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Metal-cooled reactors generally use molten metals such as sodium, potassium or a combination of sodium and potassium because of their excellent heat transfer properties so that the reactor can operate at much lower pressures and higher temperatures. The purpose of this paper is to investigate the stability of natural convection in an inclined ring filled with molten potassium under the influence of a radial magnetism.

A numerical simulation of electrically conductive fluid natural convection stability is performed on an inclined cylindrical annulus under the influence of a radial magnetism. The upper and lower walls are adiabatic, while the internal and external cylinders are kept at even temperatures. The equations governing this fluid system are solved numerically using finite volume method. The SIMPLER algorithm is used for pressure-speed coupling in the momentum equation.

Numerical results for various effective parameters that solve the problem in the initial oscillatory state are discussed in terms of isobars, isotherms and flow lines in the annulus for a wide range of Hartmann numbers (0 ≤ Ha ≤ 80), inclination angles (0 ≤ γ ≤ 90°) and radii ratios λ ≤ 6. The dependency stability diagrams between complicated situations with the critical value of the Rayleigh number RaCr and the corresponding frequency FrCr are established on the basis of the numeric data of this investigation. The angle of inclination and the radii ratio of the annulus have a significant effect on the stabilization of the magneto-convective flux and show that the best stabilization of the natural oscillatory convection is obtained by the intensity of the strongest magnetic field, the high radii ratio and inclination of the annulus at γ = 30°.

This numerical model is selected for its various applications in technology and industry.

To the best of the authors’ knowledge, the influence of the inclination of the cylindrical annulus (ring), with various radii ratio, on natural oscillatory convection under a radial magnetism has never been investigated.

The purpose of this paper is to examine the interaction effects of a transverse magnetic field and slip effects of Casson fluid with suspended nanoparticles over a nonlinear stretching surface. Mathematical modeling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed.

Governing nonlinear partial differential equations are reduced into nonlinear ordinary differential equations and then shooting method is employed for its solution. The slope of the linear regression line of the data points is calculated to measure the rate of increase/decrease in the reduced Nusselt number.

The effects of magnetic parameter (0=M=4), Casson parameter (0.1=β<8), nonlinear stretching parameter (0=n=3) and porosity parameter (0=P=6) on axial velocity are shown graphically. Numerical results were compared with another numerical approach and an excellent agreement was observed. This study reveals the fact that the Brownian motion parameter and boundary layer thickness have a direct relationship with temperature. Also, Brownian motion and thermophoresis contribute to an increase in the thermal boundary layer thickness.

Despite the immense significance and repeated employment of non-Newtonian fluids in industry and science, no attempt has been made up till now to inspect the Casson nanofluid flow with a permeable nonlinear stretching surface.

The purpose of this paper is to present an exploration of multiple slips and temperature dependent thermal conductivity effects on the flow of nano Williamson fluid over a slendering stretching plate in the presence of Joule and viscous heating aspects. The effectiveness of nanoparticles is deliberated by considering Brownian moment and thermophoresis slip mechanisms. The effects of magnetism and radiative heat are also deployed.

The governing partial differential equations are non-dimensionalized and reduced to multi-degree ordinary differential equations via suitable similarity variables. The subsequent non-linear problem treated for numerical results. To measure the amount of increase/decrease in skin friction coefficient, Nusselt number and Sherwood number, the slope of linear regression line through the data points are calculated. Statistical approach is implemented to analyze the heat transfer rate.

The results show that temperature distribution across the flow decreases with thermal conductivity parameter. The maximum friction factor is ascertained at stronger magnetic field.

In the current paper, the magneto-nano Williamson fluid flow inspired by a stretching sheet of variable thickness is examined numerically. The rationale of the present study is to generalize the studies of Mebarek-Oudina and Makinde (2018) and Williamson (1929).

To demonstrate, through numerical models, that it is possible to simulated low‐gravity phase change (melting), of an electrically conducting material (gallium), in terrestrial conditions via the application of electromagnetic fields.

A complete three‐dimensional mathematical formulation governing a phase change process in the presence of an electromagnetic field has been developed. In addition a comprehensive parametric study has been completed to study the various effects of gravity, Stefan number, Hartmann number and electromagnetic pressure number upon the phase change process.

