Variable Diffusion Research Articles

Combined Impacts of Thermal and Mass Stratification on Unsteady MHD Parabolic Flow Along an Infinite Vertical Plate With Periodic Temperature Variation and Variable Mass Diffusion

ABSTRACTThis study investigates the dynamics of unsteady MHD parabolic flow along an infinite vertical plate, with a focus on the impacts of thermal and mass stratification under periodic temperature variations and variable mass diffusion. Utilizing the Laplace transform technique for deriving exact solutions, this research innovatively integrates both thermal and mass stratification effects without resorting to approximations. The main objective is to assess how these stratifications influence flow dynamics, temperature, and concentration profiles in environments with varying magnetic fields. The study contrasts these findings against classical non‐stratification cases, offering a detailed comparison of fluid behavior under different conditions. Results indicate that thermal and mass stratifications substantially decrease velocity and stabilize temperature profiles, pointing to a damping effect on fluid motion while also controlling diffusion processes. These stratifications lead to higher Nusselt and Sherwood numbers, suggesting improved heat and mass transfer efficiencies. In contrast, the absence of stratification results in higher velocities and less stable temperature and concentration distributions. The findings underscore the significant role of stratification in optimizing fluid dynamics and enhancing the efficiency of heat and mass transfer processes, providing crucial insights for engineering and environmental applications where such conditions prevail.

Analysis of Battery-like and Pseudocapacitive Ion Intercalation Kinetics via Distribution of Relaxation Times

Abstract Improving the kinetics of electrochemical ion intercalation processes is of interest for realizing high-power electrochemical energy storage. This includes classical battery-like intercalation and pseudocapacitive intercalation processes with a capacitor-like electrochemical signature. Electrochemical methods are needed to probe the kinetics of such complex multistep processes in detail. Here, we present the use of the distribution of relaxation times (DRT) analysis of electrochemical impedance data to identify the kinetic limits of intercalation reactions. We study the lithium intercalation reaction in TiS2 from organic and aqueous electrolytes as a model system. The material can exhibit both battery-like and pseudocapacitive intercalation regimes depending on the potential range, variable diffusion lengths by adjusting its particle size, and a tunable degree of solvent cointercalation by choosing the electrolyte solvent. Using DRT, we can distinguish between the kinetic limitations imposed by solid-state ion diffusion, interfacial ion adsorption and transport, and ion desolvation processes. Thus, DRT analysis can complement existing methods, such as voltammetry or 3D-Bode analysis, to better understand the kinetics of intercalation reactions.

Theoretical and numerical analysis of problems with a boundary turning point and a variable diffusion coefficient

Theoretical and numerical analysis of problems with a boundary turning point and a variable diffusion coefficient

Soret and dufour impacts on radiative power-law fluid flow via continuously stretchable surface with varying viscosity and thermal conductivity

The intricate dynamics of mixed convective thermic and species transport in a power-law flowing fluid through a continuously stretched surface are investigated. The uniqueness of this study lies in the consideration of fluid variable thermic conductivity and viscosity, which introduces a higher degree of realism into the analysis. The transformation of similarity is used to transform the fundamental governing equations, and after that, the set of equations is processed numerically utilizing a non-similarity local approach. Furthermore, the effects of Soret and Dufour represent the cross-diffusion phenomena, accounting for the energy exchange with the surroundings. These factors collectively influence the stretching surface’s gradient velocity, affecting the thermal and species concentration rates. The findings offer a comprehensive understanding of these complex interactions, paving the way for optimizing thermic and species transport processes in various industrial applications. This study, therefore, holds significant potential for enhancing efficiency and performance in relevant industrial sectors. The main terms are the combinations of Dufour and Soret numbers that significantly impact the flow rate profile and mass transfer field. The coupled study of the nonlinear velocity, energy distribution and chemical mixture variance made the study more impactful in practicality. Skin friction variation shows limited impact with variations in the Soret number. The enhanced thermal gradient results in improved non-similarity parameters, yet it demonstrates a decrease with an increase in variable thermal diffusivity. There is a decrease in the temperature gradient as the buoyancy term reduces, while an increase is observed with changes in the Prandtl number. Similarly, the Nusselt number experiences a comparable impact due to changes in the Soret number.

