No-slip Condition Research Articles

Virtual body-fitted grid-based immersed boundary method for simulation of thermal flows with Dirichlet and Neumann boundary conditions

In this work, a virtual body-fitted grid-based immersed boundary method (IBM) combined with the thermal lattice Boltzmann flux solver (TLBFS) is proposed to efficiently simulate thermal flows with Dirichlet and Neumann boundary conditions. The method involves generating a virtual body-fitted grid along the immersed boundary and implementing the boundary conditions using a fractional step technique. In the prediction step, the finite-volume TLBFS is used to obtain the predicted flow field on the Eulerian mesh without considering the immersed boundary, while in the correction step, the correction process of the flow field is conducted on the virtual grid. Thus, the effect of the boundary is transferred to the fluid domain through the virtual grid indirectly. For Dirichlet boundary conditions, such as the no-slip condition and the specified temperature condition, the velocity and temperature corrections are considered unknowns and solved through a matrix system formed from enforcing the boundary conditions. As for the Neumann boundary condition, such as the specified heat flux condition, the temperatures at virtual layers inside the immersed body are regarded as unknowns and computed from those at virtual layers outside the wall according to the quadratic distribution. Several benchmark cases including natural, forced, and mixed convection problems are well simulated to validate the method. The numerical results are in good agreement with reference data, demonstrating the capacity of the present method to simulate thermal flows with Dirichlet and Neumann boundary conditions while requiring fewer Lagrangian points and achieving higher computational efficiency.

A coupled local front reconstruction and immersed boundary method for simulating 3D multiphase flows with contact line dynamics in complex geometries

Multi-phase flows in the presence of complex solid geometries are encountered widely throughout industrial processes to intensify mass and heat transfer processes. The efficiency of these processes relies largely on the predominant fluid dynamics regime inside the reaction vessel (e.g. trickle bed, bubble column reactor). The prevailing flow structure is influenced by many factors including the nature of the fluid-solid interactions (i.e. wetting or non-wetting). Such flows are often studied using front-capturing techniques to capture the fluid-fluid interface in combination with an auxiliary model to account for fluid-solid interactions. However, these front-capturing methods have difficulties in accurately representing the interface. Therefore, we adopted a front-tracking method: the Local Front Reconstruction Method (LFRM). In this study, LFRM is coupled with the Immersed Boundary method to incorporate the no-slip boundary condition at the solid surface. The model performance is assessed using droplet spreading simulations, where the equilibrium droplet shape (i.e. radius, height, and outline), the interfacial pressure difference, and the surface tension force are compared to analytical solutions and literature data. The results show an excellent match with the analytical solutions, and additionally superior performance to state-of-the-art volume tracking models.

The adjoint Rayleigh and Orr-Sommerfeld equations: Green function and eigenmodes

The Rayleigh and Orr-Sommerfeld equations are ODEs which arise from the linearized Euler and Navier-Stokes equation around a shear flow. In this paper, we consider the adjoints of the Rayleigh and Orr-Sommerfeld equations on [0,∞) with respect to the complex L2 product. In the viscous case, we consider a family of viscosity-dependent Navier boundary conditions, which in the limit corresponds to the no-slip condition. We rigorously establish existence and asymptotic properties of their eigenvalues, eigenmodes and Green functions away from critical layers. The adjoint operators are useful because they also allow us to deduce properties about the kernels and images of the original operators.

Marginal stability analyses for thermochemical convection and its implications for the dynamics of continental lithosphere and core–mantle boundary regions

