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This study unveils a numerical paradigm that amalgamates the partially saturated lattice Boltzmann method (PSLBM) with the non‐isothermal quantitative phase‐field (PF) model. This innovative integration equips us with a prognostic tool ready to elucidate the progression and motion of solid‐air dendritic growth in the presence of both natural and forced convection. The PSLBM is employed to compute the flow of the solution and the interaction forces between the fluid and solid dendrites. Concurrently, the PF model is utilized to simulate the formation of solid‐air dendrites. The reliability of calculating of interaction forces between the fluid and solid was confirmed through a numerical case study involving fluid flow around a stationary cylinder. The results indicate that this model is applicable for simulating the growth and evolution of single/multiple solid‐air dendrites under the influence of convection, whether they are stationary or in motion. The promotion of the upstream side dendritic arms and the inhibition of the downstream dendritic arms increase with the intensification of natural convection. As the initial undercooling is raised, the capacity of natural convection to reshape dendritic morphology gradually diminishes. With the enhancement of forced convection intensity, due to alterations in the flow pattern, the downstream dendritic arms do not consistently exhibit growth suppression. The motion of solid‐air dendrites induced by forced convection counteracts the influence of convection, resulting in slightly faster growth of the downstream dendritic arms compared to the upstream arms. Simultaneously, it fosters the formation of secondary dendritic branches in the upstream zone. [ABSTRACT FROM AUTHOR]

In a composite system possessing rigid‐rigid boundaries, the significance of thermal diffusion on the onset of triple diffusive convection is analyzed. The Darcy–Brinkman–Rayleigh–Benard model is employed to model the porous media. The regular perturbation methodology has been used to solve the governing equations of the composite system with the Boussinesq approximation. The critical thermal Rayleigh number, which determines the stability of the system, is estimated analytically. A graphical assessment of the impact of multiple physical attributes on the stability of the system is made. It is observed that the Soret parameters and solute Rayleigh numbers have a stabilizing effect, whereas the Darcy number exhibits a destabilizing effect upon the onset of triple diffusive convection in the composite system. [ABSTRACT FROM AUTHOR]

Analysis of fluid flow in a bidispersive medium with reactions is explored. The Darcy model is used in the momentum equation with the density being a linear function in temperature and salt concentration. Two cases are regarded which are heated below and salted above system and heated and salted below system. It is presumed that the equilibrium solute concentration follows a linear relationship to temperature. A linear instability and nonlinear stability theories are conducted, and from the outputs of the analysis, the Chebyshev collocation approach is used to solve the resulting eigenvalue systems. The effects of the chemical reaction and other parameters on temperature Rayleigh number are described graphically. [ABSTRACT FROM AUTHOR]

Thermosolutal convection and macrosegregation formation during the solidification of steel ingots are numerically simulated in three dimensions. The simulation is based on a fully coupled model for mass, momentum, energy, and species conservation equations. The interdendritic flow in the mushy zone is governed by Darcy's law, and the permeability term is discretized using an interpolated liquid fraction method. The numerical results for a benchmark test of macrosegregation in a Pb-Sn alloy are compared with experimental data taken from the literature. The present model is applied to simulate the solidification of industrial steel ingots. Preliminary predictions are obtained, including the positive segregation in the hot top, and the conically shaped negative segregation zone at the bottom of the ingot. The predicted variation of the segregation ratio in carbon along the vertical centreline of an ingot is compared with measurements, and generally good agreement is observed. Future attention should be paid to the precision of prediction by considering complex solidification issues, such as the sedimentation of free equiaxed grains and the formation of shrinkage cavity. [ABSTRACT FROM AUTHOR]

In the present study analysis has been performed for thermosolutal convection in a fluid-porous composite medium, consisting of a fluid-saturated porous medium followed by an overlaying clean medium. The fluid-porous composite medium is subjected to both a horizontal solutal and a thermal gradient. Top and bottom walls of the fluid-porous composite medium are assumed to be impermeable and adiabatic. The Darcy-Brinkman-Forchheimer model is used to study the flow through the fluid-porous composite medium. A single domain approach is taken into consideration for numerical simulation. The solution is done by control volume integration. A comprehensive analysis has been performed for various pertinent parameters to delineate their behavior. Results of the transport phenomenon have been provided in graphical and tabular form, for the complete understanding of the complex phenomenon. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21048 [ABSTRACT FROM AUTHOR]

The present study addresses the interaction effect of participating media radiation with the onset of double-diffusive convection in a square enclosure. Vertical walls are imposed with constant temperature and concentration, and the horizontal walls are impermeable and adiabatic. The boundaries of the enclosure are diffuse-gray, and the enclosed fluid isotropically scatters, emits, and absorbs thermal radiation. Numerical simulations have been performed for both aiding and opposing buoyancy conditions. The buoyancy ratio has been varied to simulate the effect of buoyancy driven flow and compositionally driven flow, along with transition of flow between the above. Optical properties like opacity of medium, scattering albedo, Planck number, and wall emissivity have been varied to depict their influence on flow and heat transfer. The modified MAC method is used for the solution of convective transport equations. Gradient dependent consistent hybrid upwind scheme of second order ( GDCHUSSO) is used for the discretization of the convective terms. The discrete ordinate method, with S8 approximation, is used to solve the radiative transport equation. The parametric results are provided in graphical and tabular form. Flow lines, isotherms, and isoconcentration contour maps are provided to bring clarity in the understanding of the momentum, heat, and solute transport phenomenon. The stabilization effect of thermal radiation at critical buoyancy ratio for buoyancy opposed flow is observed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (). DOI 10.1002/htj.21108 [ABSTRACT FROM AUTHOR]

