Momentum Diffusion Research Articles

Irreversibility evaluation for transport processes revisited

The entropy generation has been widely used for evaluating irreversibility of transport processes and optimize their performance. However, there still exist challenges against this methodology. This work revisits the irreversibility evaluation in typical transport processes. The irreversibility indicator of transport processes is proposed combining aspects of physical essence and practical application. It is expected to be able to recover the constitutive relation, characterize the evolution direction of process, and optimize standalone transport processes. The entropy generation rate is examined against these conditions, and results show that it fails to meet them. These failures challenge the legitimacy of entropy generation rate in characterizing transport processes’ irreversibility. In contrast, the irreversibility of heat, mass, and momentum diffusion processes can be measured by the entransy dissipation, mass entransy dissipation, and momentum entransy dissipation, respectively. A one-dimensional “volume-to-point” heat conduction and a mass diffusion optimization problem are numerically studied, respectively. Results show that the entransy dissipation-based optimization reduces the average temperature by 3–5 K, giving a better performance than entropy generation optimization, which increases the average temperature up to 17.55 K. In the mass diffusion problem, the mass entransy dissipation-based optimization reduces the average concentration by 3.67%, showing a much better performance than the entropy generation optimization, which yields a 26% increase. Finally, these irreversibility indicators are found to be equivalent to their corresponding energy dissipations.

Inspections of unsteady micropolar nanofluid model over exponentially stretching curved surface with chemical reaction

The present study considers heat transfer analysis of micropolar nanofluid flow over an exponentially stretching curved surface. The effects of Brownian motion and thermophoresis on the micropolar fluid at exponentially stretching curved surfaces are considered. The chemical reaction and slip effects are analyzed at exponentially stretching curved surface. Using boundary layer approximations, the mathematical model under the flow assumptions is developed in partial differential equations. The partial differential equations are transformed into ordinary differential equations using the dimensionless similarity variables. The dimensionless system is solved through numerical technique. The involving physical parameter effects are presented through graphs and tables. The is enhanced due to rising the values of the curvature parameter. If the curvature is increasing, the bending of the sheet is more which enhances the motion of the fluid particles due to the action of centrifugal force. The Schmidt number enhances which reduces the concentration profile because is directly proportional to the momentum diffusivity and inversely proportional to the mass diffusivity, and consequently, greater the values of conformed to the small mass diffusivity which declines the concentration function.

Numerical study of simultaneous transport of heat and mass transfer in Maxwell hybrid nanofluid in the presence of Soret and Dufour effects

The article aims to investigate the influence of copper (Cu) and a combination of copper (Cu) and aluminum oxide (Al2O3) on the simultaneous transfer of heat and mass in sodium alginate liquid moving over a circular pipe. This transport activity is modeled by the use of conservation laws with correlations for physical quantities of Cu, Al2 O3, and sodium alginate. Through cylindrical coordinates formulation, the set of partial differential equations is obtained. These models are solved numerically by the finite element method (FEM). The relaxation time associated with momentum diffusion in Maxwell fluid plays role in controlling the viscous region. Moreover, momentum relaxation time in Cu/sodium alginate is strong than that in Cu–Al2O3/sodium alginate. It is noticed from simulations that particles of Cu/ sodium alginate have a greater velocity than the velocity of Cu–Al2O3/sodium alginate. Therefore, distortion of magnetic lines by the flow of Cu/sodium alginate is more than the distortion of magnetic lines by the flow of Cu–Al2O3/sodium alginate. The rise in the thermal conductivity of sodium alginate due to simultaneous dispersion of Cu and Al2O3 is more than the rise in thermal conductivity of sodium alginate. Thus for maximum HT, the simultaneous dispersion of Cu and Al2O3 in sodium alginate is recommended.

Controversial turbulent Schmidt number value in particle-laden boundary layer flows

When solid particles, such as sediments, are transported by a turbulent boundary layer flow, the wall-normal turbulent diffusion of particle concentration has been observed to be much higher than the turbulent diffusion of momentum (the eddy viscosity). This is characterized by a turbulent Schmidt number lower than unity. By using the few available existing direct measurements of Reynolds-averaged wall-normal particle flux and our two-phase flow large eddy simulations we demonstrate that the actual turbulent Schmidt number is indeed higher than unity. The misinterpretation may be explained by settling retardation of particles in turbulent flows compared with quiescent water.

