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Keywords = thermodiffusion coefficient

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20 pages, 2800 KB  
Article
Dual Fuel Combustion Modelling Using the G-Equation Model and the Respective Tuning of Flame Stretch Parameters
by Anthony Theodore Saliba, La Xiang, Jean-Paul Mollicone, Yu Ding and Mario Farrugia
Energies 2026, 19(4), 1021; https://doi.org/10.3390/en19041021 - 14 Feb 2026
Viewed by 452
Abstract
This article presents the simulation methodology and results of dual-fuel combustion for internal combustion engines (ICE). Simulations were performed in ANSYS Forte®, which modeled flame propagation using the G-equation model, and results were validated against experimental data. The article also presents [...] Read more.
This article presents the simulation methodology and results of dual-fuel combustion for internal combustion engines (ICE). Simulations were performed in ANSYS Forte®, which modeled flame propagation using the G-equation model, and results were validated against experimental data. The article also presents results from simulations performed in Converge CFD®, which used the SAGE combustion model, presented in previous work. Typical combustion modelling challenges in such ICE simulations are discussed, and the applied methodology is described. The range of methane-air equivalence ratio was 0.47 ≤ ϕ ≤ 0.57 across four load conditions with a rotational velocity range of 1228 ≤ RPM ≤ 1800. The methane-air combustion at these low equivalence ratios led to the required tuning of the stretch factor coefficient used in the flame speed model in ANSYS Forte® due to methane’s thermo-diffusive effects at lean equivalence ratios. As a result, the flame stretch factor coefficient was found to increase with decreasing equivalence ratio. The study thus demonstrates the importance of flame stretch sensitivity and thermo-diffusive instabilities in ICE combustion through CFD combustion simulations. Full article
(This article belongs to the Section I2: Energy and Combustion Science)
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18 pages, 1108 KB  
Article
Three-Phase-Lag Effect on Rayleigh Waves in a Generalized Thermoelastic Diffusion Medium with Modified Couple Stress
by Emad K. Jaradat, Sayed M. Abo-Dahab, Rajneesh Kumar and Eslam S. Elidy
Crystals 2025, 15(7), 588; https://doi.org/10.3390/cryst15070588 - 22 Jun 2025
Cited by 2 | Viewed by 903
Abstract
This study examines the behavior of Rayleigh waves propagating through a homogeneous, isotropic material, analyzed using a three-phase-lag thermoelastic diffusion framework enhanced by modified couple stress theory. The mathematical model integrates coupled thermoelastic and diffusive effects, incorporating phase-lags associated with (1) temperature gradients, [...] Read more.
This study examines the behavior of Rayleigh waves propagating through a homogeneous, isotropic material, analyzed using a three-phase-lag thermoelastic diffusion framework enhanced by modified couple stress theory. The mathematical model integrates coupled thermoelastic and diffusive effects, incorporating phase-lags associated with (1) temperature gradients, (2) heat flux, and (3) thermal displacement gradients. By solving the derived governing equations analytically subject to stress-free, thermally insulated, and impermeable boundary conditions, we obtain the characteristic secular equation for Rayleigh wave propagation. Numerical simulations conducted on a copper medium evaluate how the secular equation’s determinant, wave velocity, and attenuation coefficient vary with angular frequency. The analysis focuses particularly on the influence of phase-lag parameters, including thermal and diffusion gradients and relaxation times. Results demonstrated that increasing the displacement gradient phase-lag elevated the secular determinant but reduced wave velocity and attenuation, while temperature gradient phase-lags exhibited the opposite trend. The study highlights the sensitivity of Rayleigh wave propagation to thermo-diffusive coupling and microstructural effects, offering insights applicable to seismic wave analysis, geophysical exploration, and material processing. Comparisons with prior theories underscore the model’s advancement in capturing size-dependent and memory-dependent phenomena. Full article
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32 pages, 2184 KB  
Article
Thermo-Mechanical and Mechano-Thermal Effects in Liquids Explained by Means of the Dual Model of Liquids
by Fabio Peluso
Thermo 2023, 3(4), 625-656; https://doi.org/10.3390/thermo3040037 - 9 Nov 2023
Cited by 4 | Viewed by 3039
Abstract
We pursue to illustrate the capabilities of the Dual Model of Liquids (DML) showing that it may explain crossed effects notable in Non-Equilibrium Thermodynamics (NET). The aim of the paper is to demonstrate that the DML may correctly model the thermodiffusion, in particular [...] Read more.
