Relaxation Time Parameter Research Articles

Construction of the absorbing boundary condition for the flow of Oldroyd-B fluid over a semi-infinite plate with magnetic effect

As a kind of non-Newtonian fluid, the Oldroyd-B fluid has widespread applications. To study the flow characteristics deeply is of great significance. In this paper, we consider a simple model of the Oldroyd-B fluid flow over a semi-infinite plate in a magnetic field. The governing equation is formulated, and the numerical solutions are obtained using the finite difference method. To deal with the semi-infinite region, the artificial boundary method is applied to construct the absorbing boundary condition (ABC) with the (inverse) z-transform, which converts the semi-infinite region to a finite one. To test the accuracy of the numerical scheme, a numerical example by introducing the source term is presented. Graphs show the rationality of the ABC by comparing the fluid flow velocity between the direct truncated boundary condition and the ABC. The effects of the amplitude, the frequency, the relaxation time parameter, the retardation time parameter, and the magnetic field on the magnitude and the cycle of flow velocity are investigated and discussed. The main findings are that the retardation time parameter promotes the velocity of the fluid flow, while the relaxation time and magnetic field hinder the fluid flow. When the relaxation time is equal to the retardation time, the Oldroyd-B fluid can approximate the Newtonian fluid. In addition, the oscillating cycle becomes shorter for a smaller relaxation time parameter or a larger magnetic field and frequency.

The photothermal interaction of a viscothermoelastic semiconducting ceramic solid sphere under the Green–Naghdi heat conduction model

This work introduces a new mathematical model for viscothermoelastic semiconducting solid spheres of ceramic materials considering the photothermal interaction using three types of the Green–Naghdi heat conduction model. The outer surface of a solid sphere is loaded thermally using ramp-type heat as a boundary condition. Following that, Laplace transforms and their inversion forms have been applied. The figures show that the mechanical relaxation time and ramp-time heat parameters have significant effects on the increase in carrier density and temperature, in addition to strain, displacement, the average of principal stresses, and the strain-energy density. The energy produced by viscothermoelastic semiconducting materials based on photothermal interaction may be controlled by the ramp-time heat parameter. The novelty of this work is to test the three types of the Green–Naghdi heat conduction model and apply the model to zirconia, a ceramic material.

Bio-convective maxwell ferrofluid flow over a flexible spinning surface

The current research findings will have potential applications in the development of drug-targeted and self-sterilizing technologies. This research investigates the bio-convective flow of Maxwell ferrofluid over a flexible spinning plate in the presence of a stationary magnetic field in this paper. This theoretical model is based on the CattaneoChristov theories, the Buongiorno microorganism model, and the Shliomis model, and it is solved using the finite element technique. Using the Galerkin weighted residual approach in COMSOL Multiphysics, the non-dimensional equations of this Maxwell ferrofluid model are numerically solved. The concentration and motility of the organism decrease with an increase in the ferromagnetic interaction number, concentration relaxation time parameter, Lewis number, and stretching parameter. In addition to increasing local heat transfer, local mass transfer, and local density of microorganisms, the ferromagnetic interaction number lowers the stress on the surface of the disk.

Extending matrix–vector framework on multiple relaxation time lattice Boltzmann method

This paper introduces an extension of a fully discrete matrix–vector form (MVF) for the lattice Boltzmann method (LBM) to handle the multiple relaxation time parameter (MRT) LBM. The proposed approach offers a more efficient and practical framework for simulating fluid flows, with the added benefit of being able to handle complex geometries using the image-based ghost (IBG) method. The advantages and limitations of this approach are discussed, including its simplicity in linear algebraic extension, parallel computing capability, computational speed, and memory usage. The results of numerical experiments demonstrate the improved computational efficiency of the proposed method, highlighting its potential for future applications in various fields of computational fluid dynamics.

Computational Modeling of High-Speed Flow of Two-Phase Hydrogen through a Tube with Abrupt Expansion

Hydrogen can become a prevalent renewable fuel in the future green economy, but technical and economic hurdles associated with handling hydrogen must be overcome. To store and transport hydrogen in an energy-dense liquid form, very cold temperatures, around 20 K, are required. Evaporation affects the achievable mass flow rate during the high-speed transfer of hydrogen at large pressure differentials, and accurate prediction of this process is important for the practical design of hydrogen transfer systems. Computational fluid dynamics modeling of two-phase hydrogen flow is carried out in the present study using the volume-of-fluid method and the Lee relaxation model for the phase change. Suitable values of the relaxation time parameter are determined by comparing numerical results with test data for high-speed two-phase hydrogen flows in a configuration involving a tube with sudden expansion, which is common in practical systems. Simulations using a variable outlet pressure are conducted to demonstrate the dependence of flow rates on the driving pressure differential, including the attainment of the critical flow regime. Also shown are computational results for flows with various inlet conditions and a fixed outlet state. Field distributions of the pressure, velocity, and vapor fractions are presented for several flow regimes.

