Velocity Equation Research Articles

Chemically Reactive Micropolar Hybrid Nanofluid Flow over a Porous Surface in the Presence of an Inclined Magnetic Field and Radiation with Entropy Generation

The present study investigates the entropy generation of chemically reactive micropolar hybrid nanoparticle motion with mass transfer. Magnetic oxide (Fe3O4) and copper oxide (CuO) nanoparticles were mixed in water to form a hybrid nanofluid. The governing equations for velocity, concentration, and temperature are transformed into ordinary differential equations along with the boundary conditions. In the fluid region, the heat balance is kept conservative with a source/sink that relies on the temperature. In the case of radiation, there is a differential equation along with several characteristic coefficients that transform hypergeometric and Kummer’s differential equations by a new variable. Furthermore, the results of the current problem can be discussed by implementing a graphical representation with different factors, namely the Brinkman number, porosity parameter, magnetic field, micropolar parameter, thermal radiation, Schmidt number, heat source/sink parameter, and mass transpiration. The results of this study are presented through graphical representations that depict various factors influencing the flow profiles and physical characteristics. The results reveal that an increase in the magnetic field leads to a reduction in velocity and entropy production. Furthermore, temperature and entropy generation rise with a stronger radiation parameter, whereas the Nusselt number experiences a decline. This study has several industrial applications in technology and manufacturing processes, including paper production, polymer extrusion, and the development of specialized materials.

Irreversible effects for SWCNT‐MWCNT/water based flow with Coriolis force over rotating frame: A numerical study

AbstractIn this study, two different types of nanofluids are used: One is the simple nanofluid consist of single‐wall carbon nanotubes (SWCNT), and the other is the hybrid nanofluid composed of single and multi‐wall carbon nanotubes (SWCNT‐MWCNT). The famous Xue model is incorporated for the thermal energy analysis. An important property related to the nanoparticles is the Brownian motion and thermal‐migration, which is described by using Buongiorno's model. The appropriate similarity transformations are used to convert the governing nonlinear partial differential equations into the nonlinear coupled ordinary differential equations for the both velocity and temperature profiles. The numerical solution is obtained for the present problem by using bvp4c Matlab routine. This code is based on the finite difference method that implements the three‐stage Lobatto IIIa formula. The comparative analysis for the entropy generation in rotating frame due to heat transfer, viscous heating, and mass diffusion is the main focus in this study. The impact of different parameters such as, rotational motion , thermomigration and Brownian motion , volume fractions of SWCNT & SWCNT‐MWCNT ,, Eckert number , Lewis number , chemical reaction parameter , Brinkman number the temperature ratio parameter and concentration difference parameter on axial and transverse velocity, temperature profile, entropy generation, and Bejan number are obtained. The obtained results for these different variables are presented through graphs and tabular form. When the solid volume fraction is enhanced, the flow and heat distribution are observed to increase. The Nusselt and Sherwood numbers for both nanofluids are investigated. The decay in Nusselt number is observed as the values of the heat source/sink parameter, thermophoresis, Brownian motion, and Eckert number are increased. However, in the case of Sherwood enhancement an increment in the value of the chemical reaction parameter, thermophoresis, Brownian motion, and Lewis number is observed. The entropy generation is enhanced as a result of increment in Brinkman number and temperature ratio. However, in the case of Bejan number, opposite trend was seen in the entropy generation. For the hybrid nanofluid, the enhancement in both heat transmission and irreversibility effect is observed as compared to simple nanofluid.