We pursue to illustrate the capabilities of the Dual Model of Liquids (DML) showing that it may explain crossed effects notable in Non-Equilibrium Thermodynamics (NET). The aim of the paper is to demonstrate that the DML may correctly model the thermodiffusion, in particular getting formal expressions for positive and negative Soret coefficient, and another “unexpected” mechano-thermal effect recently discovered in liquids submitted to shear strain, for which the first-ever theoretical interpretation is provided. Both applications of the DML are supported by the comparison with experimental data. The phenomenology of liquids, either pure or mixtures, submitted to external force fields is characterized by coupled effects, for instance mechano-thermal and thermo-mechanical effects, depending on whether the application of a mechanical force field generates a coupled thermal effect in the liquid sample or vice-versa. Although these phenomena have been studied since their discoveries, dating back to the XIX century, no firm theoretical interpretation exists yet. Very recently the mesoscopic model of liquids DML has been proposed and its validity and applicability demonstrated in several cases. According to DML, liquids are arranged on a mesoscopic scale by means of aggregates of molecules, or liquid particles. These structures share the liquid world with a population of lattice particles, i.e., elastic waves that interact with the liquid particles by means of an inertial force, allowing the mutual exchange of energy and momentum between the two populations. The hit particle relaxes the acquired energy and momentum due to the interaction, giving them back to the system a step forward and a time-lapse later, alike in a tunnel effect. Full article
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13 pages, 310 KB  
Review
Physicochemical Mechanics and Nonequilibrium Chemical Thermodynamics
by Nikolai Meerovich Kocherginsky
Entropy 2023, 25(9), 1332; https://doi.org/10.3390/e25091332 - 14 Sep 2023
Viewed by 1966
Abstract
Equilibrium thermodynamics answers the question, “by how much?” Nonequilibrium thermodynamics answers the question “how fast?” The physicochemical mechanics approach presented in this article answers both of these questions. It also gives equilibrium laws and expressions for all major transport coefficients and their relations, [...] Read more.
Equilibrium thermodynamics answers the question, “by how much?” Nonequilibrium thermodynamics answers the question “how fast?” The physicochemical mechanics approach presented in this article answers both of these questions. It also gives equilibrium laws and expressions for all major transport coefficients and their relations, which was previously impossible. For example, Onsager’s reciprocal relations only tell us that symmetric transport coefficients are equal, and even for these, the value is often not known. Our new approach, applicable to non-isolated systems, leads to a new formulation of the second law of thermodynamics and agrees with entropy increase in spontaneous processes for isolated systems. Instead of entropy, it is based on a modified Lagrangian formulation which always increases during system evolution, even in the presence of external fields. This article will present numerous examples of physicochemical mechanics can be applied to various transport processes and their equilibriums, including thermodiffusion and different surface processes. It has been proven that the efficiency of a transport process with an actual steady-state flux (as opposed to a reversible process near equilibrium) is 50%. Finally, an analogy between physicochemical mechanics and some social processes is mentioned. Full article
(This article belongs to the Special Issue Nonequilibrium Thermodynamics and Its Interdisciplinary Applications)
25 pages, 4162 KB  
Article
Comparison and Analysis of Diffusion Models: Growth Kinetics of Diiron Boride Layers on ASTM A283 Steel
by Martín Ortiz-Domínguez, Oscar Armando Gómez-Vargas, Mariana Bárcenas-Castañeda and Víctor Augusto Castellanos-Escamilla
Materials 2022, 15(23), 8420; https://doi.org/10.3390/ma15238420 - 26 Nov 2022
Cited by 11 | Viewed by 2581
Abstract
Hard-coated surfacing of a few micrometers is widely applied to increase the efficiency of tools, e.g., for cutting, forming, and casting applications. Therefore, the base thermodiffusion surface treatment is a practical solution to these issues by hardening surface layers with interstitial elements such [...] Read more.