The study sought to investigate thermosolutal convection and stability of two dimensional disturbances imposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of a chemical species using a self-consistent asymptotic method. The chemical species reacts as it diffuses into the nearby fluid causing density stratification and inducing a buoyancy force. The existence of significant temperature gradients near the plate surface results in additional buoyancy and decrease in viscosity. We derive the linear neutral results by analyzing asymptotically the multideck structure of the perturbed flow in the limit of large Reynolds numbers. The study shows that for small Damkohler numbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS) instability waves. Similarly, increasing the Damkohler numbers (which corresponds to increasing the reaction rate) has a destabilizing effect on the TS wave modes. However, for small Damkohler numbers, negative buoyancy stabilizes the boundary layer flow. [ABSTRACT FROM AUTHOR]

The study sought to investigate thermosolutal convection and stability of two dimensional disturbances imposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of a chemical species using a self-consistent asymptotic method. The chemical species reacts as it diffuses into the nearby fluid causing density stratification and inducing a buoyancy force. The existence of significant temperature gradients near the plate surface results in additional buoyancy and decrease in viscosity. We derive the linear neutral results by analyzing asymptotically the multideck structure of the perturbed flow in the limit of large Reynolds numbers. The study shows that for small Damkohler numbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS) instability waves. Similarly, increasing the Damkohler numbers (which corresponds to increasing the reaction rate) has a destabilizing effect on the TS wave modes. However, for small Damkohler numbers, negative buoyancy stabilizes the boundary layer flow. [ABSTRACT FROM AUTHOR]

The magnetic and chemical reaction effects on the onset of thermosolutal convection in a penetrative internally heated fluid are investigated for the case when the plane layer has a constant temperature and salt concentration on the upper surface and a specified heat flux and salt flux on the bottom surface. The linear instability and nonlinear stability boundaries are analyzed using the Chebyshev collocation method to calculate the corresponding eigenvalue systems according to the boundary conditions. Two distinct internal heat source functions are examined: the first kind is a constant, and the second kind is to heat the bottom half of the surface while cooling the rest. The Rayleigh number is graphically represented with the various parameter effects. The outcomes indicate that utilizing magnetic, chemical reactions, and internal heat sources has a significant influence on defining the thermosolutal convection stabilization and destabilization thresholds. For all types of internal heat sources, it is found that the magnetic field has a stabilizing effect. It is also noted that the effects of chemical reaction, heat flux, and salt flux play important factors in the stability region. [ABSTRACT FROM AUTHOR]

The intricacies of a constant horizontal pressure gradient on the onset of Soret-driven thermosolutal porous convection have been investigated. The resulting generalized eigenvalue problem is solved numerically using the Galerkin method and also the condition for the onset is obtained in a closed-form using a singleterm Galerkin method with trigonometric trial function. The results obtained from both methods are found to be in good agreement. The effect of increasing horizontal pressure gradient, Lewis number, Soret parameter, and the Vadasz number is to hasten, while the increase in the solute Darcy-Rayleigh number is to delay the onset of oscillatory convection. The presence of the horizontal pressure gradient is found to decrease the threshold value of solute Darcy-Rayleigh number beyond which the instability sets in as oscillatory. Moreover, the horizontal pressure gradient imparts a conflicting behavior on the critical wave number and critical frequency of oscillations. The numerical results attained under the limiting cases are shown to be in excellent agreement with the published ones. [ABSTRACT FROM AUTHOR]

This work examines the double diffusion of rotated Z‐shaped and sloshing fins inside a nanofluid‐porous cavity. The novelty of this research lies in its utilization of the ISPH method to handle the complex fluid‐structure interactions occurring at double diffusion within the nanofluid‐porous cavity. Two thermal/solutal conditions of the rotated Z shaped entitled C1 (Th&Ch${{T}_h}\ \& \ {{C}_h}$), and C2 (Tc&Cc${{T}_c}\ \& \ {{C}_c}$) are conducted in this work. The ISPH method solves the nonlinear systems of the fluid‐structure interactions during thermosolutal convection. The impacts of the inclined magnetic field and Soret–Dufour numbers are discussed. The Z shaped rotates circularly around its center and the four fins are sloshing on the boundaries. Natural convection is dominant because the rotation speed is slow, and the buoyancy force is strong. The obtained simulations revealed the changes in the isotherms, isoconcentration, and the nanofluid velocity under the variations of boundary conditions in Z shaped. It is seen that C1 always supports higher velocity, temperature, and concentration as well as mean Nusselt number Nu¯$\overline {Nu} $‐Sherwood number Sh¯$\overline {Sh} $ compared to C2. The Soret number plays a good role in the improvement of double diffusion and nanofluid velocity compared to the Dufour number which has fewer contributions. [ABSTRACT FROM AUTHOR]

Linear and weakly nonlinear stability analyses of thermosolutal convection in a couple‐stress fluid with effects of helical force and rotation are performed. The governing nondimensional equations are solved using the normal modes. We have shown the effect of the helical force parameter, solutal Rayleigh number, Couple stress parameter, Lewis number, Taylor number, and Prandtl number on stationary and oscillatory convection regions and presented graphically. Solutal Rayleigh number, Couple stress parameter, Lewis number, and Taylor number have a stabilizing effect on the system whereas the helical force parameter has a destabilizing effect on the system. To study heat transport by convection we have derived the Ginzburg–Landau equation. [ABSTRACT FROM AUTHOR]