Surface Effects Study: A Continuum Approach From Fundamental Modes to Higher Modes and Topological Polarization in Orthotropic Piezoelectric Materials

Abstract The primary goal of the current work is to investigate how wave propagation influences the performance of surface acoustics wave (SAW) macro- and nano-sensors. Therefore, shear horizontal (SH) waves use the surface piezoelectricity theory to explore SH waves in an orthotropic piezoelectric quasicrystal (PQC) layer overlying an elastic framework (Model I), a piezoelectric substrate, and an orthotropic PQC substrate (model II). This study employs a variable-separable technique. The theoretical forms are constructed and used to present the wavenumber of surface waves in any direction of the piezoelectric medium, based on the differential equations and matrix formulation. In addition, we take into account the surface elasticity theory in order to obtain the phase velocity equation. Two configurations are examined: an orthotropic piezoelectric material layer over an elastic framework and a piezoelectric material half-space with a nanosubstrate. Analytical expressions for frequency equations are derived for both symmetric and antisymmetric waves. This study investigates the effects of surface elastic constants, surface density, anisotropic piezoelectric constant, and symmetric and antisymmetric modes on phase velocity. This study is confined to only linear wave propagation. Additionally, the analysis is based on idealized material properties, surface properties, and characteristic length of the material.

Investigation of the Arrangement of Aluminum Fins on the Thermal Behavior of Lauric Acid as a Phase Change Material in a Two-pipe Heat Exchanger by CFD Simulation

BackgroundPhase change material (PCM) thermal storage systems store more thermal energy per unit volume than sensible heat storage systems. PCMs offer a potential solution to reduce energy consumption in various thermal engineering applications. This study aimed to examine how fin arrangement affected the thermal efficiency and melting time of PCMs. MethodsA two-dimensional numerical analysis of the melting process of lauric acid in a heat exchanger featuring two pipelines and fins was conducted using CFD simulation. In most previous investigations, the heat transfer fluid was a single-phase liquid. An enthalpy-porosity technique was used to model the solid and liquid phases of PCM. The governing equations were solved using the commercial software ANSYS Fluent 2021, and the pressure and velocity equations were coupled using the SIMPLE algorithm. Significant FindingsThe best model among the 13 tested was Model 5, which featured 6 fins and a consistent angle of 60 degrees. For Model 5, the melting time was 1818.3 seconds. Due to sensible heating, the fin's temperature (Temp) rose gradually from 300 K to 318 K. Temp then gradually increased as the PCM melted in the phase transition zone between 316.5 K and 321.2 K. Once the phase transition was complete, the PCM's Temp steadily rose from 324 K to 340 K. In Model 5, the inner wall Temp and the maximum Temp of the PCM were closest, at 327.34 K and 333.55 K, respectively. The thermal shock between the PCM and the ambient Temp caused a peak heat flux at the beginning of the PCM loading process.

Lower and upper bounds of decay to the d-dimensional magneto-micropolar equations

This paper mainly investigates the large time behavior of the magneto-micropolar equations with zero angular viscosity in Rd (d = 2, 3). The main difficulties lie in the presence of linear curl terms and the lack of micro-rotation velocity dissipation. By utilizing the effect of velocity dissipation and damping term in the equation of micro-rotational velocity, we prove the non-uniform decay and the upper bounds of decay estimates of the global solutions. Furthermore, the lower bounds of decay estimates are shown by making full use of the structure of this system and by introducing a combined quantity. The approach used here can also be applied to derive the lower and upper bounds of decay for the magneto-micropolar equations with full dissipation. We remark that the lower bounds are new even for the fully dissipative system.

Vertically heated natural convection loop model

Abstract We present a comprehensive analytical model for laminar flow in a vertically heated rectangular convection loop, with applications to oil cooling in transformer systems. Starting from an integral equation, we apply a quasi-one-dimensional approach to derive equations for both loop velocities and temperature distributions. In this model, we account for temperature-dependent dynamic viscosity and introduce cooling at the loop top and in the fin. The analytical predictions are rigorously validated against finite volume method (FVM) simulations across different geometries and heat flux conditions, demonstrating strong agreement within a 2% discrepancy range for most parameters. This model provides a viable analytical alternative to computationally intensive simulations, offering insights into natural convection dynamics within closed-loop configurations.

