Non-dimensional Factor Research Articles

Analytical solution for temperature equation of a fin problem with variable temperature-dependent thermal properties: Application of LSM and DTM-Pade approximant

Temperature variation through a longitudinal fin with linear and nonlinear temperature-dependent thermal conductivities and heat transfer coefficient, subject to radiative heat flux and convective heat transport is explained in the present examination. For the radiative heat flux, the Rosseland approximation is incorporated and convection mode of energy transmission is accounted on the fin's surface. The associated physical problem is developed in such a manner that the steady-state heat transmission problem is governed with the help of dimensionless variables signified by a second order differential equation (ODE). To solve this equation, an analytical approach, DTM-Pade, and the LSM are implemented. Moreover, the consequence of a few non-dimensional factors on the temperature field are depicted graphically. The investigation's main findings illustrate that a significant decline in the thermal field is caused by an increment in the convection and the radiation mechanism. The internal development of heat affects the thermal distribution in the fin.

Melting effect on Cattaneo–Christov and thermal radiation features for aligned MHD nanofluid flow comprising microorganisms to leading edge: FEM approach

An investigation for fluctuating temperature with Cattaneo–Christov features and self-motive bioconvective microbes immersed in the water based nanofluid has been observing with excision/accretion of the leading edge. A set of partial differential equations is transferring by implementing the similarity measures to an ordinary differential pattern. A finite element technique is employed to establish the numerical results of the set of non-linear system of equations via Matlab programming. The numerical solution's reliability and validity are determined by ascertaining convergence specifications and comparing them to established novel solutions. The formulation of boundary layer configurations for microbes propagation, fluid temperature, the volume fraction of nano-inclusions, and the fluid velocity with varying persuasive parameters have discussed. The main findings of the prevailing assessment are that an increasing trend in the ablation/slash accretion in leading-edge declines in the non-dimensional melting factor of fluid velocity and temperature, while a decreasing trend has seen with the enhancing impact of ablation/slash accretion at the leading edge that represents the flow velocity deceleration. Furthermore, a significant result is that an increase in the non-dimensional melting factor enhances the density of the liquid.

Three-dimensional nanofluid stirring with non-uniform heat source/sink through an elongated sheet

This paper numerically explores the effects of nonlinear density temperature, non-uniform heat source/sink on 3D Maxwell nanofluid flow over a stretching sheet. The combined leading velocity, thermal and species boundary layer balances transformed the problem to a class of coupled non-linear ODEs by similarity conversions subject to suitable preconditions. The dimensionless fine modelled BVP is worked out by adopting Runge-Kutta fourth-order method integrated with the shooting technique. A comprehensive study on the influence of significant thermo-physical non-dimensional factors controlling dispersals of flow characteristics is conducted. The computed results of friction factor, Nusselt and Sherwood number values for selected parameters are presented. Verification of numeric solutions is accomplished with specific circumstances published in earlier reported outcomes, an effective association is witnessed. Present analysis is of great significant interests in the cooling of metallic plates, polishing of artificial heart valves, enhancing oil recovery and separation processes in chemical industries and in petroleum extraction.

A Numerical Simulation of Soret-Dufour effect on Unsteady MHD Casson Fluid Flow past a vertical plate with Hall current and viscous dissipation

The Casson fluid model, which is very significant in the biomechanics and polymer processing industries, is another term used to describe non-Newtonian fluid behavior. This study of Casson fluid model on unsteady MHD Casson fluid flow with Soret-Dufour effect past a vertical plate embedded in porous medium in the presence of radiation with heat generation/absorption and viscous dissipation is presented in this research article as a numerical investigation of non Newtonian Casson fluid with applied effects. Regulating partial differential equations have been used to explain the mathematical model of the flow field. The Crank-Nicolson implicit finite difference approach has been used to numerically solve non-dimensionalized flow field governing equations. Concentration, temperature, and velocity profile effects of non-dimensional factors have been investigated using tables and graphs as aids. Tables have also been used to observe fluctuations in factors like skin friction, the Nusselt number, and the Sherwood number in relation to other parameters.