SUMMARY Significant compositional differences may exist in the lithospheric mantle and above the core–mantle boundary (CMB) relative to the ambient mantle. The intrinsic density differences may affect the development of thermal boundary layer (TBL) instabilities associated with lithospheric delamination and formation of thermochemical plumes. In this study, we explored the instability of two-layer thermochemical fluid using two different techniques: marginal stability analysis with a propagator-matrix method and finite element modelling. We investigated both the instabilities in lithospheric mantle (i.e. lithospheric instability) and the mantle above the CMB (i.e. plume-forming instability) using a background temperature Tbg(z) with the TBL. For lithospheric instability, we found that two-layer fluid with free-slip boundary conditions mainly undergoes the same three different convective modes (i.e. two oscillatory convection modes and one layered convection regime) as that with no-slip boundary conditions reported in Jaupart et al. However, with free-slip boundary conditions, the transitions between these convection modes occur at larger values of buoyancy number B. Free-slip boundary conditions lead to smaller critical Rayleigh number Rac, but larger convective wavelength and oscillation frequency ωc, compared with those with no-slip boundary conditions. Our numerical modelling results demonstrate that Rac and ωc predicted from the classical marginal stability analyses using Tbg(z) with TBL temperature may have significant errors when the oscillatory period is comparable with or larger than the timescale of lithospheric thermal diffusion that causes Tbg(z) to vary with time significantly. In this case, using a more gently sloped background temperature profile ignoring the TBL temperature, the stability analysis predicts more accurate stability conditions, thus presenting an effective remedy to the stability analysis. For plume-forming instability, because of the reduced viscosity in the hot and compositionally dense bottom layer, the transition to the layered convection occurs at significantly smaller B values, and in the oscillatory convection regime, Rac is larger but ωc is smaller, compared with those for lithospheric instability. Finally, our study provides a successful benchmark of numerical models of thermochemical convection by comparing Rac and ωc from numerical models with those from the marginal stability analysis.

Maximal transport of non-Newtonian fluid in an anisotropic rotating porous channel with an inclined magnetic field

This study explores the flow characteristics of a viscous, incompressible, conducting Jeffrey fluid in a rotating channel filled with anisotropic porous medium with an inclined magnetic field. The study has relevance to fluid motion in striated rock formations and seepage flow in rotating systems across insulation or geological layers. The channel's rotation axis and a principal axis of the permeability tensor are perpendicular to the walls. The flow is described by the Darcy–Brinkman model under no-slip boundary conditions, applicable in regenerative heat exchangers. Key parameters include the rotation rate and the lateral permeabilities. They have significant impacts on flow behavior. Fluid velocity consists of a primary component aligned with the pressure gradient and a secondary component influenced by the Coriolis force. The variation in lateral permeabilities affects the convexity of the velocity profile, while the magnetic field allows for control of both velocity and volumetric flow rates. The Jeffrey parameter and the inclination angle further enhance the flow behavior. This study provides comprehensive analysis through tables and figures for various values of the anisotropic Darcy number and the rotation parameter, detailing the model's physical properties. The effects of the product of skin friction and the Reynolds number are also discussed, with results aligning with the existing literature for limiting cases. These findings offer valuable insights into fluid behavior in complex environments where rotation, porous structures, and magnetic fields interact with implications for process optimization, resource recovery, and sustainable engineering practices.

Rheological impact of viscous fluid in the core region of heated curved pipe surrounded by Casson rheological fluid

The immiscible fluids can help design more efficient systems for drug delivery and understanding the blood flow through diseased arteries. It can also have implications for the design of flow control devices or medical implants that involve curved geometries. Therefore, the current article scrutinizes the characteristics of heat transfer on the flow of two immiscible Casson and Newtonian fluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with Newtonian fluid while (ii) Region 2 (peripheral) is filled with non-Newtonian Casson fluid. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Casson fluid parameter, Reynolds number, viscosity ratio, density ratio, Eckert number, and conductivity ratio on the axial velocity and temperature is studied through 2-dimensional graphs and contour plots. In addition, the volumetric flow rate and shear stress are also presented to evaluate the effects of various key parameters. The results show that the axial velocity of immiscible fluids flow increases with an increase in the values of the viscosity ratio parameter and the fluid temperature is decreased by increasing the conductivity ratio parameter.