Heat Transfer in Annular Channels with the Inner Rotating Cylinder and the Radial Array of Cylinders

Numerical investigations of heat transfer for forced, mixed, and natural convection conditions within an annular channel are carried out. The main objective was to investigate, for the first time, the effect of the radial cylinder array on heat transfer in the annular channel with the rotating cylinder. The governing equations for velocity and temperature with the Boussinesq approximation were solved using the finite-volume method. The heat transfer quantities were obtained for different Rayleigh numbers (104–106), the radius ratios (1.4–2.6), the radial cylinder spacing, and for different rotating velocities in the form of the Richardson number (10−2–104). The Prandtl number was 0.7. It has been shown that radial cylinders do not influence significantly the intensity and the local distribution of heat transfer on the inner rotating cylinder. The Nusselt number was 1.4–2.0 times higher on the radial cylinder array for all convection modes relative to the outer flat surface. For all annuli gaps with radial cylinders, the maximal values of the Nusselt number were observed with an increase of the radial spacing of cylinders.

Rayleigh wave propagation in an initially stressed orthotropic elastic solid half-space lying under inviscid liquid and viscous liquid layers

PurposeThe purpose of this article is the propagation of Rayleigh waves in a homogeneous, isotropic, initially stressed orthotropic elastic solid half-space lying under a homogeneous, viscous, inviscid liquid layer of finite thickness.Design/methodology/approachIn the presence of both viscous and inviscid liquids, it derives the phase velocity, initial stress, and wave number-dependent frequency equation for an orthotropic elastic solid. With the help of the MATLAB program, the thickness effects of liquid layers, initial stress, and viscosity on the phase velocity and attenuation coefficient of the Rayleigh wave are explained for a particular model.FindingsThe phase velocity-dependent dispersion relation of Rayleigh waves at the interface of viscous liquid and solid half-space is a function of initial stress and wave number. Rayleigh waves along the free surface of an orthotropic elastic half-space are also derived as a particular case. The classical results of an inviscid liquid are achieved when the thickness of a viscous liquid approaches zero. Well-known classical results for initially stressed orthotropic elastic solids were also derived.Originality/valueSo far, many researchers have looked into the propagation of surface waves at the interfaces of solid–inviscid liquid, solid–solid, and multilayer interfaces. But in this article, the dispersion behavior of Rayleigh wave propagation in an initially stressed homogeneous orthotropic elastic solid half-space under a double layer of viscous liquid and inviscid liquid is studied.

The North China record-breaking rainfall in July 2021: The atmospheric influential factors and precursory signal

Abstract In July 2021, the southeastern part of North China (SENC) suffered a record-breaking extreme rainfall event that caused devastating flooding and enormous losses. In this study, the major atmospheric influential factors and the precursory signal of heavy rainfall in 2021 are investigated using the correlation, regression, power spectrum, and filtering methods, the quasi-geostrophic velocity equation, observational data and numerical simulation of a linear baroclinic model (LBM). The results show that the extremity of a quasi-barotropic high anomaly over Northeast Asia (NEA) contributes to the deep anomalous upward motion within SENC by inducing positive vorticity and temperature advections. On the other hand, the anomalous southeasterly flow at the southwestern flank of the NEA high anomaly transports sufficient moisture to SENC in the lower troposphere. The local deep upward motion combined with the lower-tropospheric moisture convergence directly leads to the occurrence of this extreme rainfall event. Further analysis shows that the intensification of the NEA high in July 2021 is closely tied to the westward migration of atmospheric disturbance originating from the vicinity of Northeast Pacific-North America, which could be supported by numerical simulation in LBM. The variation of the geopotential height anomaly over Northeast Pacific-North America precedes that of the NEA high by two weeks, which is likely to provide a potential source of predictability for the extreme rainfall in SENC.

Thermal and Flow Dynamics of Magnetohydrodynamic Burgers' Fluid Induced by a Stretching Cylinder with Internal Heat Generation and Absorption

This study investigates the flow dynamics of magnetohydrodynamic Burgers' fluid induced by a stretching cylinder, emphasizing the effects of internal heat generation and absorption. A temperature-dependent heat source is integrated to examine the characteristics of thermal energy transfer within the system. By applying boundary layer theory, we transform the governing partial differential equations into a standard system of ordinary differential equations through similarity transformations. The BVP4C method is utilized to accurately solve the resulting equations for velocity and temperature profiles. Graphical representations illustrate the influence of various physical parameters on both thermal and flow profiles, supported by comprehensive analytical interpretations. To validate our findings, a comparison with existing literature is performed, confirming the consistency and significance of our results. This research offers valuable insights into the thermal and fluid behaviors of Burgers' fluids, with promising applications in the development of advanced biomedical devices.