The model of thermosolutal convection in a fluid‐saturated bidisperse porous medium of Darcy type is studied in this paper. The permeability is allowed to be horizontally isotropic for both the macro‐ and microphases. The linear instability and nonlinear stability are analyzed by taking the Soret effect into account. Furthermore, the effect of anisotropy parameter, Soret coefficient, and other physical parameters on the stability of the system are investigated. It is shown that the linear instability boundaries and the energy stability boundaries do not coincide when the layer is heated and salted from below, where a region of potential subcritical instability occurs. The results reveal that the horizontal to vertical permeability ratio plays a crucial role in the stability of the system. It is also observed that for large values of the salt Rayleigh number, the onset of thermal convection is more likely to be via oscillatory convection rather than stationary convection. Furthermore, the onset of stationary convection is significantly influenced by the presence of the Soret coefficient. [ABSTRACT FROM AUTHOR]

This research paper focuses on investigating the phenomenon of entropy generation, specifically within the context of blood flow. Blood is modeled as a three‐layered liquid model, with micropolar and Newtonian fluids occupying the center and periphery sections of the tube, respectively. A narrow glycocalyx layer adjacent to the wall is regarded as indicating a permeable area caused by the accumulation of carbohydrates and fibrous tissues within the tube wall. Further, the walls of the cylinder are taken as permeable. The objectives of this study include understanding the mechanisms and factors contributing to entropy generation in blood patterns, exploring the relationship between entropy generation and flow characteristics, and analyzing the impact of entropy generation on the overall energy efficiency of the system. The transformation of ordinary differential equations (ODEs) from partial differential equations (PDEs) can be accomplished by employing a similarity approach that combines shooting methods with the inculcation of the RK‐4 method. This integrated technique facilitates the transformation process effectively. Then, MATLAB software is used to plot graphs for accuracy purposes. Under various physical limitations, the comparison study demonstrates that trihybrid nanoliquids exhibit ultrahigh thermal efficiency compared to ordinary nanoliquids, and incorporating these nanofluids enhances entropy generation, temperature, and Bejan profiles, improving thermal conductivity and energy transfer. This integration ensures sustained performance over time, benefiting from carefully selected nanoparticles for stability optimization. As a result, these fluids are extremely useful for industrial applications, particularly filtration and ultrahigh heat. [ABSTRACT FROM AUTHOR]

The present study aims to provide a mathematical model of the Williamson fluid flow via a permeable stretching/shrinking sheet in the MHD boundary layer in the presence of a heat source, chemical reaction, and suction. This study is novel because it investigates the physical effects of thermal and solutal stratification on convective heat and mass transport using thermal radiation. The flow's PDEs are numerically solved using the BVP4c approach and the pertinent similarity variables until a stable solution is found. Through visual analysis, the effects of dimensionless factors on temperature, velocity, and concentration profiles are examined. This encompasses the mass transfer rate, the heat transfer rate, and the coefficient of friction. The results of the present analysis are found to be consistent with those of previously published studies. The findings demonstrate that enhanced temperature and concentration profiles cause the Williamson, magnetic, and permeability parameters to rise in conjunction with a drop in the dimensionless velocity. In relation to temperature, the thermal stratification parameter exhibits the opposite tendency. Regarding the solutal stratification parameter, concentration profiles are seen to show the opposite trend. Lastly, the current work will have important implications for the removal of dust and viruses from viscoelastic fluid in bioengineering, the medical sciences, and medical equipment. [ABSTRACT FROM AUTHOR]

The article presents a mechanism for the formation of equiaxed grain defects and a new approach to eliminate them during the directional solidification of single‐crystal CMSX‐4 nickel‐based superalloy blades. The standard Bridgman method produces blade castings with clusters of equiaxed grains in platform areas above the root corners containing long freckle chains. The mechanism proposed considers the curvature of the liquidus isotherm and suggests that isolated dendrite fragments move upward from the freckle channel to the melt of the platform area. The floating surviving grains settle at the columnar dendrite tips, where they continue to grow into large equiaxed grains that block the development of the single‐crystal structure in the platform area located above the root corners. To eliminate these defects from the platform, a new approach is proposed, which involves introducing inner radiation baffles along the mold height to control the liquidus isotherm curvature in the blade. This stops the movement of small dendritic fragments from the root corner to the platform area, resulting in a significant reduction of freckles at the root and obtaining a typical single‐crystal structure free of equiaxed grains in the platform. [ABSTRACT FROM AUTHOR]

Current paper explores the MHD two‐dimensional stagnation point flow over a stretchable Riga wall in the presence of porous medium. Cattaneo‐Christove heat and mass flux model is used to examine the heat and mass transfer analysis. Particular interest is paid to the analysis of entropy generation due to heat and mass diffusion. Transformations are used to convert the given partial differential equation into ordinary differential system. The governing equations are solved numerically using the built‐in shooting method. The impacts of emanating parameters are examined through graphs. The impact of various important flow parameters are discussed graphically on the entropy generation, velocity, Bejan number, concentration, and temperature profile. [ABSTRACT FROM AUTHOR]

