Fractional order transport modelling of MoS₂-vegetable oil nanofluid with hall, radiation and thermophoretic effects under isothermal and ramped boundary conditions

Impacts of Buoyancy and Joule Heating on Unsteady MHD Fluid Flow Along a Semi‐Infinite Vertical Porous Plate With Dufour, Chemical Reaction, and Radiation Effect

The modern era is a time to have cost-effective and energy-efficient technology. This demand has made nanotechnology the most effective field. The focus of this article is to increase the efficiency of engine oil (EO). The flow of EO-based Casson nanofluid containing Molybdenum disulfide (MoS 2 ) nanoparticles is investigated with ramped wall conditions and thermal radiation. Analytical results are calculated via the Laplace transform. The impact of physical parameters on isothermal and ramped conditions is illustrated graphically and discussed in detail. The researchers found that flow, mass, and energy can be controlled by using ramped conditions. The variation in concentration, temperature, and velocity is exponential for isothermal conditions and steady for ramped wall conditions. Finally, the results of Nusselt numbers, skin frictions, and Sherwood numbers on both walls of the channel for both isothermal and ramped conditions are graphically depicted and discussed. For higher values of time the results of ramped and isothermal wall conditions are identical. It is found that the nanoparticles of MoS 2 enhance the lubrication and heat transport rates of EO.

Purpose The purpose of this study is to explore the impact of Joule heating, slip conditions, Dufour and Soret effects on three-dimensional magneto-convection of nanoliquid over a rotating surface in the existence of thermal radiation, viscous dissipation and internal heat generation/absorption. Design/methodology/approach The considered physical system is modelled by a set of partial differential equations (PDEs) with conditions at surface. Then, the nonlinear PDEs are altered into a system of ordinary differential equations and they are solved numerically by the Runge−Kutta−Fehlberg method. Plotting the collected velocity, temperature and solute concentration characteristics allows one to see how relevant parameters affect the results. Calculations are made for skin friction and the rate of heat and mass transfer. Findings The outcomes are portrayed in the form of tables and graphs with a wide range of parameter involved in the study. It is observed that the local thermal energy transfer rate enriches on increasing the value of both thermal and solute slips. The solutal slip parameter suppresses the solute transport rate and thermal slip supports the solute transport. Practical implications Combining the Dufour and Soret effects is used in oil reservoirs, binary alloy solidification and isotope separation in mixtures of gases. Heat exchangers, nuclear reactors and thermal engineering can all benefit from the usage of nanofluid with Joule heating. Social implications This study is mainly useful for thermal sciences and chemical engineering. Originality/value The investigation of the effects of slip circumstances and Joule heating on magnetohydrodynamic rotating nanoliquid stream with thermal radiation and cross-diffusion makes this work unique. The discoveries produced are valuable and distinctive, and they have applications in many areas of thermal science and technology.