Thermophoretic particle deposition and heat generation analysis of Newtonian nanofluid flow through magnetized Riga plate

AbstractThe Riga surface is composed of an electromagnetic actuator that comprises a span‐wise associated array of discontinuous electrodes and an everlasting magnet mounted over a planer surface. The electro‐magneto‐hydrodynamic has an attractive role in thermal reactors, fluidics network flow, liquid chromatography, and micro coolers. Inspired by these applications, a laminar, two‐dimensional nanofluid flow with uniform heat sink‐source, thermophoretic depositions of the particles, and the Newtonian heating effect are investigated. The equations that describe the fluid motion are reduced into a system of ordinary differential equations with the help of spatial similarity variables. Numeric solutions of ordinary differential equations are executed through the Runge–Kutta–Felhberg 45 order technique via a shooting scheme. The role of various nondimensional factors on physically interesting quantities is elaborated graphically. The velocity profile rises for modified Hartmann number and decreases for porosity parameter. Thermal enhancement is high in the common wall temperature condition comparative to the case of the Newtonian heating conditions. The concentration profile is enhanced with Schmidt number, but the reverse trend is observed for the thermophoretic parameter. The rate of mass transfer is increased with Schmidt number.

Activities of 223Ra and 226Ra in Fluids From the Lost City Hydrothermal Field Require Short Fluid Residence Times

AbstractThe residence time of fluids circulating through deep‐sea hydrothermal systems influences the extent of water‐rock reactions and the flux of major and minor elements to the ocean. While the fluid residence times in numerous basaltic and gabbroic systems have been determined, those of the less studied ultramafic systems are currently unknown. Fluids that interact with mantle rocks have fundamentally different chemistries and therefore have unique influences on seawater chemistry. In this first investigation of radium isotopes in a serpentinite‐hosted system, vent fluids were discovered to contain 10–100 times greater activities of 223Ra (half‐life = 11.4 days) than observed in high‐temperature basalt‐hosted systems. The 223Ra activities of 10–109 dpm L−1 produce 223Ra/226Ra activity ratios ranging from 9 to 109. These extremely high 223Ra activities, which are accompanied by low activities of 226Ra, place significant constraints on fluid residence times and the adsorption coefficient of radium between fluid and rock. Our data constrain the nondimensional retardation factor (R) to very low values between 1 and 4, reflecting the extent to which Ra is transported more slowly than fluids due to adsorption and other processes. These results suggest that the residence time of fluids in contact with serpentinite is less than 2 y and perhaps as low as 0.5 y. They are surprisingly similar to those of basalt‐hosted systems. Thus, fluids in hydrothermal systems share similar hydrogeological characteristics despite differences in rock types, underlying porosity, and heat sources, enabling larger‐scale models of hydrothermal biogeochemistry to be developed across systems.

Effects of scour-hole depth on the bearing and uplift capacities of under-reamed pile in clay

Scouring causes reduction in the load-carrying capacity of pile foundation. The load-carrying capacity of a pile foundation can be increased by increasing the pile dimension. In the present study, under-reamed piles are considered under scour condition. In this study, bearing and uplift capacities of under-reamed pile in clay under scour condition are obtained numerically using lower bound finite element limit analysis. The effects of scour-hole shape, bulb shape, and embedment ratio are studied. The non-dimensional bearing capacity factor (Ncus) and uplift capacity factor (Fcus) are presented through design charts. Ncus and Fcus of under-reamed pile are found to be significantly higher than those of pile without bulb under scour condition. Ncus and Fcus are found to decrease significantly with scour depth. Ncus and Fcus are found to increase with the increase in under-ream angle (β). From the axial force distributions, it is found that bulb carries a significant portion of the ultimate load in axial compression and tension. With the consideration of stress history, bearing and uplift capacities of under-reamed pile are found to reduce significantly. Also, the extent of plastic shear failure in the soil is found to increase with decrease in scour depth and increase in embedment ratio.

Numerical analysis on dynamics and thermodynamics of a supercooled water droplet considering the dynamic contact angle

The dynamics and thermodynamics of a supercooled water droplet impacting on a horizontal cold surface are investigated numerically. A two-dimensional axisymmetric model that considers both the non-equilibrium solidification caused by the supercooling and the dynamic contact angle (DCA) caused by the hysteresis phenomenon is developed to simulate the impacting, spreading, retraction, and freezing processes by combining the coupled volume-of-fluid and level set air–liquid interface capturing method and the Enthalpy-Porosity phase transition method. The common Kistler DCA model is applied to iteratively calculate the real time contact angle of three-phase contact point using the contact line velocity. The DCA model makes the simulation results of the spreading factor more accurate compared with the experimental data than the static contact angle model does. The non-dimensional maximum spreading factors of the room temperature and supercooled water droplet are almost the same in the low Weber number region, but quite different in the high one. The stable spreading factor is independent of the Weber number but increases with the decrease in the contact angle and the increase in the supercooling degree. This study can deepen the understanding of the impacting-freezing mechanism of a supercooled water droplet.