A numerical investigation of the polyethylene glycol‐based tetra hybrid nanofluid flow over a stretched porous rotatory disk

AbstractPolyethylene glycol (PEG) is a great heat and mass transmissive fluid that has promising applications in medical, pharmaceutical, and electronic industries. Tetra‐hybrid nanofluids (HNFs) are the most upgraded version of heat and mass transmissive nanofluids that are synthesized by dispersing four distinct nanoparticles in the carrier fluid. The study of the flow of nanofluids and their advanced classes across rotatory disks is receiving remarkable interest in research and innovation due to their considerable applications like gas turbine rotors, aeronautical, medical equipment, rotating machinery, thermal power developing systems, and so forth. Therefore, the present paper aims to inspect the magnetohydrodynamic, steady, three‐dimensional, and incompressible flow of a non‐Newtonian tetra‐HNF over a stretched porous rotating disk. The chosen tetra‐HNF consists of four distinct nanoparticles namely, molybdenum disulfide, copper oxide, magnesium oxide, and zirconium oxide with PEG as the carrier fluid. The flow model is modified with innovative impacts of variable thermal conductivity, thermal radiation, chemical reaction, variable mass diffusivity, and suction/injection to make this research more convenient. The mathematical computation is conducted via the bvp4c numerical method, and the outputs are determined via tables and graphs. Mounting values of the Deborah number amplify the axial velocity while augmentation is noticed in the fluid's radial and azimuthal velocities for rising values of the rotation parameter. Besides, the rotation parameter aids in enhancing both the heat and mass transportation rates while the chemical reaction parameter significantly aids the mass transportation rate. One of the significant results of this inspection is that tetra‐HNF exhibits better heat and mass transportation rates than the ternary‐HNF, and the HNF whereas it has lesser skin friction than the ternary‐HNF, and the HNF.

Temporal Second-order Scheme for a Hidden-memory Variable Order Time Fractional Diffusion Equation with an Initial Singularity

Temporal Second-order Scheme for a Hidden-memory Variable Order Time Fractional Diffusion Equation with an Initial Singularity

Treatment of 3D diffusion problems with discontinuous coefficients and Dirac curvilinear sources

Three-dimensional diffusion problems with discontinuous coefficients and unidimensional Dirac sources arise in a number of fields. The statement we pursue is a singular-regular expansion where the singularity, capturing the stiff behavior of the potential, is expressed by a convolution formula using the Green kernel of the Laplace operator. The correction term, aimed at restoring the boundary conditions, fulfills a variational Poisson equation set in the Sobolev space H1, which can be approximated using finite element methods. The mathematical justification of the proposed expansion is the main focus, particularly when the variable diffusion coefficients are continuous, or have jumps. A computational study concludes the paper with some numerical examples. The potential is approximated by a combined method: (singularity, by integral formulas, correction, by linear finite elements). The convergence is discussed to highlight the practical benefits brought by different expansions, for continuous and discontinuous coefficients.

Effects of Thermal and Mass Stratification on Unsteady MHD Flow Past an Oscillating Vertical Plate Embedded in a Porous Medium with Variable Surface Conditions

oscillating vertically in its own axis in which it is embedded in a porous medium with variable heat and mass diffusion. For concentration, temperature and velocity fields, the non-dimensional governing equations are solved using the Laplace transform method for the unitary Prandtl and Schmidt numbers, when the plate is oscillating in its own plane harmonically. Numerical computations are carried out and presented in graphs for different physical parameters like thermal Grashof number, phase angle, mass Grashof number, stratificationparameter and time on concentration, velocity, temperature, plate heat flux, mass flux and skin friction. The findings of this study can be utilized to enhance comprehension of MHD flow on vertical oscillating plate in combined stratified environments. Significant findings arising from the mass and thermal stratification are compared to the scenario in which stratification is absent.

Double Phase Variable Exponent Problems with Nonlinear Matrices Diffusion

This work tackles a class of double phase elliptic problems with variable exponents and matrices diffusion. Under suitable assumptions on the data, we use critical point theory to establish both the existence and uniqueness of weak solutions to the double phase problem under consideration.

Chemically reactive flow beyond constant thermophysical characteristics

Hydromagnetic chemically reactive flow over stretching wall is discussed. Formulation is based upon consideration of Reiner-Rivlin constitutive relation. Variable thermophysical characteristics are under consideration. Radiation, heat generation and dissipation impacts exist in thermal relation. Concentration expression subject to reaction with first order is considered. Modeling with entropy optimization is made. Appropriate transformations lead to relevant differential systems. Numerical study by ND-solve is carried out. Quantities under interest are graphically analyzed. An opposite behavior detected for magnetic parameter on entropy rate and velocity. Velocity field versus magnetic field parameter decreases whereas reverse impact witnessed for variable viscosity parameter. An enhancement in thermal distribution and entropy detected for radiation. Thermal distribution enhancement is observed for generation of heat and thermal conductivity variables. Chemical reaction for concentration has decaying impact. Results of Schmidt number for concentration are similar to that of chemical reaction. Brinkman number leads to entropy rate improvement. Entropy rate upsurges against variable viscosity and mass diffusivity parameters.