Double diffusive flow in a cavity has attracted lots of attention due to its importance in many engineering fields such as ocean circulation, crystal growth, pollution transportation in air, metal manufacturing process and so on. When heat and mass transfer occur simultaneously in the double diffusive flow, the fluid flow is not only driven by the temperature gradient but also by the concentration gradient as well. In some cases, the Dufour and Soret effects will play a significant role in the double diffusive flow process. The energy flux created by the concentration gradient is called Dufour effect and the temperature gradient can cause the mass flux which is Soret effect. When taking the Soret and Dufour effects into account, the temperature and concentration equations become coupled with each other. However, the coupling diffusivities matrix can be diagonalized. The coupled system can then be transformed to two uncoupled diffusion-advection equations of two independent species. The temperature and concentration can be obtained by the inverse transformation of these two independent species. As a numerical method developed in the past two decades, lattice Boltzmann method (LBM) is powerful in simulating complex heat transfer and fluid mechanics problems. In the current study, a lattice Boltzmann model was developed and implemented for the double-diffusive convection with Soret and Dufour effects. Three distribution functions were used to compute the fluid velocity, specie 1, and specie 2, respectively. Specifically, a rectangular enclosure with horizontal temperature and concentration gradients was investigated. On the other hand, the graphics processing units (GPU) computing becomes popular since the advent of the NVIDIA’s CUDA platform, which includes both hardware components and software programming environment. The developed LBM code was adapted on the CUDA platform to accelerate the computation for parametric studies. The GPU is responsible for the parallel tasks while CPU tackles the sequential steps in the computation. To verify the improvement on computation ability by using GPU, the ratio of the computational time between CPU code and CUDA code is presented by simulating the classical natural convection process in a cavity. The computational speed can be accelerated by more than 20 times when large number of nodes is used. The fluid flow, temperature field and concentration field are presented for different Rayleigh numbers, buoyancy ratios, Prandtl numbers, Lewis numbers, aspect ratios, as well as Soret and Dufour coefficients. In addition, the results of Nusselt and Sherwood numbers are shown for different parametric conditions. As a result, lattice Boltzmann method was demonstrated as a good option to study the complex double-diffusive convection with Soret and Dufour effects in a vertical cavity.

Numerical study of double-diffusive convection in a vertical cavity with Soret and Dufour effects by lattice Boltzmann method on GPU

Transient non-Newtonian elastohydrodynamic lubrication (EHL) of elliptical point contacts was investigated numerically under both thermal and isothermal conditions. The multi-level technique used in Parts 1 and 2 of this series of papers for determining pressure and film thickness and the column-by-column relaxation technique used in Part 2 for temperature calculation were used again in this study. However, both Newtonian and non-Newtonian lubricant properties were considered, with the Ree-Eyring model being adopted in the latter case. The entrainment direction was assumed to be along the minor axis of the contact ellipse. A simplified numerical scheme for the evaluation of the equivalent shear stress and viscosity of the non-Newtonian lubricant was proposed and verified by comparing the steady-state thermal solutions without the simplification. The computing time required for a transient thermal and non-Newtonian case was typically ∼14 h on a personal computer with a 2.8 GHz central processing unit. For a steel-steel contact, the responses of the EHL films to a transient load impulse were determined for the non-Newtonian lubricant under both isothermal and thermal conditions. The isothermal non-Newtonian results were compared with those in Part 1, and the thermal results were compared with those presented in Part 2. A similar investigation for a glass-steel contact is also reported.

This article investigates numerically the effects of Hall current and rotation effects on radiating and chemically reacting unsteady MHD natural convection flow past an accelerated infinite vertical permeable plate in the presence of Soret and Dufour effects. The dimensionless coupled non-linear governing partial differential equations of the problem are solved numerically by employing finite element method. The influence of various physical parameters influencing the flow on the primary velocity, secondary velocity, temperature and the species concentration are displayed graphically whilst the numerical results of the primary skin friction, secondary skin-friction, Nusselt number and the Sherwood number are presented in tabular form. Results reveals that magnetic parameter, radiation parameter and chemical reaction rate tends to depreciate both primary and secondary velocity components whilst Hall, Soret and Dufour effects have reverse trend. Rotation parameter tends to retard fluid flow in the primary flow direction and accelerate fluid flow in the secondary flow direction. Thermal boundary layer thickness decreases with increasing radiation parameter whilst the reverse trend is noticed with increasing Dufour effect. Thermal diffusion effect causes to improve concentration boundary layer thickness whilst chemical reaction rate has reverse impact. These parameters have similar effect on the primary and secondary skin-frictions whilst opposite effect was noticed on the Nusselt and Sherwood numbers. This model problem finds an important in engineering and industrial application such as MHD generators, food processing, heat exchangers devices and internal rotation rate of the sun. HIGHLIGHTS The problem investigate the effects of Hall current and rotation effects on radiating and reacting on unsteady magnetohydrodynamics (MHD) natural convection heat and mass transfer flow over an infinite vertical porous plate embedded in a uniform porous medium taking Soret and Dufour effects into account The resulting partial differential equations governing the fluid flow are solved numerically using the finite element method. In order to determine the effects of various pertinent parameters and to investigate the important flow features, the numerical calculations for fluid velocity, temperature and species concentration are computed and shown graphically whereas skin friction, Nusselt number and Sherwood number at the plate are evaluated and depicted in tabular form The model problem finds an important in engineering and industrial application GRAPHICAL ABSTRACT