Hard-coated surfacing of a few micrometers is widely applied to increase the efficiency of tools, e.g., for cutting, forming, and casting applications. Therefore, the base thermodiffusion surface treatment is a practical solution to these issues by hardening surface layers with interstitial elements such as carbon, nitrogen, and boron. In particular, within this study, the growth kinetics of an iron boride layer on ASTM 283 steel were investigated with two diffusion models of the powder-pack boriding technique in the temperature range of 1123–1273 K with different treatment periods. The first model, called the steady-state diffusion model, used the modified version of the mass balance equations at the Fe2B/substrate growth interface, the parabolic growth law, and the solution of Fick’s second law without time dependence. At the same time, the second diffusion model was based on Goodman’s method, also called the integral heat balance method. Afterward, the diffusion coefficient of boron in the Fe2B phase was calculated by fitting the experimental data to the models. Nevertheless, the estimated value for the activation energy of ASTM A238 steel in both diffusion models was coincident (168.2 kJ∙mol−1). A mathematical analysis was implemented by means of a power series (Taylor series) to explain this similarity. The SEM examinations showed a solid tendency to saw-tooth morphology at the growth interface with the formation of the Fe2B layer, whose presence was verified by XRD analysis. The tribological characterizations, including the tests of Rockwell-C indentation, pin-on-disc, and Vickers hardness test method, were used to analyze the antiwear features of the Fe2B layers. Finally, this value of energy was compared to the literature for its experimental validation. Full article
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14 pages, 4177 KB  
Article
Effect of Temperature Gradient on Chloride Ion Diffusion in Nuclear Reactor Containment Building Concrete
by Boohyun An, Pyungyeon Cho, Remilekun A. Shittu, Tae-Yeon Kim, Paul Rostron, Akram AlFantazi and Yongsun Yi
Energies 2022, 15(15), 5581; https://doi.org/10.3390/en15155581 - 1 Aug 2022
Cited by 9 | Viewed by 2286
Abstract
Chloride diffusion through concrete is influenced by harsh environmental conditions such as high ambient temperature and relative humidity. This paper examined the influence of temperature gradient on chloride diffusion in concrete under high ambient temperature conditions. Chloride diffusion tests using cylindrical concrete samples [...] Read more.
Chloride diffusion through concrete is influenced by harsh environmental conditions such as high ambient temperature and relative humidity. This paper examined the influence of temperature gradient on chloride diffusion in concrete under high ambient temperature conditions. Chloride diffusion tests using cylindrical concrete samples were performed in constant temperature and temperature gradient conditions. In a temperature gradient condition, a much higher chloride concentration was measured than at constant temperatures, which could not be explained only by the mass diffusion driven by the concentration gradient. A new analytical model of chloride diffusion with the mass diffusion term including the temperature effect and the thermo-diffusion term including the temperature gradient effect was applied to the results, which showed that the thermo-diffusion contribution was significant. Using the analytical model with the mass diffusion (DCl) and thermo-diffusion (DT) coefficients, the service life of reactor containment buildings (RCBs) in nuclear power plants (NPPs) in the Middle Eastern and North African (MENA) region was estimated. The results showed that the service life of the RCBs could be reduced by the temperature gradient, indicating the possible application of the proposed analytical model. Full article
(This article belongs to the Special Issue New Challenges in Nuclear Energy Systems)
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16 pages, 2522 KB  
Article
A Hidden Anomaly in the Binary Mixture Natural Convection Subject to Flux Boundary Conditions
by Peter Vadasz
Physics 2021, 3(1), 144-159; https://doi.org/10.3390/physics3010012 - 23 Mar 2021
Cited by 2 | Viewed by 2925
Abstract
The problem of natural convection in a binary mixture subject to realistic boundary conditions of imposed zero mass flux on the solid walls shows solutions that might lead to unrealistic negative values of the mass fraction (or solute concentration). This anomaly is being [...] Read more.
The problem of natural convection in a binary mixture subject to realistic boundary conditions of imposed zero mass flux on the solid walls shows solutions that might lead to unrealistic negative values of the mass fraction (or solute concentration). This anomaly is being investigated in this paper, and a possible way of addressing it is suggested via a mass-fraction-dependent thermodiffusion coefficient that can have negative values in regions of low mass fractions. Full article
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12 pages, 6070 KB  
Article
Numerical Analysis of Thermophoresis of a Charged Spheroidal Colloid in Aqueous Media
by Yi Zhou, Yang Yang, Changxing Zhu, Mingyuan Yang and Yi Hu
Micromachines 2021, 12(2), 224; https://doi.org/10.3390/mi12020224 - 23 Feb 2021
Cited by 6 | Viewed by 2844
Abstract
Thermophoresis of charged colloids in aqueous media has wide applications in biology. Most existing studies of thermophoresis focused on spherical particles, but biological compounds are usually non-spherical. The present paper reports a numerical analysis of the thermophoresis of a charged spheroidal colloid in [...] Read more.