Variable viscosity characteristics of two-layered isothermal calendering phenomena with non-Newtonian fluids

Two-layer calendering using non-Newtonian fluids is used frequently in different industries to improve the working and the quality of the products. In this article, two-layer calendering of incompressible non-Newtonian fluids, that is, couple stress fluid and viscoplastic fluid in the upper and lower layer respectively is investigated. For the simplified governing equations, Lubrication approximation theory is applied. By the use of no-slip condition and non-dimensional variables, the exact solution for pressure gradient, pressure, and velocity profiles for both layers of fluid is calculated. The parameters are important from an engineering point of view like roll separating force, power delivered by rollers, torque acting by each roller, and adiabatic temperature are also calculated analytically. Additionally, the results of a couple stress parameter, viscoplastic Casson parameter, and viscosity ratios on all the parameters are also discussed and investigated in detail. Moreover, all the effects investigated are also verified with the literature results of single-layer calendering of non-Newtonian fluids by using large numeric values for the couple stress parameter and viscoplastic Casson parameter.

Prandtl boundary layer expansion with strong boundary layers for inhomogeneous incompressible magnetohydrodynamics equations in Sobolev framework

We consider the validity of Prandtl boundary layer expansion of solutions to the initial boundary value problem for inhomogeneous incompressible magnetohydrodynamics equations in the half-plane when both viscosity and resistivity coefficients tend to zero, where the no-slip boundary condition is imposed on velocity while the perfectly conducting condition is given on magnetic field. Since there exist strong boundary layers, the essential difficulty in establishing the uniform L∞ estimates of the error functions comes from the unboundedness of vorticity of strong boundary layers. Under the assumptions that the viscosity and resistivity coefficients take the same order of a small parameter and the initial tangential component of magnetic field has a positive lower bound near the boundary, we prove the validity of Prandtl boundary layer ansatz in L∞ sense in Sobolev framework. Compared with the homogeneous incompressible case considered in [33], there exists a strong boundary layer of density. Consequently, some suitable functionals should be designed and the elaborated co-normal energy estimates will be involved in analysis due to the variation of density and the interaction between the density and velocity.

Nonlinear stability analysis of thermal convection in a fluid layer with slip flow and general temperature boundary condition

The current article presents a comprehensive analysis of the influence of inconstant viscosity into thermal convection, incorporating the influence of generalized velocity (slip boundary condition) and temperature boundary conditions (physically represent imperfectly conducting boundary) within a fluid layer. Slip boundary conditions are often considered more practical than no-slip conditions (Neto et al. (2003)). Therefore, in the present work, slip boundary condition is used to discuss the effect of temperature and pressure dependent viscosity. Both linear and nonlinear stability analyses are explored, revealing a noteworthy finding: the precise alignment of the nonlinear stability boundary with the linear instability threshold. Additionally, the exchange of stability is illustrated, indicating that convection exclusively manifests in a stationary mode. The findings are derived across a spectrum of boundary scenarios, ranging from free-free to rigid-free, and rigid-rigid boundaries, encompassing both isothermal and adiabatic conditions. Notably, the slip length parameter exhibits a destabilizing effect, while convection is observed to occur more swiftly under adiabatic boundary conditions compared to isothermal conditions. The Chebyshev pseudo-spectral technique is applied to solve the eigenvalue problems obtained from linear and nonlinear stability analysis.

A numerical study on MHD Casson fluid flow in a non-uniform rough channel with temperature-dependent properties using OHAM

This study explores the complex dynamics of magnetohydrodynamic (MHD) Casson fluid in a non-uniform rough channel, focusing on the effects of temperature-dependent viscosity and variable thermal conductivity under no-slip boundary conditions. The study employs an innovative approach by utilising a rough surface with irregular textures to analyse flow patterns and assess drag forces on channel objects. A novel mathematical model, governed by continuity, momentum, and heat transfer equations, is developed and transformed into dimensionless, nonlinear Ordinary Differential Equations (ODEs) using non-dimensional quantities and fundamental assumptions. The Optimal Homotopy Analysis Method (OHAM) is applied to solve these equations to enhance convergence speed and accuracy. The research explores the impact of surface roughness on velocity profiles and temperature distributions under various physical constraints. Numerical simulations are conducted to determine skin friction coefficients and Nusselt numbers. Furthermore, the study examines the influence of confined boluses on fluid flow in diverse physiological conditions. A comprehensive analysis is performed to elucidate the combined effects of surface roughness on fluid passage, including flow separation, pattern alterations, pressure distribution and drop, heat transfer characteristics, and flow resistance. The intricate interplay between temperature-dependent viscosity, varying thermal conductivity, and surface roughness is thoroughly investigated to explain the complex dynamics of MHD Casson fluid movement in non-uniform channels. Implementing a magnetic field over the rough, non-uniform channel is found to provide stability and prevent fluid overflow. This research has significant real-world applications, including soil erosion prevention, blood flow regulation in arteries, and optimisation of hydropower channels and penstocks. By enhancing our understanding of flow dynamics through rough and non-uniform channels, this study contributes valuable insights into both theoretical fluid mechanics and practical engineering applications.