A theoretical exploration was reported to highlight the electrically viscous conducting fluid within a coaxial cylinder. Both the outer surface of the inner cylinder and the inner surface of the outer cylinder were porous, heated, and cool, respectively. The action of a simultaneous radial transverse magnetic field and velocity slip were imposed across the coaxial cylinder. For appropriate insight into the physical problem, the thermal Rosseland diffusion approximation was used to indicate the radiative heat flux in the energy equation. The aim is to investigate the effects of isothermal and isoflux conditions on slip-upshot heat transfer in a vertical coaxial cylinder due to nonlinear thermal radiation. The steady-state and unsteady solutions of the physical problem were provided and solved via regular perturbation and implicit finite different domains, respectively. It was noted that the magnetic and suction parameters reduced the fluid velocity and skin friction under both isothermal and isoflux conditions. Conversely, the Grashof number, thermal radiation, and injection parameters increased the fluid velocity, fluid temperature, and skin friction, with a more significant effect observed under isothermal conditions on the surfaces of the coaxial cylinder. Additionally, the sensitivity analysis revealed that the radiation parameter is highly sensitive under isothermal conditions, followed by the temperature difference parameter. In contrast, under isoflux conditions, the injection parameter shows extreme sensitivity, with the radiation parameter being the next most sensitive. The result reveals an excellent agreement between the analytical and numerical results at maximum time.

The corrosion behaviour of stainless steels and Ni-based alloys in nitrate salts under thermal cycling conditions in concentrated solar power plants

The rheology of different materials at the micro and macro levels is an area of great interest to many researchers, due to its important physical significance. Past experimental studies have proved the efficiency of the utilization of nanoparticles in different mechanisms for the purpose of boosting the heat transportation rate. The purpose of this study is to investigate heat and mass transport in a pseudo-plastic model past over a stretched porous surface in the presence of the Soret and Dufour effects. The involvement of tri-hybrid nanoparticles was incorporated into the pseudo-plastic model to enhance the heat transfer rate, and the transport problem of thermal energy and solute mechanisms was modelled considering the heat generation/absorption and the chemical reaction. Furthermore, traditional Fourier and Fick’s laws were engaged in the thermal and solute transportation. The physical model was developed upon Cartesian coordinates, and boundary layer theory was utilized in the simplification of the modelled problem, which appears in the form of coupled partial differential equations systems (PDEs). The modelled PDEs were transformed into corresponding ordinary differential equations systems (ODEs) by engaging the appropriate similarity transformation, and the converted ODEs were solved numerically via a Finite Element Procedure (FEP). The obtained solution was plotted against numerous emerging parameters. In addition, a grid independent survey is presented. We recorded that the temperature of the tri-hybrid nanoparticles was significantly higher than the fluid temperature. Augmenting the values of the Dufour number had a similar comportment on the fluid temperature and concentration. The fluid temperature increased against a higher estimation of the heat generation parameter and the Eckert numbers. The impacts of the buoyancy force parameter and the porosity parameter were quite opposite on the fluid velocity.