Thermophoresis of charged colloids in aqueous media has wide applications in biology. Most existing studies of thermophoresis focused on spherical particles, but biological compounds are usually non-spherical. The present paper reports a numerical analysis of the thermophoresis of a charged spheroidal colloid in aqueous media. The model accounts for the strongly coupled temperature field, the flow field, the electric potential field, and the ion concentration field. Numerical simulations revealed that prolate spheroids move faster than spherical particles, and oblate spheroids move slower than spherical particles. For the arbitrary electric double layer (EDL) thickness, the thermodiffusion coefficient of prolate (oblate) spheroids increases (decreases) with the increasing particle’s dimension ratio between the major and minor semiaxes. For the extremely thin EDL case, the hydrodynamic effect is significant, and the thermodiffusion coefficient for prolate (oblate) spheroids converges to a fixed value with the increasing particle’s dimension ratio. For the extremely thick EDL case, the particle curvature’s effect also becomes important, and the increasing (decreasing) rate of thermodiffusion coefficient for prolate (oblate) spheroids is reduced slightly. Full article
(This article belongs to the Special Issue Morphology and Mechanics in Microfluidics)
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19 pages, 1581 KB  
Article
A Finite Element Simulation of the Active and Passive Controls of the MHD Effect on an Axisymmetric Nanofluid Flow with Thermo-Diffusion over a Radially Stretched Sheet
by Bagh Ali, Xiaojun Yu, Muhammad Tariq Sadiq, Ateeq Ur Rehman and Liaqat Ali
Processes 2020, 8(2), 207; https://doi.org/10.3390/pr8020207 - 7 Feb 2020
Cited by 60 | Viewed by 5189
Abstract
The present study investigated the steady magnetohydrodynamics of the axisymmetric flow of a incompressible, viscous, electricity-conducting nanofluid with convective boundary conditions and thermo-diffusion over a radially stretched surface. The nanoparticles’ volume fraction was passively controlled on the boundary, rather than actively controlled. The [...] Read more.
The present study investigated the steady magnetohydrodynamics of the axisymmetric flow of a incompressible, viscous, electricity-conducting nanofluid with convective boundary conditions and thermo-diffusion over a radially stretched surface. The nanoparticles’ volume fraction was passively controlled on the boundary, rather than actively controlled. The governing non-linear partial differential equations were transformed into a system of nonlinear, ordinary differential equations with the aid of similarity transformations which were solved numerically, using the very efficient variational finite element method. The coefficient of skin friction and rate of heat transfer, and an exact solution of fluid flow velocity, were contrasted with the numerical solution gotten by FEM. Excellent agreement between the numerical and exact solutions was observed. The influences of various physical parameters on the velocity, temperature, and solutal and nanoparticle concentration profiles are discussed by the aid of graphs and tables. Additionally, authentication of the convergence of the numerical consequences acquired by the finite element method and the computations was acquired by decreasing the mesh level. This exploration is significant for the higher temperature of nanomaterial privileging technology. Full article
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15 pages, 1141 KB  
Article
Thermophoresis: The Case of Streptavidin and Biotin
by Doreen Niether, Mona Sarter, Bernd W. Koenig, Jörg Fitter, Andreas M. Stadler and Simone Wiegand
Polymers 2020, 12(2), 376; https://doi.org/10.3390/polym12020376 - 7 Feb 2020
Cited by 20 | Viewed by 5488
Abstract
Thermophoretic behavior of a free protein changes upon ligand binding and gives access to information on the binding constants. The Soret effect has also been proven to be a promising tool to gain information on the hydration layer, as the temperature dependence of [...] Read more.