A numerical study of heat and mass transfer characteristic of three-dimensional thermally radiated bi-directional slip flow over a permeable stretching surface

Within fluid mechanics, the flow of hybrid nanofluids over a stretching surface has been extensively researched due to their influence on the flow and heat transfer properties. Expanding on this concept by introducing porous media, the current study explore the flow and heat and mass transport characteristics of hybrid nanofluid. This investigation includes the effect of magnetohydrodynamic (MHD) with chemical reaction, thermal radiation, and slip effects. The nanoparticles, copper, and alumina are combined with water for the formation of a hybrid nanofluid. Using the self-similar method for the reduction of Partial differential equations (PDEs) to the system of Ordinary differential equations (ODEs). These nonlinear equation systems are solved numerically using the bvp4c (boundary value solver) technique. The effect of the different physical non-dimensional flow parameters on different flow profiles such as velocity, temperature, concentration, skin friction, Nusselt and mass transfer rate are depicted through graphs and tables. The velocity profiles diminish with the effect of magnetic and slip parameters. The temperature and concentration slip parameters reduce the temperature and concentration profile respectively. The higher values of magnetic factor lessened the skin friction coefficient for both slip and no-slip conditions. An elevation in the thermal slip parameter reduced the boundary layer thickness and the heat transfer from the surface to the fluid. The Nusselt number amplified with the climbing values of the radiation parameter. The mass transfer rate depressed with the solutal slip parameter. Comparison is made with the published work in the literature and there is excellent agreement between them.

A comparative study of shale oil transport behavior in graphene and kerogen nanopores with various roughness via molecular dynamics simulations

Understanding the transport behavior of molecules within nanopores is crucial in various fields, including nanofluidic, bioengineering and geophysics. To elucidate oil flow within shale organic nanopores, the simplified carbon nanopores (e.g., graphene and CNTs) and realistic kerogen nanopores have been extensively applied. The variation in pore structure models leads to divergent findings in oil flow behavior. This study employs molecular dynamics simulations to compare alkane flows within graphene and kerogen nano-slits with similar surface roughness. We observe that using graphene nanopores with ultra-smooth surfaces may introduce errors of several orders of magnitudes in flux calculations. Conversely, when accounting for similar roughness, the static characteristics and flow behaviors in graphene and kerogen slit pores are largely comparable. The relative error of flux and the flow velocity could be lower than 6% when using graphene to replace the realistic kerogen. Alkane molecules exhibit a parabolic velocity profile, with a no-slip condition adjacent to the rough surfaces. In addition, when applying the Hagen-Poiseullie equation for alkane flow in rough nanopores, Gibbs dividing surface is recommended for defining the pore radius, reducing the error of flux predicted to below 10%. Our work fulfills the gap in accessing the suitability of using graphene as a model for oil transport in shale organic nanopores, and provides valuable insights and guidance for future studies on nanofluidic in shale, including molecular simulations, nanofluidic experiment designs, and multi-scale modeling.