Comparison of urban airflow between solar-induced thermal wall and uniform wall temperature boundary conditions by coupling CitySim and CFD

A Numerical Approach of Hydromagnetic Flow Past Magnetic Field Inclination Wavering Tilted Porous Plate With Dufour and Soret Effects

The objective of the present work is to examine the characteristics of unsteady incompressible magnetohydrodynamic fluid flow around a permeable rotating vertical cone. The effects of thermal radiation, viscous dissipation, and the Soret and Dufour effects are investigated in the analysis of heat and mass transfer. The viscosity of the fluid is considered inversely proportional to the temperature, and the thermal conductivity of the fluid is considered directly proportional to the temper-ature. The governing equations are converted into ordinary differential equations using suitable similarity transformations, which are then solved numerically using bvp4c from MATLAB. Results obtained in this study are in excellent correlation with previously conducted studies. The results demonstrate that the Dufour and Soret effects subsequently reduce the heat transit rate (by –3.3%) and mass transit rate (by –1.2%) of the system. It is also detected that fluids with higher viscosity tend to increase tangential skin friction (+8.9%) and azimuthal skin friction (+8.3%). The heat transit rate of the system is found to be more efficient for fluids with higher viscosity and lower thermal conductivity and Eckert numbers. Further-more, the thickness of the momentum, thermal, and concentration boundary layers significantly reduces while the heat and mass transit rates (+17.8% and +18.3%, respectively) of the system become more efficient for greater values of the un-steadiness parameter.

The combined effects of diffusion-thermo and radiative absorption on free convective hydromagnetic heat-generating chemically reactive flow of Cu-water nanofluid past an instantaneously accelerated unlimited vertical plate nested in a porous medium are investigated. A comparative analysis is executed for both isothermal and ramped conditions. The set of transformed domain equations has been obtained using a closed form of the Laplace transform method with the help of the Heaviside step function. Graphical and tabular explanations are provided for the physical characteristics of several flow parameters affecting the problem. Graphs are generated using MATLAB computing software. Findings of the problem manifest that the diffusion-thermo parameter and the radiation absorption parameter intensify the velocity and fluid temperature in the entire fluid area. This augmentation is most prominent for copper nanoparticles. Concentration, temperature, and velocity profiles in the case of ramped conditions are less than in isothermal conditions. Furthermore, the ramped parameter amplifies the heat transfer rate while reversing the mass transfer rate. It is also established that the volume concentration of nanoparticles enhances the heat transfer rate. The present study is of great interest in numerous fields of industry and machine-building applications.

The use of foreign gases in laboratory film cooling experiments is attractive since variable density ratios can be achieved with coolant-to-freestream temperature ratios near unity, often reducing the cost and difficulty of the experimental campaign. In adiabatic effectiveness experiments employing pressure sensitive paint along with the mass transfer analogy to heat transfer, isothermal surfaces are often an experimental requirement. Furthermore, low temperature laboratory experiments using thermal techniques often employ relatively close matches between the coolant and freestream temperatures. Using foreign gases, however, introduces off-diagonal couplings of heat and mass transport, which can produce unexpected results in film cooling experiments. In particular, the Dufour effect — also called the diffusion-thermo effect — which is the transfer of thermal energy by mass transfer processes, can manifest in surface temperatures that break the traditional bounds of thermal adiabatic effectiveness experiments: outside the upper and lower bounds of the coolant and freestream temperature. Beyond the expected confusion for the researcher, this effect can also be detrimental to those that assume that matching the coolant and freestream temperatures are the necessary and sufficient conditions to ensure isothermal surface conditions in traditional pressure sensitive paint experiments. In this work, the influence of cooling gas selection, experimental temperature, and experimental freestream turbulence conditions are explored on a simulated leading edge with compound injection from a cylindrical cooling hole. Air, argon, carbon dioxide, helium, and nitrogen coolants were analyzed due to their use in prior film cooling studies. The Dufour effect was found to be significant when using helium as the coolant, though temperature separation was also observed in argon and carbon dioxide cases. Additionally, elevated experiment temperatures generally increased temperature separation. Finally, high freestream turbulence intensity was found to reduce, but not eliminate, the Dufour effect in helium experiments.