Meander Response of the Kuroshio in the East China Sea to Impinging Eddies

AbstractBoth observations and an idealized model demonstrate that the path of a western boundary current, like the Kuroshio, can be perturbed by the impingement of an ocean eddy. When a strong cyclonic (anti‐cyclonic) eddy approaches the axis of the Kuroshio in the East China Sea, the current path can be repelled (attracted) by the eddy. The subsequent disruption occurs primarily near the interaction region and propagates downstream, forming a dissipating wavelike fluctuation. The spatial‐temporal evolution of Kuroshio axis shift by impinging eddy can be explained by idealized vorticity dynamics on the current‐eddy interaction process, and the magnitude of current path shift is shown to be determined by two nondimensional factors: the ratio of eddy strength to the Kuroshio strength; and the ratio of horizontal shearing strength in the background to that in the current.

A new system of singular integral equations for a curvilinear crack in bonded materials

The modified complex potentials (MCPs) functions are used to develop a new system of singular integral equations (SIEs) for a curvilinear crack in the upper part of bonded materials subjected to shear mode stress with the help of continuity conditions for resultant force and displacement functions. The unknown dislocation distribution function is mapped into a square root singularity function by using curved length coordinate method and the traction along the crack as the right hand term. The Gaussian quadrature rules were used to obtain the numerical solution for a new system of SIEs in order to compute the nondimensional stress intensity factors (SIFs) for these problems. Our results agree with those of the previous works. The findings have revealed that the nondimensional SIFs depend on the elastic constant ratio, crack geometries and the position of the cracks.

Characterizing shear-thinning fluids transitioning from rheology- to inertia-dominated flow regimes in porous media

Understanding and predicting non-Newtonian fluid flows in porous media is crucial for many geophysical and environmental problems. Although extensive studies have investigated nonlinear flow for shear thinning fluids, the critical Reynolds number (Rec) for identifying nonlinearity in transition from rheology-dominated to inertia-dominated flows remains unclear. To determine Rec, we conducted hundreds of direct numerical simulations of power law fluids with diverse fluid rheology (quantified by a power law exponent n) through a variety of pore geometries which are characterized by a non-dimensional hydraulic shape factor (β). The numerically-derived pressure gradient and fluid flux were used to compute the bulk viscosity ~ Reynolds number curves, which were further employed to determine Rec. With knowing Rec, we established a predictive function between Rec and (β, n). This function allows for the estimation of Rec based on the measurable properties (β, n) via imaging technique. Our mechanistic modelling work sheds light on predicting nonlinear flow for non-Newtonian fluids at the continuum scale by knowing under what conditions the inertial effects are significant.

Correlation between CBR value and effective strength parameters for engineered fills

It is a tradition in Tanzania to use the California bearing ratio (CBR) value for the design of embankments. To assess the stability of embankments, slope stability calculations are performed, for which the effective strength parameters are needed. CBR values can be determined from the effective strength parameters based on Meyerhof’s general bearing capacity equations. Contrary to that, from a given CBR value, the effective friction angle is not easily calculated directly, as the relationship between the non-dimensional bearing capacity factors and the friction angle is complex. Moreover, only the resulting CBR value is known, not the strength contribution of the effective cohesion. Present study presents results from disturbed samples obtained from test pits and boreholes which were tested in order to determine the particle size distribution curves and Atterberg limits. On representative samples from different soil groups (AASHTO classes), CBR tests were performed to assess the quality of the fill material. Moreover, a set of isotropically consolidated, drained (CID) triaxial tests were carefully planned on the granular materials (AASHTO classes: A-2-4, A-2-6 and A-2-7) in order to investigate the relationship between CBR value and effective strength parameters of the materials when used as fill (normally consolidated conditions) at different stress levels. Based on 18 CID triaxial tests, a correlation was established which can be used directly to calculate effective strength parameters from CBR values.