Hard gluon evolution in the last stage of the bottom-up thermalization

The study of how fast thermalization in heavy ion collisions occurs has been one of the central topics in the heavy ion community. In the weak coupling picture this thermalization occurs from ‘the bottom up’: high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. In this scheme we apply a model on parton energy loss to discuss the effects of medium expansion on the thermalization problem and estimate the average transverse momentum diffusivity for thermalization in a Bjorken expanding medium.

RETRACTED: Impact of ohmic heating on energy transport in double diffusive Oldroyd-B nanofluid flow induced by stretchable cylindrical surface

The most important and significant research topic in mechanical and industrial engineering is the fluid flow with heat transport by a stretched surface because of the numerous applications. The impact of heat transport on product quality can be noticed in the field of chemical engineering, polymer processing, glass fiber production, hot rolling, metal extrusion, production of paper, and drawing of plastic films and wires. In light of such foregoing applications, an attempt is made to model the thermal and solutal diffusion phenomena in Oldroyd-B nanofluid flow over a stretching cylinder by using Buongiorno's model and Cattaneo-Cristov theory. To explore the heat flow mechanism in the flow, the effects of heat source/sink with ohmic heating are also considered. Additionally, the influence of chemical reactions is used to investigate the solutal transport process in nanofluid flow. The mathematical formulation section of the manuscript depicts the mathematical modeling of momentum, heat, and mass diffusion equations. The effect of dimensionless physical constraints on the flow, temperature, and concentration distributions of Oldroyd-B nanofluid flow are investigated using the homotopy analysis method (HAM) in Wolfram Mathematica. In the results and discussion section, graphical findings are displayed and physically justified. A section of concluding remarks is added at the end of the text to emphasize the study's major findings.

Axisymmetric radiative titanium dioxide magnetic nanofluid flow on a stretching cylinder with homogeneous/heterogeneous reactions in Darcy-Forchheimer porous media: Intelligent nanocoating simulation

Modern nanomaterials coating processes feature high temperature environments and complex chemical reactions required for the precise synthesis of bespoke designs. Such flow processes are extremely complex and feature both heat and mass transfer in addition to viscous behaviour. Intelligent nano-coatings exploit magnetic nanoparticles and can be manipulated by external magnetic fields. Mathematical models provide an inexpensive insight into the inherent characteristics of such coating dynamics processes. Motivated by this, in the current work, a novel mathematical model is developed for dual catalytic reactive species diffusion in axisymmetric coating enrobing forced convection boundary layer flow from a linearly axially stretching horizontal cylinder immersed in a homogenous non-Darcy porous medium saturated withmagnetic nanofluid. Homogeneous and heterogeneous reactions, heat source (e.g. laser source) and non-linear radiative transfer are included. The Tiwari-Das nanoscale model is deployed. A Darcy-Forchheimerdrag force formulation is utilized to simulate both bulk porous drag and second order inertial drag of the porous medium fibres. The magnetic nanofluid is an aqueous electroconductive polymer comprising base fluid water and magnetic TiO2 nanoparticles. The TiO2 nanoparticles are one chemically reacting species (A) and a second species (B) is also present (e.g. oxygen) which also reacts chemically. Viscous heating and Ohmic dissipation are also included to produce a more physically realistic thermal analysis. The non-linear conservation equations proposed here with species diffusion (species A and B) are transformed via an appropriate stream function and scaling variables into a set of non-linear united multi-degree ODEs. The rising nonlinear ordinary differential boundary value problem is solved with four-point Gauss-Lobotto formulae in the MATLAB bvp5c routine. Validation is conducted with an Adams-Moulton predictor–corrector numerical scheme (AM2 coded in Unix). The widespread visualization of velocity, temperature, species A concentration, species B concentration, skin friction, local Nusselt number and species A and B local Sherwood numbers is included. For the higher Schmidt number the momentum diffusion rate exceeds the species diffusion rate and this will produce a depression in concentration values. Further, increasing Darcian parameter retards the local Nusselt number magnitudes since higher permeability corresponds to sparsity in the solid fibres, reduction in thermal conduction and a concomitant cooling of the cylinder surface.