The impact of fractional derivative on thermomechanical interactions in two-dimensional skin tissues throughout hyperthermia treatment

This work aims to study the influence of fractional derivatives and thermal relaxation time on two-dimensional biological tissues using an eigenvalue-based approach. Understanding the heat transfer mechanism and its thermomechanical interactions with the skin tissue of patients is crucial for the successful implementation of thermal treatment procedure. The study employs Laplace and Fourier transforms, and the resulting formulations are applied to human tissues undergoing regional hyperthermia treatment for tumor therapy. The numerical inversion process for Laplace and Fourier transformations utilizes the Stehfest numerical inverse method. The results demonstrate that thermal relaxation time and fractional order parameter significantly influence all analyzed distributions. The numerical findings suggest that thermo-mechanical waves propagate through the skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

Electrohydrodynamic peristaltic microfluidic flow with thermal and molecular analysis featuring sloped configurations

This study examines the simultaneous impacts of thermal and molecular transfer of non-Newtonian fluid propelled by the collective impact of electroosmosis and peristaltic pumping via inclined channel. Internal frictional heating and heat generation are also taken into consideration. The electrohydrodynamic phenomenon is described by the nonlinear Poisson–Boltzmann equation. The problem is modulated mathematically through a system of coupled non-linear differential equations in wave frame of reference. Using the regular perturbation method around a small wave number δ, we obtain sequential solutions for stream function ψ, electric potential ϕ, velocity u, pressure gradient dpdx, temperature θ and concentration Ω distributions. The influences of newly arising parameters such as the electroosmotic parameter me, relaxation time parameter λ1, retardation time parameter λ2, wave number δ, Reynold’s number Re, heat generation parameter β, Prandtl number Pr, Schmidt number Sc, Froude number Fr and Soret number Sr on physical characteristics are analyzed graphically. There is an inverse correlation between the parameters of relaxation time and retardation time and their effects on axial velocity, concentration, and temperature distributions. In particular, the temperature of the fluid increases as the EDL parameter, relaxation time parameter, viscous dissipation parameter, and Reynolds number increase, but decreases as the retardation time parameter increases. Moreover, the axial pressure gradient increases as Reynolds number and inclination angle increase, while it decreases as Froude number increases. The current model has applicability in the chemical industry, reservoir engineering, micro-fabrication, and biomedical applications, where electroosmotic effects on heat and mass movement are crucial.

Effects of rotation and temperature‐dependent viscosity on thermal convection in Oldroydian fluid saturating porous media: A modified stability analysis

AbstractThe onset of thermal convection in an incompressible Oldroydian fluid‐saturating porous media is examined to study the combined impact of uniform rotation and temperature‐dependent viscosity. A characteristic equation from the basic hydrodynamic equations governing the Brinkman–Oldroyd model is derived using linear stability theory and modified Boussinesq approximation. For various combinations of stress‐free and slip‐free boundaries, the expressions for the Darcy–Rayleigh numbers for both non‐oscillatory as well as oscillatory convection with linear and exponential temperature‐dependent viscosity are derived, using the “weighted residual method.” The effects of rotation, variable viscosity parameter, strain retardation and stress relaxation time parameters and other fluid parameters on non‐oscillatory and oscillatory convection are investigated numerically and the results are presented graphically. From the analysis, it is found that overstability is the preferred mode of onset of convection. The rotation, the coefficient of specific heat variations (due to temperature variation), and the strain retardation time have a stabilizing influence on the stability of the system, whereas the stress relaxation imparts a destabilizing effect. Additionally, it is noticed that the variable viscosity parameter and Brinkman‐Darcy number stabilize the system for each set of boundary conditions.