A Diffusion Model to Describe Water Absorption by Red Rice during Soaking: Variable Mass Diffusivity, Variable Volume, Use of Boundary-Fitted Coordinates

This article aims to carry out experiments on water absorption by husked red rice at constant temperatures of 28, 40, and 50 °C. The description of the absorption kinetics and the analyses of the water distribution and volumetric expansion of each grain, at a given instant, were carried out using a diffusion model. In order for the model to be as close as possible to the real physical situation, the mesh necessary to numerically solve the diffusion equation was generated from the photograph of a grain. Thus, the diffusion equation was written in Boundary-Fitted Coordinates (BFCs). The solution of the diffusion equation written in generalized coordinates was then discretized in space and time, using the Finite Volume method, with a fully implicit formulation, considering the variable volume and variable mass diffusivity as functions of the local moisture content. Optimizations based on the Levenberg–Marquardt algorithm make it possible to determine the parameters of an exponential function relating mass diffusivity and the local moisture content for each temperature. Statistical indicators (chi-square, determination coefficient, and Student’s t-test) allowed us to conclude that the proposed model was very satisfactory for all temperatures, making it possible to simulate the water absorption, water distribution, and volumetric expansion of the grain over time.

Assessment of Hysteresis Models for LiFePO4

The selection of the cathode material is an important task in the design phase of batteries for mobile applications. One material of increasing interest is LiFePO4 (LFP) due to its improved energy density, good thermal stability and durability. In contrast to other commonly used cathode materials, LFP features a clear phase separation between the lithium rich and the lithium poor phase, leading to a pronounced voltage plateau over wide ranges of state of charge (SOC). The level of this plateau also changes for charge and discharge operation, even at very low C-rates. This voltage hysteresis in combination with the wide plateau gives some ambiguity to the correlation between voltage and SOC, which is a challenge for battery management systems. Thus its correct description is crucial if a cell model is meant to serve as virtual twin supporting control function development and calibration. Beyond that, a highly dynamic battery development process requires models that run significantly faster than real-time and parametrization processes which allow for accurate validation and easy adaptation to modified electrodes. A simulation approach complying with these requirements is the electrochemical pseudo-two dimensional (P2D) model, though adaptions to the core model are needed to appropriately capture hysteresis-affected voltage plateau characteristics for phase-separating materials such as LFP.The goal of this study is to extend an existing P2D framework with two approaches capable of describing hysteresis effects and analyzing these extensions regarding result plausibility, computational cost and effort of parametrization. The first model of interest is based on the one-state hysteresis model proposed by Plett. This approach allows for fast simulation and accurate reproduction of the charge and discharge voltages at low C-rates but lacks deeper physical consideration of the phase-separating origin of the hysteresis and thus might lose accuracy to predict system responses on dynamic pulses. In this approach, the voltage hysteresis is not a simulation result, it is due to the input of two separate open circuit voltages for charge and discharge. The second model of interest applies variable solid diffusion (VSSD) featuring a reduced Fickian diffusion coefficient in the plateau region. Lower diffusion at a given C-rate leads to steeper concentration gradients between lithium rich and lithium poor phase. With this approach, effective phase boundaries within the representative particles can be obtained. In the limiting case, when the Fickian diffusion coefficient becomes zero or even negative at some lithium concentration, phase separation persists also when no current is applied. In this setting, the voltage hysteresis at low C-rates is an emergent phenomenon, it is not an input. The physical basis of the approach also allows to consider mechanical stresses and their impact on the voltage gap between charge and discharge. Concentration gradients cause a mismatch of volume demands and thus lead to local stresses, which in turn alter the chemical potential.Results emphasizing advantages and disadvantages of the two hysteresis models are presented. Charge and discharge simulations are performed for several C-rates and the voltage hysteresis is extrapolated to infinitely small currents. Furthermore, the effect of resting phases with zero current as in Galvanostatic Intermittent Titration Technique measurements is discussed. As hysteresis models are often tested only on charge/discharge cycles with constant currents over large SOC regions, the responses of the simulation models are also assessed in pulse tests and dynamic profiles giving a realistic picture of automotive applications. Here special focus is put on energetical aspects of the one-state model and on intra-particle concentration profiles for the VSSD model.