The flow through porous medium accounts for numerous applications in various fields namely, agriculture, geothermal sciences, and engineering. Furthermore, dissolution‐driven convection in porous media has grabbed great attention in recent years due to its practical applications in long‐term geological storage of carbon dioxide, in the production of mineral deposits, and other industrial applications. In this regard, the current numerical analysis focuses on addressing the thermal instability of dissolution‐driven convective phenomena of a power‐law fluid through a porous horizontal domain with a first‐order chemical reaction. For linear stability analysis, the method of normal modes has been employed to solve governing dimensionless equations which give rise to an eigenvalue problem. The bvp4c routine in MATLAB R2020a has been used to solve the raised problem for the onset of convection. The impact of Damköhler number, Péclet number, and power‐law index on the onset of convection has been investigated. The role of these critical parameters is found to be highly significant in stabilizing the system. An increase in the power‐law index causes stabilization or destabilization in the system, depending on the Péclet number. An enhancement in the magnitude of Damköhler number makes the system stable for all values of the Péclet number. Also, Damköhler and critical Rayleigh number are inter‐related, that is, an increment in Damköhler number results in the enhancement of critical Rayleigh numbers, which in turn leads to stabilization of the system. The critical wave number is observed to have a remarkable influence on Damköhler number as well as power‐law index. [ABSTRACT FROM AUTHOR]

Several iterative finite element methods are analyzed for a steady‐state double‐diffusive natural convection model, which contains the diffusion of temperature and concentration and can simulate heat and mass transfer phenomena. These iterations include the Stokes‐type, Newton‐type, and Oseen‐type iterative methods. Then, based on the uniqueness condition, stability and convergence of these iterative methods are proved for the considered model. Finally, some numerical examples are presented for validating the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The impact of the magnetic field, heat source, and variable gravity field on the stability of convective phenomena in a porous layer are investigated numerically. Three types of gravity variations, such as linear, parabolic, and cubic functions are considered. For linear and nonlinear theories, the method of normal modes has been employed to solve governing dimensionless equations. It is found that the onset of convection is delayed by increasing the Hartmann number and gravity variation parameter and enhancement of the internal heat source makes the system stable. The subcritical instability region increases as the Hartmann number and gravity variation parameter increase. [ABSTRACT FROM AUTHOR]

In this article, we examined the effect of heat and mass transfer flow of two immiscible Jeffrey fluids in a vertical channel. The highly nonlinear coupled ordinary differential equations are evaluated using regular perturbation parameters, for small values of perturbation parameter. The effect of Jeffrey's parameter on the flow and the effects of various physical parameters entering into the problem on dimensionless velocity, temperature, and concentration distribution is illustrated graphically. We observe that the Jeffrey parameter, thermal, and mass Grashof number enhance the fluid flow, while the chemical reaction parameter suppresses the fluid flow, also it is established that the Nusselt number is boosted by enhancing the thermal and mass Grashof number. We observed that the results are in very good agreement with the results obtained for a viscous fluid. [ABSTRACT FROM AUTHOR]

In this study, the start of thermosolutal penetrative convection in a horizontal fluid layer heated and salted from below was investigated analytically and graphically in the presence of throughflow and changeable gravity field effects. The normal mode technique is used to test the system's stability properties. The mathematical expressions for stationary and oscillatory Rayleigh numbers are obtained as a function of the governing parameters. The analysis demonstrates that the vertical throughflow, gravity parameter, and heat source effect all have a considerable influence on the beginning of convective motion in double‐diffusive flow. The impacts of variable gravity, vertical throughflow, and heat source parameters, as well as other physical parameters such as Solutal Rayleigh numbers and Lewis numbers, on stationary and oscillatory convection, are studied and illustrated graphically, and some previously published results are recovered in the limiting cases. [ABSTRACT FROM AUTHOR]

Stably stratified layers may be present at the top of the electrically conducting fluid layers of many planets either because the temperature gradient is locally subadiabatic or because a stable composition gradient is maintained by the segregation of chemical elements. Here we study the double‐diffusive processes taking place in such a stable layer, considering the case of Mercury's core where the temperature gradient is stable but the composition gradient is unstable over a 800 km‐thick layer. The large difference in the molecular diffusivities leads to the development of buoyancy‐driven instabilities that drive radial flows known as fingering convection. We model fingering convection using hydrodynamical simulations in a rotating spherical shell and varying the rotation rate and the stratification strength. For small Rayleigh numbers (i.e., weak background temperature and composition gradients), fingering convection takes the form of columnar flows aligned with the rotation axis and with an azimuthal size comparable with the layer thickness. For larger Rayleigh numbers, the flows retain a columnar structure but the azimuthal size is drastically reduced leading to thin sheet‐like structures that are elongated in the meridional direction. The azimuthal size decreases when the thermal stratification increases, following closely the scaling law expected from the linear planar theory (Stern, 1960, https://doi.org/10.1111/j.2153-3490.1960.tb01295.x). We find that the radial flows always remain laminar with local Reynolds number of order 1–10. Equatorially symmetric zonal flows form due to latitudinal variations of the axisymmetric composition. The zonal velocity exceeds the non‐axisymmetric velocities at the largest Rayleigh numbers. We discuss plausible implications for planetary magnetic fields. Plain Language Summary: Convection occurs in planetary interiors due to local changes of density, which can be produced by changes of temperature or chemical composition. In particular, convection occurs in the electrically conducting fluid layers located deep inside planets and is at the origin of the generation of planetary magnetic fields. However, for many planets, the upper part of this electrically conducting region might not be subject to standard convection because the gradients of either temperature or chemical composition produce a further increase of the density with depth, leading to the formation of a stable layer. In some cases, the gradients of these two components act in opposition. Such might be the case of the upper part of Mercury's core, where the stable layer is maintained by the thermal gradient, but the compositional gradient is unstable. This situation is prone to fingering convection, where fluid instabilities release the potential energy associated with the compositional gradient. Here we show that fingering convection consists of sheet‐like flows with a narrow longitudinal size of approximately 1 m in Mercury‐like conditions. Strong zonal (i.e., east/westward) flows also form. The presence of fingering convection in stable layers might have important consequences for the magnetic fields observed at the planet's surface. Key Points: Fingering convection in a Mercury‐like stable layer produces thin sheet‐like radial flows that are elongated in the meridional directionThe radial flows are always laminar and their azimuthal length is expected to be about 1 m in planetary coresStrong zonal flows form as a by‐product of the latitudinal variations of the composition transport [ABSTRACT FROM AUTHOR]