Bearing and uplift capacities of under-reamed piles in soft clay underlaid by stiff clay using lower-bound finite element limit analysis

Ensuring a safe foundation design in soft clay is always a challenging task to engineers. In the present study, the effectiveness of under-reamed piles in soft clay underlaid by stiff clay is numerically studied using the lower-bound finite element limit analysis (LB FELA). The bearing and uplift capacities of under-reamed piles are estimated through non-dimensional factors Ncul and Fcul, respectively. These factors increased remarkably and marginally compared to Ncul and Fcul of the piles without bulbs when the bulb is placed in stiff and soft clay, respectively. For a given ratio of undrained cohesion of stiff to soft clay (c2/c1), the factors Ncul and Fcul moderately increased with the increase in the length-to-shaft-diameter ratio (Lu/D) and adhesion factors in soft clay (αs1) and stiff clay (αs2). The variation of radial stress along the pile-soil interface, distribution of axial force in the under-reamed piles, and state of plastic shear failure in the soil are also studied under axial compression and tension. The results of this study are expected to be useful for the estimation of the bearing and uplift capacities of under-reamed piles in uniform clay and soft clay underlaid by stiff clay.

Predicting the effect of the rib pitch on thermal performance factor of small channels plate heat exchangers fitted with Y and C shapes obstacles

This study presents a numerical analysis of a laminar counter flow inside small channels plate heat exchanger fitted with Y and C shape obstacles. Using the Computational Fluid Dynamics CFD, an advanced and modern simulation technique, the influence of the geometrical parameters (such as geometry, rib pitch) on the flow characteristics, the thermal and the hydrodynamics performance of the PHE (plate heat exchanger) is investigated numerically. The main goal of this work is to increase the flow turbulence, enhance the heat transfer and the thermal efficiency by inserting new obstacles forms. The computational domain is a conjugate model which is developed by the Computer Aided Design CAD software Solidworks. The results, obtained with Ansys Fluent, show that the presence of the shaped ribs provides enhancement in heat transfer and fluid turbulence. The CFD analysis is validated with the previous study. The non-dimensional factors such as the Nusselt number Nu, the skin friction factor Cf and the thermo-hydraulic performance parameter THPP are predicted with a Reynolds number Re range of 200–800. The temperature and the velocity distribution are presented and analyzed. The Y ribs and the C ribs offer as maximum THPP values respectively about 1.44 and 2.6 times of a smooth duct.

A Modelling and Validation Approach for Predicting Particle Concentrations of Airborne Dust during the Filling Process of Cylindrical Silos

Traditionally, when undertaking feasibility studies for designing new storage facilities such as storage silos, engineers will extract design information from experiments and evaluate potential risks associated with health and safety, suitability design for reliable material flow, and quality of products. The simulation approach applied incorporates Computational Fluid Dynamics (CFD), and Discrete Element Modelling (DEM) approaches and experimental tests will be used for validating these simulation results. One important aspect related to handling fine and dusty materials (particles smaller than 100 microns) is the associated risk of dust explosions, which needs to be evaluated before the commissioning of storage silos; to evaluate the accumulation of fines during the silo filling process, simulations and experiments were conducted. Alumina and salt were used here as reference materials for calibration and the validation purposes. The validation efforts are significant due to the fact that the data that is accessible in simulations is vastly different to the accessible data in experiments, which is restricted by measurement techniques and equipment. Such restrictions are observed in the evaluation of particle concentrations in a large confined volume. A new methodology has been developed to evaluate concentrations in both simulations and experiments by employing a non-dimensional factor [k], here called “Concentration Rank Factor” (CRF). A significant finding of this research is that experiments and simulations can be compared using CRF. It has been found to be within 2% of the experiment averaged value of 0.64.

Lateral free-field responses and kinematic interaction of monopiles to obliquely incident seismic waves in offshore engineering

This paper studies the lateral free-field response and dynamic interaction of monopiles with a partially/fully saturated porous seabed under a seawater layer, subjected to vertically and obliquely incident P and SV wave excitations. The solution of the coupled three-dimensional water-pile-soil vibration problem is developed using a rigorous semi-analytical method. Results for the free-field soil displacement and kinematic interaction factors of the pile head are obtained: the presence of water layer will increase or decrease the lateral free-field displacement for the P wave case, depending on whether the soil is fully saturated or partially saturated; the presence of water layer will have little influence, increase or decrease the lateral free-field displacement for the SV wave case, depending on the incident angle. Besides, the non-dimensional lateral kinematic interaction factors for both P wave and SV wave cases, with different water depths, are illustrated over a broad non-dimensional frequency range. Similar to the free-field responses, monopile responses can generally be amplified or reduced with the presence of a water layer, depending on the saturation degrees of soil and incident angles in P wave case and SV wave case, respectively.