Thermal analysis for convective transport of nanoparticles with effective phenomenon of damped shear-thermal flux: A fractional model

The researchers are interested to enhance the temperature characteristics of convection heat transportation investigation. The studies based on nanofluids are accomplished because these phenomena exhibit an abnormal elevation in thermal transportation. This analysis captures historical impacts on heat and momentum transfer that traditional models ignore by using the Caputo fractional derivative in to model damped shear-thermal flux in nanofluid convection. In this manuscript, the natural convection flow, as well as heat transference of nanofluids, is studied. The classical expressions are fractionalized with the help of constitutive shearing stress expression along with Fourier relation. The Caputo kernel (power-law and non-local) engenders the damping on gradients of momentum and temperature; consequently, transportation approaches are affected by the histories entirely of the previous and current time. The fractional differential equations of velocity as well as temperature are solved analytically by invoking Laplace and the finite Sine-Fourier transform method. In a particular case, the solution to the classical model is also found. Moreover, these solutions are described in respect of the Lorenzo-Hartley G-function together with the Mittag-Leffler function. This investigation exposes that rising nanoparticle volume fraction improves the heat transfer rate, however the skin friction coefficient is affected by time and fractional parameters. The influences of diverse parameters are debated graphically. This study has numerous operations in thermal engineering.

Numerical estimation of wave breaking forces on seawalls

ABSTRACT This paper presents a computationally efficient numerical scheme to estimate wave forces from plunging breakers on vertical rigid seawalls. The approximated velocity equation, an asymptotical solution of the Green-Naghdi equation in the Camassa-Holm scaling, is utilized to obtain the evolution of the free surface and the depth-averaged horizontal velocity over time, leading to the formation of a plunging breaker. The uniform dynamic pressure along the depth is obtained by utilizing the unsteady Bernoulli equation. The wave forces on seawalls are then determined using Froude-Krylov theory, with adjustments for diffraction effects. The results, while being comparable to some existing formulations, notably differ with some others. This highlights the limitations imposed by the inherent assumptions in the existing empirical formulations and underlines the importance of the proposed methodology that is founded on an accurate modelling of the wave breaking process to estimate wave breaking forces on seawalls.

Comparative analysis of buoyancy-driven hydromagnetic flow and heat transfer in a partially heated square enclosure using Cu-Fe3O4 and MoS2-Fe3O4 nanofluids

Purpose This study aims to investigate entropy generation through natural convection and examine heat transfer properties within a partially heated and cooled enclosure influenced by an angled magnetic field. The enclosure, subjected to consistent heat production or absorption, contains a porous medium saturated with a hybrid nanofluid blend of Cu-Fe3O4 and MoS2-Fe3O4. Design/methodology/approach The temperature and velocity equations are converted to a dimensionless form using suitable non-dimensional quantities, adhering to the imposed constraints. To solve these transformed dimensionless equations, the finite-difference method, based on the MAC (Marker and Cell) technique, is used. Comprehensive numerical simulations address various control parameters, including nanoparticle volume fraction, Rayleigh number, heat source or sink, Darcy number, Hartmann number and slit position. The results are illustrated through streamlines, isotherms, average Nusselt numbers and entropy generation plots, offering a clear visualization of the impact of these parameters across different scenarios. Findings Results obtained show that the Cu-Fe3O4 hybrid nanofluid exhibits higher entropy generation than the MoS2-Fe3O4 hybrid nanofluid when comparing them at a Rayleigh number of 106 and a Darcy number of 10–1. The MoS2 hybrid nanofluid demonstrates a low permeability, as evidenced by an average Darcy number of 10–3, in comparison to the Cu hybrid nanofluid. The isothermal contours for a Rayleigh number of 104are positioned parallel to the vertical walls. Additionally, the quantity of each isotherm contour adjacent to the hot wall is being monitored. The Cu and MoS2 nanoparticles exhibit the highest average entropy generation at a Rayleigh number of 105 and a Darcy number of 10–1, respectively. When a uniform heat sink is present, the temperature gradient in the central part of the cavity decreases. In contrast, the absence of a heat source or sink leads to a more intense temperature distribution within the cavity. This differs significantly from the scenario where a uniform heat sink regulates the temperature. Originality/value The originality of this study is to examine the generation of entropy in natural convection within a partially heated and cooled enclosure that contains hybrid nanofluids. Partially heated corners are essential for optimizing heat transfer in a wide range of industrial applications. This enhancement is achieved by increasing the surface area, which improves convective heat transfer. These diverse applications encompass fields such as chemical engineering, mechanical engineering, surface research, energy production and heat recovery processes. Researchers have been working on improving the precision of heated and cold corners using various methods, such as numerical, experimental and analytical approaches. These efforts aim to enhance the broad utility of these corners further.