The results show that the application of an electromagnetic filed can be used to simulate key melting characteristics found for actual low‐gravity. However, the resulting three‐dimensional flow field in the melted region differs from actual low‐gravity. The application of an electromagnetic field creates a flow phenomenon not found in actual low‐gravity or previously seen in two‐dimensional problems.

Future work may include the use of oscillating electromagnetic fields to enhance convection in energy storage systems in a low‐gravity environment.

The ability to suppress unwanted convective flows in a phase change process without the high magnetic fields necessary in magnetic field only suppression systems.

This work fills a void in the literature related to conducting fluids and the effects of magnetic and electromagnetic fields.

The study of novel exponential heat source phenomena across a flowing fluid with a suspension of microparticles and nanoparticles towards a convectively heated plate has been an open question. Therefore, the impact of the exponential heat source in the transport of nano micropolar fluid in the existence of magnetic dipole, Joule heating, viscous heating and convective condition effects has been analytically investigated. Influence of chemical reaction has also been exhibited in this discussion.

The leading equations are constructed via conservation equations of transport, micro-rotation, energy and solute under the non-transient state situation. Suitable stretching transformations are used to transform the system of partial differential equations to ordinary. The transformed ODEs admit numerical solution via Runge–Kutta fourth order method along with shooting technique.

The effects of pertinent physical parameters characterizing the flow phenomena are presented through graphs and discussed. The inclusion of microparticles and nanoparticles greatly affects the flow phenomena. The impact of the exponential heat source (EHS) advances the heat transfer characteristics significantly compared to usual thermal-based heat source (THS). The thermal performance can be improved through the effects of a magnetic dipole, viscous heating, Joule heating and convective condition.

The effectiveness of EHS phenomena in the dynamics of nano micropolar fluid past an elongated plate which is convectively heated with regression analysis is for the first time investigated.

The purpose of this paper is to emphasize the peristaltic mechanism of power-law fluid in an elastic porous tube under the influence of slip and convective conditions. The effects of different waveforms on the peristaltic mechanism are taken into account.

The governing equations are rendered dimensionless using the suitable similarity transformations. The analytical solutions are obtained by using the long wavelength and small Reynold’s number approximations. The expressions for velocity, flow rate, temperature and streamlines are obtained and analyzed graphically. Furthermore, an application to flow through an artery is determined by using a tensile expression given by Rubinow and Keller.

The principal findings from the present model are as follows. The axial velocity increases with an expansion in the estimation of velocity slip parameter and fluid behavior index, and it diminishes for a larger value of the porous parameter. The magnitude of temperature diminishes with an expansion in the Biot number. The flux is maximum for trapezoidal wave and minimum for the triangular wave when compared with other considered waveforms. The flow rate in an elastic tube increases with an expansion in the porous parameter, and it diminishes with an increment in the slip parameter. The volume of tapered bolus enhances with increasing values of the porous parameter.

The current study finds the application in designing the heart-lung machine and dialysis machine. The investigation further gives a superior comprehension of the peristaltic system associated with the gastrointestinal tract and the stream of blood in small or microvessels.

Natural convection in finite enclosures is a common phenomenon in various thermal applications. To provide the thermal design guidelines, this study aims to numerically explore the potential of using internal baffles and nanofluids to either enhance or suppress heat transport in a vertical annulus. Furthermore, the annular-shaped enclosure is filled with aqueous-silver nanofluid and the effects of five distinct nanoparticle shapes are examined. In addition, the influence of baffle design parameters, including baffle position, thickness and length, is thoroughly analyzed.

The finite difference method is used in conjunction with the alternating direction implicit and successive line over relaxation techniques to solve nonlinear and coupled partial differential equations. The single phase model is used for nanofluid which is considered as a homogeneous fluid with improved thermal properties. The independence tests are carried out for assessing the sufficiency of grid size and time step for obtaining results accurately.

The baffle dimension parameters and nanoparticle shape exhibit significant impact on the convective flow and heat transfer characteristics, leading to the following results: sphere- and blade-shaped nanoparticles demonstrate around 30% enhancement in the heat transport capability compared with platelet-shaped nanoparticles, which exhibit the least. When considering the baffle design parameter, either a decrease in the baffle length and thickness or an increase in baffle height leads to an improvement in heat transport rate. Consequently, a threefold increase in baffle height yields a 40% improvement in thermal performance.