Effects of endwall clearances of variable diffuser vane on centrifugal compressor performance

To ensure the variable diffuser vane can rotate around a pivot fluently in practical applications, there have to be clearances between vanes and diffuser walls. As the compressor pressure ratio increases, the effects of the vane endwall clearances are enhanced and cannot be ignored. This paper investigates the effects of both-side vane endwall clearances on the centrifugal compressor performance. Results show that the existence of endwall clearances mainly enlarges the flow capacity of the vane diffuser and decreases the compressor efficiency, and these effects are more significant as the vane stagger angle decreases. A one-side endwall clearance of 2.7% of the diffuser width increases the choke mass flow rate by as much as 20% and decreases the compressor peak efficiency by 2.7%. Due to the non-uniform flow along span at the impeller outlet, the shroud-side vane endwall leakage plays a more important role than the hub-side in affecting the compressor performance. In additions, the respective contributions of the vane throat, the hub-side and the shroud-side endwall clearances to the increases of the vane choke mass flow rate are quantitatively studied. The flow physics and loss mechanisms of the endwall leakage are revealed.

Micro-CT images and variable effective diffusivity as tools in the analysis of Cariniana estrellensis (Raddi) Kuntze seeds hydration

Micro-CT images and variable effective diffusivity as tools in the analysis of Cariniana estrellensis (Raddi) Kuntze seeds hydration

Analysis of axisymmetric thermoelastic diffusive half-space with variable material properties using hyperbolic two-temperature model

The aim of the current study is to investigate the variable thermal conductivity and diffusivity impact on the transient response of an axisymmetric thermodiffusive elastic half-space under axisymmetric thermal, mechanical, and concentration loads in the light of hyperbolic two-temperature generalized fractional thermoelastic diffusion model. With the help of Kirchhoff’s transform, the governing equations are converted into linear form. The resulting equations are solved by imposing the combined Laplace–Hankel transform. In converted space, the solutions for different field quantities are presented in compact form. The copper material is considered for numerical computation. By employing a mathematical inversion procedure, the solutions are converted into the original space. Numerically computed solutions for various physical quantities are illustrated in the form of graphs to show the impact of variable thermal conductivity and diffusivity, hyperbolic two temperature, and fractional parameters. Validation of the obtained results is also presented.

Analysis of the tri-hybrid Maxwell nanofluid flow with temperature-dependent thermophysical characteristics on static and dynamic surfaces employing Levenberg-Marquardt artificial neural networks

Using the Levenberg-Marquardt Artificial Neural Network (LM-ANN) model, this study applies computational neuroscience to the analysis of flow, heat, and mass transport characteristics. The novel characteristics of MHD Maxwell tri-hybrid nanofluid passing through static and moving wedge with temperature-dependent thermophysical properties (thermal conductivity, viscosity, diffusivity, and electrical field) in permeable, radiative, and mixed convection processes are investigated in this paper. Nonlinear PDEs are transformed into nonlinear ODEs using similarity variables. A dataset for the LM-ANN is generated across various scenarios by varying parameters such as the temperature-dependent viscosity parameter ( 0.07 − 0.1 ) , variable diffusivity parameter ( 0.4 − 2.5 ) , thermal buoyancy parameter ( 0.1 − 0.5 ) , nonlinear thermal buoyancy parameter ( 0.2 − 0.5 ) , thermal radiation ( 1 − 1.5 ) , buoyancy ratio parameter ( 0.2 − 0.5 ) , chemical reaction parameter ( 1 − 3 ) , and Schmidt number ( 1 − 3 ) using the Bvp5c numerical algorithm. The testing, training, and validation procedure of LM-ANN is utilized to examine the estimated solutions of specific situations, and the proposed algorithm is then validated. After that, the proposed LM-ANN is validated using regression analysis, MSE, and histogram analysis. The prescribed approach impeccably mirrors the recommended and cited findings, evincing a precision level within the realm of 10−9. Results indicate that increasing the permeability parameter from 1 to 1.2 and the temperature-dependent thermal conductivity parameter from 0.4 to 2.5 enhances the Nusselt number. Additionally, increasing the chemical reaction parameter from 1 to 3 leads to an increase in the Sherwood number. The significance of this study lies in its potential applications in industries such as aerospace, chemical processing, and energy systems, where efficient heat and mass transfer processes are crucial. For instance, the findings can be applied to enhance cooling techniques in high-performance aerospace components, optimize reactor designs in chemical plants, and improve thermal management in power generation systems.