The impact of energy‐based volumetric internal heating and magnetic field‐dependent (MFD) viscosity on the onset of ferrothermal porous convection for different types of boundary conditions is investigated. The lower and upper boundaries are considered to be either rigid or stress‐free. The lower boundary is insulating, while at the upper boundary a Robin type of thermal condition is applied. Besides this, a general type of boundary conditions is invoked on the magnetic potential. The stability eigenvalue problem is solved numerically using the Galerkin‐type of weighted residuals technique with the Rayleigh number, Rt ${R}_{t}$ as the eigenvalue. The results obtained for different boundary combinations are found to be qualitatively similar though not quantitatively. The effect of Biot number, MFD viscosity, and porous parameters is to hinder, while the influence of internal heat source strength, magnetic number, and the nonlinearity of fluid magnetization is to advance the onset of convection. The rigid and conducting boundaries offer a more stabilizing influence on the onset when compared to stress‐free and insulating boundaries. The convection cells get contracted the most when the boundaries are rigid and also when the upper boundary is conducting. The results delineated under the limiting cases are found to be in good agreement with those available in the literature. [ABSTRACT FROM AUTHOR]

The present level of literature on the subject matter indicates that nothing is known on the heat transfer across the couple stress rheological fluid flowing over a vertical avenue with Robin (mixed) wall conditions. The obtained conservation equations of the model are solved through DTM (differential transform method) and RPM (regular perturbation method). The nondimensional parameters obtained are a couple stress parameter, Brinkman number, mixed convection parameter, and Biot number. The computations reveal that flow acceleration and thermal enhancement is induced with increasing mixed convection parameter and Brinkman number for symmetric and asymmetric conditions. Increasing couple stress parameters dwindle the velocity and temperature for symmetric and asymmetric cases. The large values of the mixed convection parameter and Brinkman number increase the Nusselt values at the left wall and reduces at the right wall. The mass flow rate is augmented with the mixed convection parameter and Brinkman number but it is reduced with the couple stress parameter. The DTM, RKSM, and RPM solutions are in good agreement. [ABSTRACT FROM AUTHOR]

This research is on the melting process of slag in non‐inner lining furnaces. In this electric furnace, slag is solidified into the lining of the inner wall during the melting process by means of water cooling of the outer wall. It is a self‐supporting lining electric furnace. In this study, the slag melting process was simulated using ANSYS software, and the electromagnetic field, temperature field, and furnace lining thickness of the self‐supporting lining were analyzed at different electrode insertion depths. The results show that the self‐supporting lining can be formed under the three insertion depth of the electrodes, and the thickness of the lining increases with the insertion depth of the electrode. [ABSTRACT FROM AUTHOR]

In an anisotropic porous matrix with a Soret coefficient, the onset of double‐diffusive convection is investigated analytically using weakly nonlinear analysis. The momentum equation is expressed using a generalized Darcy model with a time derivative term. The Newell–Whitehead–Segel equation is acquired, thereby examining the Eckhaus and zigzag secondary instabilities. Nusselt and Sherwood numbers are used to examine convection onset by quantifying heat and mass movement. Heat and mass transmission dynamics are graphically depicted as a consequence of several parameters. An increase of the positive value of the Soret parameter enhances heat transport, whereas, an increase of the negative value of the Soret parameter reduces it. [ABSTRACT FROM AUTHOR]

The effect of variable gravity on rotating convection in a sparsely packed porous layer is studied numerically. For gravity force variation, the linear, parabolic, cubic, and exponential functions are considered. Boundary conditions for the governing equations are considered to be either free or rigid. The normal mode method is employed, and the resulting eigenvalue problem is solved numerically for free–free and rigid–rigid boundaries using bvp4c in MATLAB R2020b. The influence of Darcy number (Da $Da$), gravity variation parameter (δ1 ${\delta }_{1}$), and Taylor number (Ta $Ta$) on the stability of the system is investigated graphically. It is confirmed that the gravity variation parameter and Taylor number delay the onset of convection and Darcy number enhances the onset of convection. The size of convection cells decreases on raising the variable gravity parameter and rotation parameter, while the Darcy number amplifies the size of convection cells. It is also observed that the system is stable for exponential gravity function and less stable for the cubic gravity function. [ABSTRACT FROM AUTHOR]

The article studies the macrosegregation phenomena that occur during solidification of steel ingot castings using a computational multi-fluid dynamics approach. The authors describe four different cases, which include feeding-induced macrosegregations in one-dimensional unidirectional solidification, macrosegregations caused by thermosolutal buoyancy driven flow, macrosegregations caused by grain sedimentation and macrosegregations caused by thermosolutal convection.