Understanding the impact of nanoparticle shapes and baffle design parameters on flow and thermal behavior will enable engineers to provide valuable insight on thermal management and overall system efficiency. Therefore, the current work focuses on exploring buoyant nanofluid flow and thermal mechanism in a baffled annular-shaped enclosure. Specifically, an internal baffle that exhibits conductive heat transfer through it is considered, and the impact of baffle dimensions (thickness, length and position) on the fluid flow behavior and thermal characteristics is investigated. In addition, the current study also addresses the influence of five distinct nanoparticle shapes (e.g. spherical, cylindrical, platelet, blade and brick) on the flow and thermal behavior in the baffled annular geometry. In addition to deepening the understanding of nanofluid behavior in a baffled vertical annulus, the current study contributes to the ongoing advancements in thermal applications by providing certain guidelines to design application-specific enclosures.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

The purpose of this paper is to examine the combined effects of thermal radiation and magnetic field of molybdenum disulfide nanofluid in a channel with changing walls. Water is considered as a Newtonian fluid and treated as a base fluid and MoS₂ as nanoparticles with different shapes (spherical, cylindrical and laminar). The main structures of partial differential equations are taken in the form of continuity, momentum and energy equations.

The governing partial differential equations are converted into a set of nonlinear ordinary differential equations by applying a suitable similarity transformation and then solved numerically via a three-stage Lobatto III-A formula.

All obtained unknown functions are discussed in detail after plotting the numerical results against different arising physical parameters. The validations of numerical results have been taken into account with other works reported in literature and are found to be in an excellent agreement. The study reveals that the Nusselt number increases by increasing the solid volume fraction for different shapes of nanoparticles, and an increase in the values of wall expansion ratio α increases the velocity profile f′(η) from lower wall to the center of the channel and decreases afterwards.

In this paper, a numerical method was utilized to investigate the influence of molybdenum disulfide (MoS₂) nanoparticles shapes on MHD flow of nanofluid in a channel. The validity of the literature review cited above ensures that the current study has never been reported before and it is quite new; therefore, in case of validity of the results, a three-stage Lobattoo III-A formula is implemented in Matlab 15 by built in routine “bvp4c,” and it is found to be in an excellent agreement with the literature published before.

The purpose of this paper is to formulate and analyse a convergent numerical scheme and apply it to investigate the coupled problem of fluid flow with heat and mass transfer in a porous channel with variable transport properties.

This paper derives the model by assuming a fully developed Brinkman flow with temperature-dependent viscosity and incorporating viscous dissipation, variable transport properties and nonlinear heat and mass sources. For the numerical formulation, the nonlinear sources are treated in semi-implicit manner, whereas the non-constant transport properties are treated by lagging in time leading to decoupled diagonally dominant systems. The consistency, stability and convergence results are derived. The method of manufactured solutions is adopted to numerically verify the theoretical results. The scheme is then applied to investigate the impact of relevant parameters, such as the viscosity parameter, on the flow.

Based on the numerical findings, the proposed scheme was found to be unconditionally stable and convergent with first- and second-order accuracy in time and space, respectively. Physical results showed that the flow parameters have influence on the flow fields, particularly, the flow is enhanced by increasing porosity and viscosity parameters and the concentration decreases with increasing diffusivity, whereas both the temperature and Nusselt number decrease with increasing thermal conductivity.

Numerically, the proposed numerical scheme can be applied without concerns on time steps size restrictions. Non-physical solutions cannot be computed. Physically, the flow can be increased by increasing the viscosity parameters. Pollutants with higher diffusivity will have their concentration decreased faster than those of lower diffusivity. The fluid temperature would decrease faster if its thermal conductivity is higher.

A fully coupled fluid flow with heat and mass transfer problem having nonlinear properties and nonlinear fractional sources and sink terms, presumably, has not been investigated in a general form as done in this study. The detailed numerical analysis of this particular scheme for the identified general model has also not been considered in the past, to the best of the author’s knowledge.