Chaotic characteristics of thermal convection at smaller verse larger Prandtl number through fractal and fractional differential operators from nanofluid

ABSTRACT Nanofluids with a smaller and larger Prandtl number reflect the dominations of thermal diffusivity and momentum diffusivity, respectively. This fact shows how much heat is carried away by how much fluid through transference from one point to another point. For the sake of the above fact, the thermal convection at a smaller versus larger Prandtl number through fractal and fractional differential operators is investigated from the nanofluid on the basis of certain nanoparticles and base fluid. The nanofluid as a base fluid is ethylene glycol and nanoparticles are titanium dioxide, copper, silver and aluminium oxide. For the first time in the literature, mathematical modeling is proposed via fractal and fractional differential operators of Caputo-Fabrizio and Atangana-Baleanu. The numerical schemes of chaotic models have been presented by invoking the Adams-Bashforth-Moulton method as a powerful technique for simulations. The thermophysical properties of the nanofluid have been traced out chaotically by comparative analysis of fractal and fractional differential operators of Caputo-Fabrizio and Atangana-Baleanu. Finally, two-dimensional chaotic attractors, three-dimensional chaotic attractors and each type of nanoparticle have been discussed for smaller, medium and larger values of Prandtl number by emphasizing the role of fractal and fractional differential operators.

An effective description of momentum diffusion in a charged plasma from holography

We discuss the physics of momentum diffusion in a charged plasma. Following the holographic strategy outlined in [1] we construct an open effective field theory for the low-lying modes of the conserved currents. The charged plasma is modeled holographically in terms of a Reissner-Nordström-AdSd+1 black hole. We analyze graviton and photon fluctuations about this background, decoupling in the process the long-lived momentum diffusion mode from the short-lived charged transport mode. Furthermore, as in the aforementioned reference, we argue that the dynamics of these modes are captured by a set of designer scalars in the background geometry. These scalars have their gravitational coupling modulated by an auxiliary dilaton with long-lived modes being weakly coupled near the spacetime asymptopia. Aided by these observations, we obtain the quadratic effective action that governs the fluctuating hydrodynamics of the charge current and stress tensor, reproducing in the process transport data computed previously. We also point out an interesting length scale lying between the inner and outer horizon radii of the charged black hole associated with Ohmic conductivity.

Effect of Thermophoresis on Heat Diffusion in Isobutane/Copper‐Oxide Nanofluid under Pool Boiling Condition: Numerical Investigation

Understanding thermophoresis in nanorefrigerants stands challenging for a long period despite the phenomenon is attributed for the motion dynamics of particles in nanofluids. Influence of thermophoretic mobility of copper‐oxide nanoparticles on the heat transfer behavior of isobutane (R600a) refrigerant is reported in this work. Pool boiling of the isobutane/copper‐oxide nanofluid is numerically simulated in computational fluid dynamics utilizing both single and two‐phase approaches. Mobility of particles in the saturated refrigerant is studied, and the time scales associated with (Brownian and momentum) diffusions are numerically solved. The temperature contour of the liquid pool is validated with the experimental data, and the properties of the nanorefrigerant such as thermal conductivity, viscosity, and specific heat are estimated in ANSYS Fluent. 5% increase in thermal conductivity and marginal reduction in specific heat of the nanorefrigerant for 0.01% volume fraction of copper‐oxide nanoparticles is witnessed. Mobility of particles due to temperature gradient is found higher near the heater; however, thermophoretic velocity is predicted to be lower because of the narrow temperature gradient. Numerical results showed that the time scale for momentum diffusion is shorter (in the order of e+03) than Brownian diffusion, and hence the momentum diffusion is found to be the predominant mode of heat transfer in nanorefrigerant.

Power generalization of the linear constitutive equations of heat and mass transfer and the variants of writing the equations of momentum transfer, heat and diffusion arising from them

Currently, when solving problems of heat and mass transfer, linear constitutive equations are used - in hydrodynamics, the viscous stress tensor is proportional to the strain rate tensor (Newton's rheological ratio), in heat transfer, the heat flux density is linearly related to the temperature gradient (Fourier's heat conduction law), in mass transfer, the diffusion flux density proportional to the concentration gradient (Fick's law). When writing these linear governing equations, proportionality coefficients are used, which are called the viscosity coefficient, thermal conductivity coefficient and diffusion coefficient, respectively. Such constitutive equations are widely used to describe the processes of heat and mass transfer in a laminar flow regime. For turbulent flows, these equations are unsuitable, it is necessary to introduce into consideration the empirical turbulent coefficients of viscosity μt, thermal conductivity λt and diffusion Dt. However, to describe turbulent flows, it is possible to go in another way - to modify the linear constitutive relations by giving them a nonlinear power-law form. Two-parameter power-law generalizations of Newton's, Fourier's and Fick's formulas for shear stress, heat flux density and diffusion, which, depending on the value of the exponents, can be used to describe the processes of heat and mass transfer both in laminar and turbulent fluid flow. Also, this generalization can be used to describe the behavior of power-law fluids and flows of polymer solutions exhibiting the Toms effect.