Combined electroosmotic and pressure driven flow through soft nanochannel grafted with partially ion-penetrable polyelectrolyte layers

ABSTRACT This study explores the coupled effects of pressure-driven and electroosmotic flows in a soft nanochannel filled with non-Newtonian ionised liquid, where the inner walls are coated with a polymer layer. The ion partitioning effect occurs due to the Born energy, arising from the dielectric permittivity difference between the polyelectrolyte medium and the ionised liquid. The model incorporates the nonlinear Poisson-Boltzmann equation, the modified Darcy-Brinkman equation in the polyelectrolyte layer (PEL), the Cauchy momentum equation in the electrolyte domains and the continuity equation for incompressible fluids. Using the Debye-Hückel approximation for analytical results, the study validates numerical findings. The study considers the no-slip boundary condition on the walls and examines the impact of volume charge density of PEL, bulk electrolyte concentration, non-Newtonian fluid rheology and polymer layer characteristics and applied pressure gradient on flow modulation and ionic transport in the nanochannel. We provide rigorous mathematical results showing how electrohydrodynamic factors like charged PEL, flow behaviour index, EDL thickness, ion partitioning parameters, Debye-Hückel parameter and softness parameters influence the strength of the potential and the total flow modulation. We illustrate ion selectivity in the soft nanochannel and the friction factor across its walls, considering ion partitioning effects.

The hydraulically smooth limit of flow over surfaces with spanwise heterogeneity

Wall slip is conventionally obtained through riblets or grooves. As riblets are macroscopic objects, it is usually not practical to discuss slip patterns at the hydraulically smooth limit. Per Nikuradse, the smooth limit is when the characteristic length of the surface pattern is comparable to the viscous length scale. Recent studies show the possibility of slip at the microscopic scale, making slip patterns at the hydraulically smooth limit relevant. In this study, we leverage a high-fidelity pseudo-spectral code and study flow over surfaces featuring alternating strips of slip and no-slip wall conditions. The wavelength of the surface pattern, denoted as l, varies from 1.5 times the half channel height to 2 viscous units (plus units), eventually approaching the anticipated hydraulically smooth limit. The presence of surface slip gives rise to a slip velocity at the wall, denoted as Us, which contributes to drag reduction. The surface spanwise heterogeneity leads to secondary flows and intensifies turbulent mixing, consequently leading to drag increase. This drag increase effect can be parameterized using the “roughness function” ΔU+. The sum of Us+ and −ΔU+ determines whether the surface increases or reduces drag. Here, the superscript ＋ denotes normalization by the wall units. In most cases, the slip velocity at the wall Us+ predominates over −ΔU+, resulting in drag reduction. However, when l is a few viscous units, the roughness function ΔU+ does not vanish and overwhelms the slip velocity, giving rise to a net drag increase. Considering that the wall is a mixture of slip and no-slip conditions, this drag increase at the anticipated hydraulically smooth limit is unexpected. To gain an insight into the mechanism responsible for this drag increase, we derive a Navier–Stokes-based decomposition of the roughness function. Here, we generalize the definition of the roughness function such that it is a function of the wall-normal coordinate, thereby overcoming the difficulty of measuring the roughness function when the log region is narrow and hard to define. Analysis shows that when l is a few plus units, secondary flows contribute to a slightly positive ΔU+, while turbulent and viscous contributions, by and large, cancel out, ultimately leading to an overall drag increase at the anticipated hydraulically smooth limit. The evidence in the paper suggests that the hydraulically smooth limit does not exist for certain surfaces.

A Navier-slip model for liquid film thickness in gas–liquid slug flow in capillaries

ABSTRACT The motion of a long gas bubble in a continuous liquid phase in a small diameter channel results in a thin liquid film between the bubble and the channel wall. Generally, a free-slip (zero shear) boundary condition is applied at the gas–liquid interphase boundary which is applicable only at low gas velocities. However, at increased flow rates of gas phase, shear stress at the gas–liquid interface is non-negligible. Applying non-zero shear at the interface requires knowledge of velocity profile in the gas phase. In this work, we circumvent this problem by using a slip length like parameter to take into account the velocity gradient in the gas phase. The slip length is infinite for the free-slip condition at the interface and zero for the no-slip condition. An expression is derived for the film thickness in terms of slip length and capillary number and is compared with the experimental data and other correlations available in the literature.