Natural convection flow and heat transfer of generalized Maxwell fluid with distributed order time fractional derivatives embedded in the porous medium

<p>Numerical simulation was performed for unsteady natural convection flow and heat transfer in a porous medium using the generalized Maxwell model and fractional Darcy's law with distributed order time fractional derivatives. The finite volume method combined with the fractional <italic>L1</italic> scheme was used to solve strongly coupled governing equations with nonlinear fractional convection terms. Numerical solutions were validated via grid independence tests and comparisons with special exact solutions. The effects of porosity, Darcy number, and relaxation time parameters on transport fields are presented. The results illustrate that porosity and permeability have opposite influences on temperature and velocity profiles. Moreover, the relaxation time parameters have remarkable effects on velocity profiles, and the variations possess significant differences.</p>

Dynamic response of a long cylinder under thermal shock in micropolar thermoelasticity.

In this manuscript, the dynamic response of a long cylinder subjected to an asymmetric thermal shock is investigated within the framework of generalized micropolar thermoelasticity. The displacement and micro-rotation are assumed to vanish at the surface. Laplace transformation techniques are used to solve the problem. The solution is obtained in the transformed field using an innovative direct approach. Furthermore, we obtain the inverse transformations using a numerical method based on Fourier expansion. The obtained results are carefully presented through graphical representations and discussed extensively across different relaxation time values. It is evident that the relaxation time parameter significantly influences all the distributions. The displacement distributions are always continuous, whereas all other functions, including temperature variation, stress distribution, and micro-rotation, exhibit discontinuity at the wave front. The results obtained hold significant importance in various technological applications and in the manufacturing of mechanical components.

Flash boiling and pressure recovery phenomenon during venting from liquid ammonia tank ullage

Liquid ammonia stored at elevated pressures undergoes phase change during tank venting. The paper describes a CFD model able to reproduce the INERIS experiment performed using 12 m3 volume tank when 300 kg of ammonia were vented during 460 s from the ullage through the pipe to the atmosphere. The model is based on the volume-of-fluid method combined with Lee’s model for mass transfer between phases. Extensive calibration trials were conducted to examine the impact of surrounding temperature conditions. It allowed to establish the range of time relaxation parameter values of Lee evaporation-condensation model specific for liquid ammonia tank venting. Simulations reproduced accurately the experimentally measured final pressure in the tank and the amount of ammonia released during venting. Liquid ammonia boiling is triggered by reduction of pressure and takes place throughout the liquid causing the pressure recovery phenomenon. Numerical simulations demonstrated that pressure recovery phenomenon is driven by the characteristic time delay associated with the rise of vapour bubbles generated by flash boiling and the subsequent release of evaporated ammonia into the tank ullage space. The developed CFD model can be used as a contemporary tool for safety engineering and development of tank management strategies for liquid ammonia storage.

Flow Dynamics of Eyring–Powell Nanofluid on Porous Stretching Cylinder under Magnetic Field and Viscous Dissipation Effects

The current paper scrutinized the flow dynamics of Eyring–Powell nanofluid on porous stretching cylinder under the effects of magnetic field and viscous dissipation by employing Cattaneo–Christov theory. In order to study impacts of thermophoretic force and Brownian motion, the two-phase (Buongiorno) model is considered. As a consequence, very nonlinear PDEs that govern flow problem were formulated, transformed into ODEs via relevant similarity variables, as well as tackled by utilizing R-K-45 integration scheme along with the shooting technique in the MATLAB R2018a software. Consequently, the numerical simulations reveal that Eyring–Powell fluid, curvature, velocity ratio parameters have the propensity to raise nanofluid velocity. Nanofluid temperature shows an increasing pattern with magnetic, curvature, dissipative heating, and thermophoresis parameters. Besides, Prandtl number, Eyring–Powell fluid, velocity ratio, thermal relaxation time, and porous parameters indicate the declining impact against the nanofluid temperature. Hence, the porous medium reasonably and successfully managed nanofluid temperature as well as the overall thermal system in terms of system cooling. The concentration profile gets fall down with escalating values of Schmidt number, magnetic, curvature, dissipative heating, thermophoresis, Brownian motion, and solutal relaxation time parameters. Moreover, coefficient of the skin friction gets rise for larger values of Eyring–Powell fluid, magnetic and curvature parameters however porous medium and velocity ratio parameters reveal the opposite trends on it. The magnetic, curvature, Eyring–Powell fluid, velocity ratio, and dissipative heating parameters indicate increasing impacts on both Nusselt N u and Sherwood S h numbers even though both N u and S h get cut down with the porous medium parameter. Moreover, an excellent and sound agreement was attained up on comparing coefficients of the skin friction for the current result against that of previously published literatures under some limiting cases.

