifying both the necking defect and the associated velocity profiles in the molten extruded film.