Heavy quark dynamics in a strongly magnetized medium

We present a calculation of the heavy quark momentum diffusion coefficients in a strongly magnetized medium, within the Lowest Landau Level (LLL) approximation. In particular, we use the Hard Thermal Loop (HTL) resummed effective gluon propagator, generalized for a hot and magnetized medium. Using this effective HTL gluon propagator along with the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Going beyond the static limit of the heavy quark, we also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

Spectral reconstruction details of a gradient-flowed color-electric correlator

In a recently published work we provide a proof-of-concept of a novel method to extract the heavy quark momentum diffusion coefficient from color-electric correlators on the lattice using gradient flow. The transport coefficient can be found in the infrared limit of the corresponding spectral function which is reconstructed through perturbative model fits of the correlator data. In this proceedings report we want to give more detailed insights into the systematic uncertainties of this procedure and compare our results with other studies.

Mixed convective transport in Maxwell hybrid nano-fluid under generalized Fourier and Fick laws

Generalized laws of Fourier and Fick based on thermal and solutal relaxation times are used in the development of the system of PDEs related to simultaneous transport of heat and species in Maxwell fluid with mono and hybrid nano particles. The developed systems of PDEs are solved numerically by using the finite element method (FEM). Implementation of the FEM algorithm is discussed. The parametric study is carried out by performing various theoretical and numerical experiments. Related outcomes are presented in the form of graphs and numerical data. Convergence is ensured and grid-independent solutions are derived. Thermal relaxation parameter tends to lower down the temperature of the fluid and thermal boundary layer becomes shorter for higher values of thermal relaxation parameter. Concentration relaxation parameter has shown a decreasing impact on the diffusion of species in Maxwell fluid. Deborah number has reduced the diffusion of momentum in Maxwell fluid. Convective transport of both heat and species is compromised when Deborah's number is increased. It is also noticed from simulations that Deborah number for mono nano-Maxwell fluid has greater value relative to that for hybrid nano-Maxwell fluid. The simulations have also confirmed that the effective thermal conductivity of the Maxwell fluid due to the simultaneous dispersion of copper and aluminium oxide is greater than the thermal conductivity of pure Maxwell fluid and mono nano-Maxwell fluid. Therefore, simultaneous dispersion of copper and aluminium oxide for optimized heat transfer. Thermal and concentration relaxation memory effects are responsible for reducing thermal and concentration boundary layer thickness respectively. It is also noted that heat transport rate in hybrid nano-Maxwell fluid is greater than that in mono nano-Maxwell fluid and pure Maxwell fluid. Thermal memory effects play significant role in increasing the wall heat flux.

Sediment load determines the shape of rivers

Understanding how rivers adjust to the sediment load they carry is critical to predicting the evolution of landscapes. Presently, however, no physically based model reliably captures the dependence of basic river properties, such as its shape or slope, on the discharge of sediment, even in the simple case of laboratory rivers. Here, we show how the balance between fluid stress and gravity acting on the sediment grains, along with cross-stream diffusion of sediment, determines the shape and sediment flux profile of laminar laboratory rivers that carry sediment as bedload. Using this model, which reliably reproduces the experiments without any tuning, we confirm the hypothesis, originally proposed by Parker [G. Parker, J. Fluid Mech 89, 127-146 (1978)], that rivers are restricted to exist close to the threshold of sediment motion (within about 20%). This limit is set by the fluid-sediment interaction and is independent of the water and sediment load carried by the river. Thus, as the total sediment discharge increases, the intensity of sediment flux (sediment discharge per unit width) in a river saturates, and the river can transport more sediment only by widening. In this large discharge regime, the cross-stream diffusion of momentum in the flow permits sediment transport. Conversely, in the weak transport regime, the transported sediment concentrates around the river center without significantly altering the river shape. If this theory holds for natural rivers, the aspect ratio of a river could become a proxy for sediment discharge-a quantity notoriously difficult to measure in the field.