Thermophoretic behavior of a free protein changes upon ligand binding and gives access to information on the binding constants. The Soret effect has also been proven to be a promising tool to gain information on the hydration layer, as the temperature dependence of the thermodiffusion behavior is sensitive to solute–solvent interactions. In this work, we perform systematic thermophoretic measurements of the protein streptavidin (STV) and of the complex STV with biotin (B) using thermal diffusion forced Rayleigh scattering (TDFRS). Our experiments show that the temperature sensitivity of the Soret coefficient is reduced for the complex compared to the free protein. We discuss our data in comparison with recent quasi-elastic neutron scattering (QENS) measurements. As the QENS measurement has been performed in heavy water, we perform additional measurements in water/heavy water mixtures. Finally, we also elucidate the challenges arising from the quantiative thermophoretic study of complex multicomponent systems such as protein solutions. Full article
(This article belongs to the Special Issue Synthesis, Characterization and Simulation of Soft Matter with EUSMI)
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25 pages, 2325 KB  
Article
Structural, Thermodiffusive and Thermoelectric Properties of Maghemite Nanoparticles Dispersed in Ethylammonium Nitrate
by Kakoli Bhattacharya, Mitradeep Sarkar, Thomas J. Salez, Sawako Nakamae, Gilles Demouchy, Fabrice Cousin, Emmanuelle Dubois, Laurent Michot, Régine Perzynski and Véronique Peyre
ChemEngineering 2020, 4(1), 5; https://doi.org/10.3390/chemengineering4010005 - 8 Jan 2020
Cited by 18 | Viewed by 5078
Abstract
Ethylammonium nitrate (ionic liquid) based ferrofluids with citrate-coated nanoparticles and Na + counterions were synthesized for a wide range of nanoparticle (NP) volume fractions ( Φ ) of up to 16%. Detailed structural analyses on these fluids were performed using magneto-optical birefringence and [...] Read more.
Ethylammonium nitrate (ionic liquid) based ferrofluids with citrate-coated nanoparticles and Na + counterions were synthesized for a wide range of nanoparticle (NP) volume fractions ( Φ ) of up to 16%. Detailed structural analyses on these fluids were performed using magneto-optical birefringence and small angle X-ray scattering (SAXS) methods. Furthermore, the thermophoretic and thermodiffusive properties (Soret coefficient S T and diffusion coefficient D m ) were explored by forced Rayleigh scattering experiments as a function of T and Φ . They were compared to the thermoelectric potential (Seebeck coefficient, Se) properties induced in these fluids. The results were analyzed using a modified theoretical model on S T and Se adapted from an existing model developed for dispersions in more standard polar media which allows the determination of the Eastman entropy of transfer ( S ^ NP ) and the effective charge ( Z 0 e f f ) of the nanoparticles. Full article
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12 pages, 2372 KB  
Article
Thermal Property Measurement of Nanofluid Droplets with Temperature Gradients
by Dong-Wook Oh
Energies 2020, 13(1), 244; https://doi.org/10.3390/en13010244 - 3 Jan 2020
Cited by 7 | Viewed by 2648
Abstract
In this study, the 3ω method was used to determine the thermal conductivity of nanofluids (ethylene glycol containing multi-walled carbon nanotubes (MWCNTs)) with temperature gradients. The thermal modeling of the traditional 3ω method was modified to measure the spatial variation of thermal conductivity [...] Read more.
In this study, the 3ω method was used to determine the thermal conductivity of nanofluids (ethylene glycol containing multi-walled carbon nanotubes (MWCNTs)) with temperature gradients. The thermal modeling of the traditional 3ω method was modified to measure the spatial variation of thermal conductivity within a droplet of nanofluid. A direct current (DC) heater was used to generate a temperature gradient inside a sample fluid. A DC heating power of 14 mW was used to provide a temperature gradient of 5000 K/m inside the sample fluid. The thermal conductivity was monitored at hot- and cold-side 3ω heaters with a spacing of 0.3 mm. Regarding the measurement results for the hot and cold 3ω heaters, when the temperature gradient was applied, the maximum thermal conductivity difference was determined to be 3% of the original value. By assuming that the thermo-diffusion of MWCNTs was entirely responsible for this difference, the Soret coefficient of the MWCNTs in the ethylene glycol was calculated to be −0.749 K−1. Full article
(This article belongs to the Special Issue Photo Thermal Conversion and Pool Boiling Heat Transfer of Nanofluid)
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21 pages, 960 KB  
Article
Finite Element Analysis of Thermo-Diffusion and Multi-Slip Effects on MHD Unsteady Flow of Casson Nano-Fluid over a Shrinking/Stretching Sheet with Radiation and Heat Source
by Liaqat Ali, Xiaomin Liu, Bagh Ali, Saima Mujeed and Sohaib Abdal
Appl. Sci. 2019, 9(23), 5217; https://doi.org/10.3390/app9235217 - 30 Nov 2019
Cited by 92 | Viewed by 3827
Abstract
In this article, we probe the multiple-slip effects on magnetohydrodynamic unsteady Casson nano-fluid flow over a penetrable stretching sheet, sheet entrenched in a porous medium with thermo-diffusion effect, and injection/suction in the presence of heat source. The flow is engendered due to the [...] Read more.