Entropy generation analysis on Darcy-Forchheimer Maxwell nanofluid flow past a porous stretching sheet with threshold Non-Fourier heat flux model and Joule heating

This research paper inspects the flow characteristics of a magnetohydrodynamic (MHD) Maxwell nanofluid in the presence of a Darcy-Forchheimer (DF) model applied to a stretching sheet. Additionally, numerical analysis is performed to evaluate the findings, utilizing a nanofluid composed of copper (Cu) suspended in water. The energy equation in this study incorporates thermal radiation, viscous dissipation, the Cattaneo-Christov heat flux model, and joule heating. The entropy generation is then determined based on the obtained solutions for temperature and velocity, in compliance with the flow constraints. By applying suitable similarity transformations, the conservative equations of energy and momentum are transformed into nonlinear ordinary differential equations (ODEs). To solve these equations, a bvp4c method implemented through Matlab software is employed. By taking into account pertinent characteristics like the relaxation Prandtl number, magnetic parameter, time parameter, radiation parameter, and others, one can analyse the normalized shear stress at the wall, temperature profile, and rate of heat flux. For practical purposes, the local Nusselt and number of skin frictions are determined for various modified values of the physical constraints. This provides vital insights about the system's behavior under various settings. The graphical results indicate that the velocity profile exhibits a decrease as the volume fraction, magnetic parameter, Maxwell fluid parameter, and inertia coefficient parameter increase. The entropy generation demonstrates an increase with growing values of the Brinkman number and magnetic parameter. On the other hand, entropy generation declines with increasing values of the temperature ratio parameter. The Bejan number exhibits the opposite behavior of the entropy generation. Specifically, as the Bejan number increases, the entropy generation decreases, and vice versa.

Numerical Simulation Method for Flash Evaporation with Circulating Water Based on a Modified Lee Model

Flash evaporation processes are widely adopted in the desalination, food processing, waste heat recovery and other industries for heat extraction or product separation. In this paper, a pressure-driven phase transition model is developed by improving the Lee model and combined with the VOF (Volume of Fluid) method to numerically simulate the flash evaporation process. In this modified Lee phase transition model, the driving force for the rates of the local phase transition is calculated using the local temperature and static pressure magnitude. Numerical simulations are carried out in a water-circulating flash chamber and compared with the experimental results to obtain the values of the time relaxation parameters. And the non-equilibrium fraction of the outlet water can be effectively obtained under different conditions of flow rate, inlet temperature and initial liquid level height. The time relaxation factor takes values from 0.195 to 0.43 (Pout,v = 19.9 kPa) and from 0.31 to 0.92 (Pout,v = 31.2 kPa) with increasing superheat. In addition, the model can effectively represent the evolution of the unstable flow flash evaporation from the initial rapid boiling state to dynamic equilibrium.

Computational biomedical simulations of Cattaneo Christov heat flux model in diseased arteries with a combination of aneurysm and stenosis

In present article, computational biomedical simulations of Cattaneo Christov heat flux model in diseased arteries with a combination of aneurysm and stenosis is implemented in order to investigate its effects on the blood flow across the cylinder, the magnetic field is also applied. Stenosis causes a decrease in cross sectional area of the vascular lumen and is produced by the addition of fats and other hydrocarbons below the vascular endothelium of the arterial wall. For the heat transfer, Fourier law has parabolic nature which represents the temperature field moves fast with initial disturbance and spreads in whole substance. Cattaneo introduced additional parameter of relaxation time in the classical Fourier's law to get around this problem, creating the option of carrying heat by the motion of thermal waves with a slow pace. Using a mild stenotic assumption, we normalized the bi-directional, non-linear momentum and energy equations and reduce them to a unidirectional flow. Using the finite difference method, we discretized the associated partial differential equations. The resulting algebraic problem is solved numerically by using Matlab software. As a result, numerical solutions are obtained and these results are used to test the effects of different emerging parameters on flow pattern that are demonstrated in velocity, temperature, wall shear stress and flow rate profiles. The cross-sectional behavior of the blood flow patterns is also developed using streamlines for general readers.

Refined Schemes for Computing the Dynamics of Elastoviscoplastic Media

For a stable numerical solution of the system of equations governing an elastoviscoplastic continuous medium model, a second-order explicit-implicit scheme is proposed. An explicit approximation is used for the equations of motion, and an implicit approximation, for the constitutive relations containing a small relaxation time parameter in the denominator of the nonlinear free terms. A second-order implicit approximation for isotropic and anisotropic elastoviscoplastic models is constructed to match the orders of approximation of the explicit elastic and implicit adjustment steps. Refined formulas for correcting the stress deviators after the elastic step are derived for various viscosity function representations. The resulting solutions of the second-order implicit approximation for the stress deviators of the elastoviscoplastic equations admit passage to the limit as the relaxation time tends to zero. The correcting formulas obtained via this passage to the limit can be treated as regularizers of the numerical solutions to the elastoplastic systems.