Insights into the dynamics of wake flame in a freely falling droplet

The combustion of a freely falling dodecane droplet has been studied experimentally in a droptower-like facility under ambient conditions. A unique ignition mechanism is used by igniting the droplet in pendant mode and releasing it to fall freely. This unveils a different type of droplet wake flame behavior which is explored in this study. Initially, the droplet flame transitions from fully enveloped to a wake flame configuration due to forward extinction. The wake flame has similar characteristics as a laminar lifted triple-flame. As the droplet accelerates, the flame stand-off increases continuously. The change in wake flame topology and intensity occurs in two different regimes corresponding to different droplet diameters. A new non-dimensional parameter has been derived to account for the local balance between buoyancy and momentum diffusion that alters the fuel availability. To explain the flame topological evolutions and transitions for different droplet diameters and Reynolds numbers, a theoretical formulation has been proposed based on the momentum diffusion from surrounding due to relative motion. Further, at very high Reynolds number, flame stretching or shedding regime occurs, causing momentary spikes in flame intensity due to the interaction with asymmetric vortex shedding induced by the Bernard–Von Karman instability. Interestingly, the flame shedding height follows the buoyant flickering scaling, even for the momentum-dominant droplet wake flame. Additionally, the circulation build-up mechanisms are shown to be responsible for the flame shedding events for droplet wake flame at high Reynolds number.

Study of Momentum Diffusion with the Effect of Adiabatic Focusing

Abstract The momentum diffusion of charged energetic particles is an important mechanism of the transport process in astrophysics, the physics of fusion devices, and laboratory plasmas. In addition to the momentum diffusion term for a uniform field, we obtain an additional momentum diffusion term due to the focusing effect of the large-scale magnetic field. After evaluating the coefficient of the additional momentum diffusion term, we find that it is determined by the sign of the focusing characteristic length and the cross helicity of the turbulent magnetic field. Furthermore, by deriving the mean momentum change rate contributed from the additional momentum diffusion term, we identify that the focused field provides an additional momentum loss or gain process.

Ab initio coupling of jets to collective flow in the opacity expansion approach

We calculate the leading corrections to jet momentum broadening and medium-induced branching that arise from the velocity of the moving medium at first order in opacity. These results advance our knowledge of jet quenching and demonstrate how it couples to collective flow of the quark-gluon plasma in heavy-ion collisions and to the orbital motion of partons in cold nuclear matter in deep inelastic scattering at the electron-ion collider. We also compute the leading corrections to jet momentum broadening due to transverse gradients of temperature and density. We find that these effects lead to both anisotropic transverse momentum diffusion proportional to the medium velocity and anisotropic medium-induced radiation emitted preferentially in the direction of the flow. We isolate the relevant sub-eikonal corrections by working with jets composed of scalar particles with arbitrary color factors interacting with the medium by scalar QCD. Appropriate substitution of the color factors and light-front wave functions allow us to immediately apply the results to a range of processes including $q \rightarrow q g$ branching in real QCD. The resulting general expressions can be directly coupled to hydrodynamic simulations on an event-by-event basis to study the correlations between jet quenching and the dynamics of various forms of nuclear matter.

Second law analysis of pseudo‐plastic nanofluid stream past a stretching sheet with a sliding consequence

AbstractThe entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power‐law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power‐law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power‐law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production.

Nonlinear thermal radiation and temperature dependent viscosity effects on MHD heat and mass transfer in a thin liquid film over a stretching surface

This paper describes nonlinear thermal radiation effects on MHD heat and mass transfer in a thin liquid film over a permeable unsteady stretching surface taking temperature-dependent fluid viscosity with convective boundary condition. For the non-linearity of the momentum, energy and mass diffusion equations, the problem is solved numerically. At first, Similarity transformations is used to the governing equations to reduce the equations into a set of ordinary differential equations. Then the resulting nonlinear ordinary differential equations are solved using Runge-Kutta-Felberg method with shooting technique. Different physical parameters effects on heat and mass transfer in a thin liquid film are presented graphically. It is found that increase in the unsteadiness parameter leads to increase in the velocity distribution, temperature and concentration gradient. Further, increase in the value of magnetic parameter results in a decrease in the velocity profile and increase in the temperature and concentration gradient. For enhancement of thermal radiation decreases the temperature gradient of the thin film flow. Also, for increase in viscosity variation parameter is to decrease velocity distribution but reverse effects shown in case of temperature and concentration gradient.