In this article, we probe the multiple-slip effects on magnetohydrodynamic unsteady Casson nano-fluid flow over a penetrable stretching sheet, sheet entrenched in a porous medium with thermo-diffusion effect, and injection/suction in the presence of heat source. The flow is engendered due to the unsteady time-dependent stretching sheet retained inside the porous medium. The leading non-linear partial differential equations are transmuted in the system of coupled nonlinear ordinary differential equations by using appropriate transformations, then the transformed equations are solved by using the variational finite element method numerically. The velocity, temperature, solutal concentration, and nano-particles concentration, as well as the rate of heat transfer, the skin friction coefficient, and Sherwood number for solutal concentration, are presented for several physical parameters. Next, the effects of these various physical parameters are conferred with graphs and tables. The exact values of flow velocity, skin friction, and Nusselt number are compared with a numerical solution acquired with the finite element method (FEM), and also with numerical results accessible in literature. In the end, we rationalize the convergence of the finite element numerical solution, and the calculations are carried out by reducing the mesh size. Full article
(This article belongs to the Section Nanotechnology and Applied Nanosciences)
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14 pages, 879 KB  
Article
Thermo-Diffusion and Multi-Slip Effect on an Axisymmetric Casson Flow over a Unsteady Radially Stretching Sheet in the Presence of Chemical Reaction
by Faraz Faraz, Syed Muhammad Imran, Bagh Ali and Sajjad Haider
Processes 2019, 7(11), 851; https://doi.org/10.3390/pr7110851 - 14 Nov 2019
Cited by 58 | Viewed by 3711
Abstract
The objective of this article is to investigate the impacts of thermo-diffusion effect on unsteady axisymmetric Casson flow over a time-dependent radially stretching sheet with a multi-slip parameter and the force of chemical reaction. We employed an established similarity transformation to this non-linear [...] Read more.
The objective of this article is to investigate the impacts of thermo-diffusion effect on unsteady axisymmetric Casson flow over a time-dependent radially stretching sheet with a multi-slip parameter and the force of chemical reaction. We employed an established similarity transformation to this non-linear partial differential system to convert it into a system of ordinary differential equations. The numerical results are attained for this system by using KELLER-BOX implicit finite difference scheme. It has great reliability and accuracy even a very short time period for computational simulation. The impacts of influential flow parameters on fluid flow are sketched through graphs and the numerical results are thoroughly argued. The temperature, velocity and wall concentration control parameters are analyzed. (i) It is witnessed that chemical reaction is not favorable to enhance the velocity profile. (ii) Multi-slip parameters vary inversely with velocity profile. (iii) The fluid concentration in its boundary layer decreases with the increase of heavier species, the parameter of the reaction rate and the exponent of power law for fluids having Prandtl number = 10.0, 15.0, 20.0 and 25.0. Moreover, the skin-friction-coefficient factor and Nusselt-number are compared with the published work. A strong numerical solution agreement is being observed. Full article
(This article belongs to the Special Issue Optimization of Heat and Mass Exchange)
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18 pages, 1021 KB  
Article
Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction
by Bagh Ali, Yufeng Nie, Shahid Ali Khan, Muhammad Tariq Sadiq and Momina Tariq
Processes 2019, 7(9), 628; https://doi.org/10.3390/pr7090628 - 17 Sep 2019
Cited by 98 | Viewed by 5037
Abstract
The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed [...] Read more.
The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations with the aid of appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The effects of various physical parameters on the velocity, temperature, solutal concentration, and nanoparticle concentration profiles as well as on the skin friction coefficient, rate of heat transfer, and Sherwood number for solutal concentration are discussed by the aid of graphs and tables. An exact solution of flow velocity, skin friction coefficient, and Nusselt number is compared with the numerical solution obtained by FEM and also with numerical results available in the literature. A good agreement between the exact and numerical solution is observed. Also, to justify the convergence of the finite element numerical solution, the calculations are carried out by reducing the mesh size. The present investigation is relevant to high-temperature nanomaterial processing technology. Full article
(This article belongs to the Special Issue Fluid Flow and Heat Transfer of Nanofluids)
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