The Role of Rubrene Concentration on Dielectric Parameters of Nematic Liquid Crystal

In this study, the dielectric parameters of E7 coded nematic liquid crystal (NLC) composites containing the different amounts of rubrene fluorescent dye were investigated. E7, E7+0.5 wt.% Rubrene, and E7+1.0 wt.% Rubrene samples were prepared. Frequency dependent dielectric constants (ɛ′ and ɛ′′), dielectric anisotropy (Δε′), and ac conductivity (σac) graphs of rubrene doped E7 NLC composites were obtained by dielectric spectroscopy method and compared with pure E7 NLC. By using these graphs, relaxation frequency (fR), relaxation time (τR), dielectric strength (δɛ′), and crossover frequency (fc) parameters of the E7 NLC and its rubrene doped composites were determined. An increase in fR from 3.045 MHz to 3.697 MHz for 0 V and from 627 kHz to 686 kHz for 40 V was observed with increasing rubrene concentration. On the other hand, a decrease in τR from 0.052 μs to 0.043 μs for 0 V and from 0.254 μs to 0.232 μs for 40 V was seen with increasing rubrene concentration. Furthermore, an increase in fc from 1.145 MHz to 1.298 MHz was obtained with increasing rubrene concentration. The results show that the dielectric parameters change with the concentration of rubrene and it is thought that this study will provide a basis for investigating the dielectric properties of rubrene doped NLC composites. Moreover, it is concluded that the produced composites are a suitable base material for electro-optical device applications such as smart displays, photonics and electrical circuit elements.

Oblique stagnation point flow of magnetized Maxwell fluid over a stretchable Riga plate with Cattaneo-Christov heat flux and convective conditions

The current work deals with the oblique stagnation point flow phenomenon of a rate-type Maxwell fluid with the significance of the Cattaneo-Christov double diffusion theory. The Cattaneo-Christov theory is illustrated through the modified form of Fourier’s and Fick’s laws. The steady magnetized flow mechanism is observed in two dimensions through a stretchable convective Riga plate. In the mass and heat transfer analysis, the consequences of chemical reactions and thermal radiation are also incorporated. With the contribution of relevant dimensionless quantities, the setup of dimensionless equations is acquired which further takes the form of nonlinear equations. The physical significance of the numerous parameters on different features of the flow phenomenon is graphically exhibited. The interesting physical quantities are computed and numerically evaluated relative to the pertinent parameters. This study reveals that the thermal relaxation time parameter lowers the rate of heat transfer, and the thermal Biot number enhances the rate of heat transport. Moreover, the Deborah number minimizes the flow field of both tangential and axial velocities.

A modified dynamic Lee model for two-phase closed thermosyphon (TPCT) simulation

A modified model consisting of a dynamic Lee model, volume of fluid model, and continuum surface force model is developed. The modified model investigates heat transfer characteristics of the vapor–liquid phase change process and details of the two-phase flow during operation of a two-phase closed thermosyphon. The mass transfer time relaxation parameters for the Lee phase change model are the most critical coefficients which determine the rate of the vapor–liquid phase change. A dynamic adjustment of the mass transfer time relaxation parameters for the Lee phase change model is realized based on the amount of mass transfer between the vapor and liquid phases and the values of the mass transfer time relaxation parameters become stabilized. The relative error between the modified model and experimental data for the temperature distribution is 5%, representing an acceptable agreement. Compared with the original model, the maximum thermal resistance errors in evaporation section and condensation section are reduced by 19.3% and 107.1%, respectively. These results indicate that the modified model can provide good corrections with high accuracy.

Some exact and approximate solutions to a generalized Maxwell–Cattaneo equation

AbstractThe simple heat conduction equation in one‐space dimension does not have the property of a finite speed for information transfer. A partial resolution of this difficulty can be obtained within the context of heat conduction by the introduction of a partial differential equation (PDE) called the Maxwell–Cattaneo (M‐C) equation, elsewhere called the damped wave equation, a special case of the telegraph equation. We construct a generalization to the M‐C equation by allowing the relaxation time parameter to be a function of temperature. In the balance of the paper, we present a variety of special exact and approximate solutions to this nonlinear PDE.