The consistent splitting scheme involving a mixed finite element method for considering the influence of the Forchheimer-extended Brinkman–Darcy model in the momentum equation is applied to double-diffusive convection in a fluid-saturated porous medium. It is shown that the method is robust and can accurately predict flow, pressure distribution, temperature and concentration fields. The numerical scheme may be an alternative to some other existing methods for the solution of porous thermosolutal convection problems since its implementation is very handy. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The primary challenge in the majority of heat transfer applications, in view of design perspective, is to maximize the thermal transport with the minimum generation of entropy. This paper addresses the numerical investigation of buoyant convection and entropy generation processes of Al2O3–water nanofluid inside a vertical annular configuration having two coaxial cylinders. The vertical cylindrical surfaces are imposed with sinusoidal thermal distribution having different phase deviation and amplitude, while the horizontal surfaces are retained adiabatic. In this analysis, the numerical computations of conservation equations governing the physical process are performed using the time‐splitting technique and line overrelaxation methods. Detailed numerical simulations are performed for broad ranges of critical parameters, such as Rayleigh number, phase deviation, amplitude ratio, and nanoparticle volume fraction. From the vast numerical experiments, we systematically identified the suitable parameter regimes at which enhanced thermal transport has been produced with minimum entropy generation. Furthermore, the critical quantities, such as thermal dissipation and entropy generation, could be effectively monitored by a particular selection of phase deviation (γ) and amplitude ratio (ε). It has been identified that these parameters have more influence on thermal transport as well as entropy production as compared to other parameters of the analysis. [ABSTRACT FROM AUTHOR]

The effect of thermal diffusion on the onset of double‐diffusive convection is analyzed by considering a composite system of the fluid‐saturated porous layer. The porous layer of the composite system is modeled employing the Darcy–Brinkman–Rayleigh–Benard model. The boundaries of the composite system are assumed to be rigid‐rigid under normal gravitational force. The governing equations satisfying the Darcy–Brinkman–Rayleigh–Benard model are solved using the regular perturbation method. A mathematical expression is derived for the critical thermal Rayleigh number by solving the coupled equation. The impact of various physical parameters on the onset of convection is graphically represented under the influence of the Soret effect and the stability of the system is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we apply a reconstructed higher‐order compact scheme on nonuniform grids to the problem of double‐diffusive natural convection in a vertical porous annulus. The Darcy model is adopted for the fluid flow coupled with energy and mass equations. Computations are carried out in the regime 1≤A≤10, 1≤κ≤50, 1≤Le≤200, −40≤N≤40, and 20≤Ra≤2000, where A is the aspect ratio, κ is the radius ratio, Le is the Lewis number, N is the buoyancy ratio, and Ra is the thermal Rayleigh number. Extensive computations are carried out to investigate the influence of these parameters on the flow and a general pattern of heat and mass transfer characteristics emerges from the study. Particular attention has been paid to the transient flow behavior while investigating the influence of κ on the N=−2 buoyancy ratio configuration. [ABSTRACT FROM AUTHOR]

In this review article, research papers related to recent developments in Ni-superalloy technologies have been reviewed in order to provide an insight into recent achievements and the potential for further study, research, and development in this field. In this paper, studies on various aspects of Ni-based superalloys are reviewed, such as production methods, which include widely used casting methods, as well as unconventional alternative procedures, novel techniques, or simulation and prediction of certain alloy casting properties. Reviewing was done by categorising the papers into 4 major categories: manufacturing of Ni-based superalloys, effects of alloying elements, physical and mechanical properties of Ni-based superalloys, and defects in Ni-based superalloys. The process used to make Ni-superalloy parts can have a huge impact on the production process efficiency, the final product's quality and properties, and the defects formed in it. Investment casting is one of the most common methods for making Ni-superalloy parts. Manufacturing covers studies on various casting methods used to make Ni-based superalloy components, novel techniques and methods developed to improve casting procedures to produce better products, and alternative manufacturing methods like AM and HIP processing. Similar to production process, the role of alloying elements is also very important. Even minor changes in their compositions can cause significant changes in the final product. Simultaneously, these alloying elements appear to be more efficient in the development of new methods to control product quality, suppress defect formation, and improve material properties such as the creep and fatigue. As a result, the effects of various alloying elements used in castings of Ni-based superalloys are thoroughly examined. A material's properties are its most important components. They assist the industrialist in selecting or developing a material based on the needs of the application/use. With this in mind, many researchers have conducted extensive research on physical and mechanical properties, as well as how to improve them. Fatigue life, stress rupture, creep properties, impact ductility, strain response, stress relaxation behaviour, and so on are some of the most important physical and mechanical properties of Ni-superalloys. This article thoroughly reviews various studies on these properties, how and by what factors they are affected, and how they can be improved. Another important factor to consider when making Ni-superalloy castings is defect formation, which can affect the properties of the final product. Freckle defects, hot tears, porosities, and slivers are some of the major defects that occur in Ni-superalloys during the casting process. This article also reviews in detail about these defects, how they form, and how they affect the final product. These defects were found to have a significant influence on a variety of properties, such as creep, fatigue behaviour, and fracture mechanism. Topics and areas such as reinforcement of Ni-superalloys with the help of CNCs and 3D printing of Ni-superalloys that can provide scope for potential future research are highlighted based on the above-reviewed papers. [ABSTRACT FROM AUTHOR]