Coulomb drag induced non-local resistance in double graphene layers.

We study the effect of Coulomb drag between graphene layers in presence of viscosity term. To do this, we use the simple model of Stokes equations for drift velocities in active and passive layers, known as Pogrebinskii's approach. The solution to these equations allows us to find the potential distribution, and thus the non-local drag resistance of passive layer. It is shown that in viscous regime the non-local resistance may take negative values, in contrast, the ohmic regime results in positive non-local resistance for all drag strengths. Additionally, we discuss the influence of magnetic field on the non-local drag magnetoresistance.

Flow field characteristic in a novel cyclone-granular bed coupled separator

The three-dimensional flow field in a novel cyclone-granular bed coupled separator was discussed experimentally with a five-hole probe system. The airflow behaviors in the annular space, separation space, and central outlet were addressed. Several significant phenomena (the squeezing effect, the top flow loop, and the rectification effect) were observed and analyzed. By comparing the three-dimensional velocity distribution in the coupled separator with different structure parameters (the coupling space index, rc=0.37/0.44), the combined effect between the two efficient gas purifiers was demonstrated and the importance of the tangential velocity was clarified. For this purpose, the equations for the tangential velocity at four circumferential positions were fitted using regression analysis with a wide array of experimental data and effectively characterized prior experimental outcomes.

Application of a New Mean Velocity Equation of Flow in a Natural Stream of 8.5m3/s, Its Verification and Extrapolation: Copper Creck River, Virginia (USA)

Application of a New Mean Velocity Equation of Flow in a Natural Stream of 8.5m3/s, Its Verification and Extrapolation: Copper Creck River, Virginia (USA)

Heat transfer on MHD oscillatory flow in a vertical double-passage channel

Thermal propagation of MHD oscillatory flow of optically thin fluid in a vertical double-passage with varying temperature was investigated. The thermal distribution of the fluid flow is enhanced through a perfectly thin conductive baffle, which divides the channel into two passages. The equations governing the fluid flow are formulated based on purely oscillatory flow with pressure gradient. The flow velocity and thermal equations governing the flow are analytically solved. The closed-form results gotten were analysed for the influences of Reynolds number, magnetic term, thermal convection term, Peclet number and frequency of oscillation on the flow and heat transfer characteristics with the aid of graphs. It was observed that magnetic parameter reduces the flow rate in the channel.