Variable-order fractional diffusion: Physical interpretation and simulation within the multiple trapping model

The physical interpretation of a variable-order fractional diffusion equation within the framework of the multiple trapping model is presented. This interpretation enables the development of a numerical Monte Carlo algorithm to solve the associated subdiffusion equation. An important feature of the model is variation in energy density of localized states, when the detailed balance condition between localized and mobile particles is satisfied. The variable order anomalous diffusion equations under consideration can be applied to the description of transient subdiffusion in inhomogeneous materials, the order of which depends on the considered spatial and/or time scale. Examples of numerical solutions for different situations are demonstrated. Considering variable-order fractional drift, we calculate and analyze the transient current curves of the time-of-flight method for samples with varying density of localized states.

Theoretical study of the expansion of Roper's theory on the laminar jet diffusion flame length in 2D and 3D in natural gas and hydrogen mixtures

In this work, three mathematical models were developed to study the laminar jet diffusion flame in mixtures of natural gas, hydrogen, and CO2 by extending and applying Roper's theory. Model M1 consists of derivation of the Roper's original equation described in the two-dimensional steady state without convection, thus showing the theoretical equations for the length of the diffusion flame for burners with circular, square, and rectangular cross sections and for regimes in which the flames are dominated by the momentum effects, the buoyancy effect, and in the transition regime. Models M2 and M3 extend the Roper's original theory by deriving analytical solutions of the two- and three-dimensional diffusion flame equation with convection in steady and transient states, taking into account the spatially variable velocity and diffusion coefficients. The flame lengths obtained with models M1 and M2 were compared with model M3 by Relative Percentage Difference (RPD) considering 5 mixtures of NG-H2-CO2. For t = 0.1, the maximum RPD in the circular cross-section for M1 in Gas20:60%NG-25%H2–15%CO2 was 14.75%, while for M2 in Gas14:70%NG-15%H2–15%CO2 was 6.47% and the minimum RPD in Gas1:100%NG was 9.78% and 4.83% for M1 and M2, respectively. The same analysis was developed for the square and rectangular (Fr ≪ 1) cross-sections and showed good agreement. The model M3 was tested under transient conditions, studying the effects of time and velocity on the distribution of the profile in the radial direction, in order to better understand the flame phenomenon, which cannot be observed with the Roper's original model M1. Finally, the models M2 and M3 were validated with experimental results and other analytical solutions showing a good performance considering the characteristics of each mixture.

An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion

Abstract This article investigates the unsteady mixed convention two-dimensional flow of magnetohydrodynamic Casson hybrid nanofluids (alumina oxide and titanium oxide nanoparticles with base fluid water) flow through porous media over a linearly stretched sheet. We analyzed the heat and mass transfer in mixed convection, thermal radiation, variable thermal conductivity, variable mass diffusivity, and chemical reaction in the presence of thermophoresis and Brownian motion. A system of partial differential equations is reduced to a solvable system of ordinary differential equations by applying a suitable similarity transformation. We used the Runga–Kutta method along with the shooting procedure to solve the flow, heat, and mass transfer equations along with boundary conditions. The results obtained from MATLAB codes are compared with previously published results of the same type in a limiting case. The results of the velocity, temperature, and concentration profile of the hybrid nanofluid for varying different flow parameters are obtained in the form of graphs, while the rate of shear stress, rate of heat, and mass transfer are expressed in tables. We noticed that velocity and temperature diminish as an unsteady parameter increases; however, the reverse trend was observed in the nanoparticle concentration profile. With an increase in the thermal radiation parameter, the resultant velocity and temperature profile improves, while the concentration of nanoparticle profiles decreases. The velocity and temperature increase with higher Brownian motion, while the velocity increases and temperature decreases with higher thermophoresis.

Theoretical investigation of thermal and mass stratification effects on unsteady flow across a vertical oscillating plate with periodic temperature variation and variable mass diffusion

AbstractThis research paper examines the combined effects of thermal and mass stratification on unsteady flow past a vertical oscillating plate with periodic temperature variation and variable mass diffusion. The Laplace transform technique is introduced to deal with the linear coupled parabolic equations satisfying initial as well as boundary conditions and obtained solutions in closed form for concentration, temperature, and velocity. For example, to find the Laplace transform of an exponentially ordered piece wise continuous function , one can uses the formula , t being the time and s is a parameter. In this study, we explore the effects of different factors such as plate amplitude, plate frequency, thermal Grashof number, and the mass Grashof number on the concentration, velocity, and temperature profiles and shows them graphically. We see a decline in the fluid's velocity for thermal and mass stratification. Most interestingly, in presence of higher temperature gradient, as the frequency of the oscillations increases close to the plate surface, the fluid velocity declines. The reason behind this is that the flow system has a plate with very high fluctuations. We have found that the fluid's temperature goes up while the concentration goes down when there is a decrease in the thermal stratification and a rise in the mass stratification.