This study deals with the roles of a magnetic field and circular rotation of a circular cylinder on the dissemination of solid phase within a nanofluid-filled square cavity. Two wavy layers of the non-Darcy porous media are situated on the vertical sides of a cavity. An incompressible smoothed particle hydrodynamics (ISPH) method was endorsed to carry out the blending process concerning solid phase into nanofluid and porous media layers. Initially, the solid phase is stationed in a circular cylinder containing two open gates. Implications of a buoyancy ratio (N = −2: 2), Hartmann number (Ha = 0: 100), rotational frequency (ω = 1 : 10) , Darcy parameter (D a = 10 − 2 : 10 − 5 ) , Rayleigh number (R a = 10 3 : 10 6) , nanoparticles parameter (φ = 0 : 0.06) , and amplitude of wavy porous layers (Α = 0.05 : 0.15) on the lineaments of heat/mass transport have been carried out. The results revealed that the diffusion of the solid phase is permanently moving toward upward except at opposing flow mode (N < 0) toward downward. The lower Rayleigh number reduces the solid-phase diffusions. A reduction in a Darcy parameter lessens the nanofluid speed and solid-phase diffusions in the porous layers. A reduction in D a from 10 − 3 to 10 − 5 diminishes the maximum of streamlines | ψ | max by 13.19% at N = − 2 , by 46.75% at N = 0 , and by 74.75% at N = 2. [ABSTRACT FROM AUTHOR]

The problem of complex and various ingot moulds has bothered special steel enterprises. Herein, three ingot‐weight‐compatible (IWC) designs are described. The 39 tons mould is adapted to cast at most 45 tons of molten steel. The effect of three IWC designs on shrinkage cavity, porosity and macrosegregation is studied. The simulation is based on a polyphase coupled model for momentum, energy, and mass conservation equations. On the basis of the experimental results and previous literature, the interfacial heat transfer coefficient is established. Through finite difference method (FDM) simulation, the effect of the three IWC designs on the solidification is studied. The predictions of shrinkage porosity and macrosegregation are obtained. With the increase of ingot weight, the shrinkage cavity from the hot top is deeper in the three IWC designs. The Niyama criterion is found to be the condition under G/L0.5 < constant (G and L are the temperature gradient and cooling rate, respectively). With this criterion, the extent of centerline shrinkage porosity is predicted. Subsequently, utilizing the three compatible designs, the simulated results uncover that the centerline shrinkage porosity is serious. In addition, it is significant to note that the macrosegregation shows different characteristics. [ABSTRACT FROM AUTHOR]

The stability of fluid flow in an anisotropic porous medium of Brinkman type is investigated. Anisotropy in the permeability is considered such that its longitudinal principal axis is oriented arbitrarily with the horizontal, while transversely it is isotropic. A fourth‐order eigenvalue problem obtained by performing a linear stability analysis is solved numerically using the Chebyshev collocation and the compound matrix methods. The critical Reynolds number and the critical wave number are computed for different values of porous parameter, orientation angle of the principal axis and the mechanical anisotropy parameter. The porous and the mechanical anisotropy parameters disclose contrasting contributions to the stability of fluid flow. The orientation angle instills either stabilizing or destabilizing effects on the fluid flow depending on the value of anisotropy parameter. Besides, the streamlines of the perturbation modes are presented for various values of orientation angle and anisotropy parameter. For the Darcy case, a simple analytical method is employed and established that the flow is stable for all infinitesimal perturbations. [ABSTRACT FROM AUTHOR]

Thermohaline convection (THC) in porous media is frequently investigated using the problem of porous enclosure. Most of the existing modeling‐based studies are limited to 2‐D simulations, because 2‐D assumption is widely used to deal with computational requirement of 3‐D numerical solutions. Analytical solutions serve as an alternative to deal with computational requirement of numerical solutions. Existing analytical solutions of THC are mostly limited to 2‐D and also under steady‐state regime. In this work, we develop a meshless 3‐D semianalytical solution for the problem of THC in a porous box under crossed thermal and solute gradients, for both steady state and transient regimes. The semianalytical solution is developed using the Fourier series (FS) method applied to the vector potential form of the governing equations. The extension to transient solutions represents an important technical feature of this work, as the applications of the FS method to density‐driven problems have been limited to steady‐state conditions. The FS solution is validated against a finite element solution obtained using COMSOL Multiphysics. Numerical experiments show the worthiness of the developed FS solution as a benchmark because it clearly allows making distinction between different numerical techniques. The effects of governing parameters on three‐dimensional THC have not been investigated previously. We perform a detailed parameter sensitivity analysis to address this gap. A vortex convective flow is observed and the orientation and intensity of the flow is sensitive to the gravity number. The increase in the temperature gradient reduces the salinity flux. Key Points: Existing numerical and analytical studies of thermohaline convection (THC) are limited to 2‐D and steady‐state conditionsA semianalytical solution is developed for THC in 3‐D box with crossed heat‐salinity gradients at both transient and steady‐state regimesObservations: a single vortex flow with orientation dependent on the Gravity number and different transient and steady‐state behaviors [ABSTRACT FROM AUTHOR]