Magnetohydrodynamic Motions of Oldroyd-B Fluids in Infinite Circular Cylinder That Applies Longitudinal Shear Stresses to the Fluid or Rotates Around Its Axis

Two classes of magnetohydrodynamic (MHD) motions of the incompressible Oldroyd-B fluids through an infinite cylinder are analytically investigated. General expressions are firstly established for shear stress and velocity fields corresponding to the motion induced by longitudinal shear stress on the boundary. For validation, the expression of the shear stress is determined by two different methods. Using an important remark regarding the governing equations for shear stress and fluid velocity corresponding to the two different motions, this expression is then used to provide the dimensionless velocity field of the MHD motion of the same fluids generated by a cylinder that rotates around its symmetry axis. Obtained results can generate exact solutions for any motion of this kind of Oldroyd-B fluids. Consequently, both types of motions are completely solved. For illustration, some case studies are considered, and adequate velocity fields are provided. The steady-state components of these velocities are presented in different forms whose equivalence is graphically proved. The influence of the magnetic field on the fluid behavior is graphically investigated. It was found that the fluid flows slower, and a steady state is earlier reached in the presence of a magnetic field. The fluid behavior when shear stress is given on the boundary is also investigated.

Reference equations for pulse wave velocity, augmentation index, amplitude of forward and backward wave in a European general adult population

Pulsatile hemodynamics have been shown to be independent predictors of cardiovascular events. The aim of the current study was to describe four pulsatile hemodynamic markers in a large, well-established, population-based cohort and to provide reference equations for sex- and age-based standardization of these measurements. 6828 adult participants from the Austrian LEAD (Lung, hEart, sociAl, boDy) cohort study, who were free from overt cardiovascular disease, non-diabetic based on blood test results, and had no history of pharmacological treatment for hypertension, dyslipidemia, and diabetes, comprised the “reference population”. Carotid-femoral pulse wave velocity (cfPWV), augmentation index (AIx), amplitude of forward wave (Pf), and backward wave (Pb) were described in different age categories for both sexes. Sex-specific reference equations for cfPWV, AIx, Pf, and Pb with age as the predictive variable were created using the Lambda-Mu-Sigma (LMS) method. All four parameters increased with age. CfPWV and Pf were higher in males than females, especially in young and middle-age groups (P < 0.001). AIx was higher in females than males in all age categories (P < 0.001). Pb was also higher in females than males in age groups older than 40 years (P < 0.01). Reference equations for the skewness (Lambda), median (Mu), and coefficient of variation (Sigma) values were determined, enabling the calculation of sex- and age-standardized values (z-scores) for each individual’s pulsatile hemodynamic measurement, and an online application was developed. Reference equations derived from a large population-based dataset constitute a suitable tool for the standardization of pulsatile hemodynamics and for the accurate interpretation of vascular aging.

Investigating thermal conduction dynamics in ternary Carreau–Yasuda nanofluids under convective boundary conditions and exponential heat source/sink effects

The analysis of the Carreau–Yasuda nanofluid (CYNF) across a stretching surface has practical applications in several fields, such as heat exchange, engineering, and material science. Scholars may discover novel perspectives for increasing heat transfer performance, establishing advanced materials, and enhancing the efficiency of multiple engineering systems by studying the behavior of CYNF in this particular instance. The energy transfer through trihybrid CYNF flow with the effect of magnetic dipole across a stretching sheet is examined in the present study. The ternary hybrid nanofluid (THNF) has been prepared by the addition of ternary nanoparticles (NPs) in the water (50%) and ethylene glycol (50%). Titanium dioxide (TiO2), silicon dioxide (SiO2), and aluminum oxide (Al2O3) are used in base fluid. The fluid velocity and heat transfer are examined under the impact of Darcy–Forchheimer, chemical reaction, convective condition, activation energy, and exponential heat source. The fluid flow has been stated in form of velocity, energy, and concentration equations. The set of modeled equations is simplified to non-dimensional form of ordinary differential equations (ODEs) by using similarity substitutions. Numerically, the system of lowest order ODEs is calculated through the parametric continuation method. It has been noticed that the temperature field augments against the variation of viscous dissipation and heat source term. Furthermore, the magnetic dipole has significant impact to enhance the thermal curve of THNF whereas falloffs the velocity profile. It can be noticed that the energy propagation rate enhances with the rising numbers of ternary NPs, from 1.22% to 5.98% (nanofluid), 2.30% to 9.61% (hybrid nanofluid), and 3.23% to 11.12% (trihybrid nanofluid).