Impacts of heterogenous-homogeneous reactions in the flow of Prandtl nanofluids with convective heating process

This research article discusses the 3-D flow of magnetized Prandtl nanoliquid by convectively heated surface utilizing homogeneous-heterogeneous reactions. An extendable surface produces the flow. Thermophoresis and random development are investigated. Thermal transport for the convective method is accounted. The Prandtl material is an electrical conducting via applying a magnetic field. Appropriate non-dimensional factors correspond to the non-linear differential equations. Acquired non-linear differential frameworks are comprehended via the optimal homotopic procedure. Physical amounts like surface drag force and rate of the heat transfer are investigated through sketches. It is seen that the impacts of Biot and Hartman numbers on the concentration and the temperature are very comparative. Both the concentration and the temperature are improved for growing estimations of Biot and Hartman numbers.

Normally loaded inclined strip anchors in cohesionless soil

Plate anchors are among the most effective anchorage systems that are widely used to resist horizontal and inclined uplift loads in many offshore and onshore applications. Previous research on plate anchors has largely focused on the horizontal or vertical breakout problems, with limited attention directed towards obtaining a full characterization of the effects of anchor orientation angle. The present study utilizes displacement-based finite element analyses to investigate the stability and performance of strip anchor embedded in cohesionless soil for plate inclination angles ranging from 0° to 90° from horizontal, where the applied load is normal to and acts at the center of the plate. This study investigates the effects of scale and roughness, along with the geometry of the failure mechanism for various plate orientations and embedment depths. The analyses, presented in terms of a non-dimensional breakout factor Nq, show that the breakout factor increases significantly with an increase in the inclination, especially for angles greater than 45° in loose sand and greater than 60° in dense sand. The analyses also show that scale effects (anchor width) can affect capacity. Finite element analyses have been used to introduce simple design charts relating the breakout factor to the embedment depth and relative density. Comparisons to experimental and numerical studies showed good agreement.

A Derivation of Stiffness and Damping Coefficients for Short Hydrodynamic Journal Bearings with Pseudo-Plastic Lubricants

ABSTRACTA new derivation considering the non-linear terms has been proposed to calculate stiffness and damping coefficients for short hydrodynamic journal bearings lubricated with pseudo-plastic fluids. The proposed method has relaxed the constraint of small perturbation method applicable to only small values of non-Newtonian factor α. An analytical solution is also given. The non-linear Reynolds equation is solved with a more reasonable boundary condition ∂p*/∂z* = 0 at the location of z*=0 while the analytical pressure distribution is obtained by seven-point Gauss-Legendre integral formula. When the non-dimensional non-Newtonian factor α is small, the stiffness and damping coefficients of computed by the proposed method can agree well with those from small perturbation method, which could verify the proposed derivation. As for large non-dimensional non-Newtonian factor α, the stiffness coefficients $K_{XX}^*$ , $K_{XY}^*$ and $K_{YX}^*$ as well as the damping coefficients $C_{XX}^*$ , $C_{XY}^*$ and $C_{YX}^*$ decrease with the increasing of non-dimensional non-Newtonian factor α. The significance of the derivation is that it can relax the constraint of small α and simplify the computation process.

Numerical solution for the thermally insulated cracks in bonded dissimilar materials using hypersingular integral equations

The new system of hypersingular integral equations (HSIEs) for the thermally insulated inclined cracks and thermally insulated circular arc cracks subjected to remote shear stress in bonded dissimilar materials was formulated by using the modified complex potentials (MCPs) function method with the continuity conditions of the resultant force, displacement and heat conduction functions. This new system of HSIEs is derived from the elasticity problem and heat conduction problem by using crack opening displacement (COD) function and temperature jump along the crack faces. The appropriate quadrature formulas were used to solve numerically the new system of HSIEs for the unknown COD function and the known traction along the crack as the right hand term. Numerical solutions for the value of nondimensional stress intensity factors (SIFs) at all the cracks tips are illustrated. The comparison of nondimensional SIFs for the cracks with and without thermal is also illustrated.