The motivation of the current article is to explore a numerical investigation on steady triply diffusive convection in a vertical channel. Heat is exchanged from the external fluid with the plates. The reference temperature is taken as equal and also as different for the external fluid. Solutions in the absence of viscous dissipation and buoyancy forces are also obtained as special cases. General solutions including the effects of viscous dissipation and buoyancy forces are obtained analytically using the method of perturbation. The analytical solutions can be used only if the Brinkman number is small. Hence to know the flow properties for all values of Brinkman number, we resort to numerical solutions. The effects of thermal Grashof number, solutal Grashof number, and the chemical reaction parameter on the flow field are evaluated numerically. The obtained results are validated against previously published results for special case of the problems. [ABSTRACT FROM AUTHOR]

In this study, the influence of constant through flow and varying downward gravity field on the onset of Darcy‐Brinkman convection in a porous medium layer is examined numerically. We considered two cases of gravity field variations: (a) linear and (b) parabolic. A higher‐order Galerkin‐weighted residual technique and QZ procedure are used to get the numerical solution for the entire Darcy numbers amid Da = 0 (Horton‐Rogers‐Lapwood convection) and Da → ∞ (Rayleigh Bénard Convection). It is obtained that the through flow, the downward gravity field and the Darcy number are to holdup the beginning of convection. It is also obtained that the system is more stable for linear variation of gravity field in comparison to the parabolic variation. [ABSTRACT FROM AUTHOR]

The onset of triply cross‐diffusive convection in a viscoelastic fluid‐saturated porous layer is investigated as the study is found very relevant for describing natural phenomena (contaminant transport, underground water flow, improved oil recovery, polymer processing). A modified Darcy‐Oldroyd‐B model is used to describe the viscoelastic fluid flow in a porous medium with full cross‐diffusion terms in the diffusivity matrix. A normal mode analysis yields an exact dispersion equation of fifth degree and accordingly the criterion for the onset of stationary and oscillatory convection is obtained. The numerical computations are carried out for diffusivity elements experimentally determined for lysozyme‐sodium chloride‐bovine serum albumin (BSA)‐water system. Instability is found to occur via oscillatory mode for a certain choice of governing parameters. The relaxation and retardation viscoelastic parameters portray opposing contributions on the oscillatory onset and an increase in the relaxation parameter is to increase the range of retardation parameter up to which the oscillatory convection is preferred. The cross‐diffusion is to either delay/hasten the onset of instability based on the magnitude of the stratifying agents. Even minute variations in the cross‐diffusion elements indict complete change in the linear instability criteria. The topology of neutral curves disclosed the occurrence of disconnected closed convex oscillatory neutral curve revealing the requirement of three critical solute Darcy‐Rayleigh numbers to state fully the instability criteria instead of the usual single value; a novel result ensured from the study. Moreover, the nature of instability for Oldroyd‐B, Maxwell and Newtonian fluids turns out to be dissimilar for the same governing parameters. [ABSTRACT FROM AUTHOR]

The onset of buoyancy‐driven convective motion in a nanofluid saturated anisotropic porous medium layer is examined numerically in the occurrence of uniform internal heat source under the variable gravity field. Three kinds of gravity force variation functions: (a) G(z) = −z (linear), (b) G(z) = −z2 (parabolic), and (c) G(z) = −z3 (cubic) are considered. Wide‐range governing parameters impacts are inspected on the beginning of convective motion under the zero nanoparticle flux situation at the boundaries using the higher term Galerkin technique. It is established that the thermal anisotropy parameter η and the gravity variation parameter λ delay the arrival of convective motion, while the mechanical anisotropy parameter ξ, the internal heating parameter Hs, the nanoparticle Rayleigh‐Darcy number Rnp, the modified diffusivity ratio NAnf, and the modified nanofluid Lewis number Lenf rapid the start of convective motion. The size of the convective cells reduces on raising the internal heating parameter Hs, while the gravity variation parameter λ, the mechanical anisotropy parameter ξ, the thermal anisotropy parameter η, the nanoparticle Rayleigh‐Darcy number Rnp, the modified diffusivity ratio NAnf, and the modified nanofluid Lewis number Lenf amplify the dimension of the convective cells. It is also detected that the arrangement is more unstable for case (c), while it is more stable for case (a). [ABSTRACT FROM AUTHOR]

The present article investigates the study of double‐diffusive convection on peristaltic flow under the assumption of long wavelength and low Reynolds number. The mathematical modeling for a two‐dimensional flow, along with double diffusion in nanofluids, is considered. The motivation of the present research work is to analyze the effects of the magnetic field and thermal radiation on a peristaltic flow through a porous medium in an asymmetric channel. The heat flux of the linear approximation employs the thermal radiation of the flow problem. The effect of thermal radiation and double diffusion is an important aspect of research due to its application in public health potential. Infrared radiation techniques are indeed used to treat many skin‐related diseases. It can also be used as a measure of thermotherapy in some bones to enhance the blood circulation. It is found that approximately 80% of blood flow increases with radiation. The governing equations are analytically solved by using Homotopy analysis method with the help of the symbolic software Mathematica. The results of the velocity, pressure rise, temperature, solutal (species) concentration, and nanoparticle volume fraction profiles are graphically shown. In the present study focused on double diffusion of a peristalsis under the assumption of long wavelength and low Reynolds number. Magnetic field and porous medium are considered in this research article. The theory of double diffusive convection flow is used in many biomedical applications such as radiofrequency heating for the treatment of modality that kills the unwanted tissues, laser treatment in cornea, and destruction of tumors. [ABSTRACT FROM AUTHOR]