Pizza3: A general simulation framework to simulate food-mechanical and food-deconstruction problems

Current mesh-based simulation approaches face significant challenges in continuously modeling the mechanical behaviors of foods through processing, storage, deconstruction, and digestion. This is primarily due to the limitations of continuum mechanics in dealing with systems characterized by free boundaries, substantial deformations, mechanical failures, and non–homogenized mechanical properties. The dynamic nature of food microstructure and the transformation of the food bolus, in relation to its composition, present formidable obstacles in computer-aided food design. In response, the Pizza3 project adopts an innovative methodology, utilizing an explicit microstructural representation to construct and subsequently deconstruct food products in a modular, Lego-like fashion. Central to this simulation approach are “food atoms”, conceptualized from the principles of smoothed particle hydrodynamics. These units are significantly larger than actual atoms but are finely scaled to represent both solid and liquid states of food faithfully. In solid phases, food atoms interact via pairwise forces akin to bond-peridynamic methods, thus extending the capabilities of continuum mechanics to encompass large deformations and fracturing phenomena. For liquids, the model employs artificial conservative and dissipative forces, enabling the simulation of a variety of phenomena within the framework of partial compressibility. The interaction dynamics between rigid and soft objects and fluids are accurately captured through Hertzian contact mechanics, offering a versatile parameterization applicable to impermeable (but possibly penetrable) surfaces and enforcing no-slip conditions. The efficacy of this framework is showcased through the successful modeling of three time-dependent 3D scenarios, each rigorously validated against established analytical and experimental models. Advancing beyond these initial applications, the framework is further extended to more intricate cases inadequately addressed in current literature. This extension sheds light on the underlying mechanisms of in-mouth texture perception, offering new insights and tools for food engineering and design.

Analyzing the 3D-MHD flow of a sodium alginate-based nanofluid flow containing alumina nanoparticles over a bi-directional extending sheet using variable porous medium and slip conditions

Abstract The sodium alginate (SA)-based nanofluid flow comprising alumina nanoparticles on a bi-directional extending sheet has many applications, which include thermal management, automotive radiators, industrial heat exchangers, conductive coatings, flexible electronics, electromagnetic shielding, solar panels, etc. A numerical study based on the SA-based nanofluid flow containing alumina nanoparticles over a bi-directional extending sheet in the presence of variable Darcy porous media has not yet been examined. Therefore, this study focuses on numerically investigating the flow behavior of a nanofluid of SA containing nanoparticles of alumina (Al2O3) over a bi-directional extending sheet. The variable Darcy porous media, magnetic field, thermal radiation, and thermal-dependent and space-dependent heat sources are applied to examine heat transfer flow. The velocity and thermal slip conditions have been used in the present model. The model is first shown as partial differential equations and is then converted to ordinary differential equations (ODEs). A numerical technique called bvp4c MATLAB function is applied to solve the modeled ODEs. The model is validated with previously published results. From the obtained results, it is found that high magnetic factor increases the thermal distribution, skin frictions, and heat transfer rate and reduces the velocity profiles along both directions. The Casson factor reduces the skin friction, heat transfer rate, and velocity profiles along both directions while increasing the thermal distribution. High velocities and temperature distributions of a SA-based nanofluid flow containing alumina nanoparticles are found for the scenario of no-slip condition when matched to the slip condition. It is concluded from the observed results that the percentage increase is higher for the no-slip conditions compared to the slip conditions.

Analysis of peristalsis transport in flow of non-Newtonian fluid with modified Darcy’s law

Nanofluids present novel applications in various era of engineering and medical sciences like lubricants, medication delivery, cancer treatment, and microchip cooling. Investigating the peristaltic transport of a magnetohydrodynamic (MHD) Williamson nanofluid model in a horizontally asymmetrical channel is the main goal of this article. A porous medium allows the flow to take place according to the revised Darcy’s law. Hybrid nanoparticles based on aluminum oxide are used to improve the thermal properties. The classical aspects with implementation of Buongiorno approach namely thermophoretic effects and Brownian impact is elaborated. The extension in heat equations is proceeded with utilization of Joule heating and viscous dissipation outcomes. There are no-slip conditions linked to the channel borders. By adhering to the lubricating strategy and employing the homotopy perturbation method, the issues are resolved. Graphs and tables are used for physical analysis of the relevant parameters. It is examined that velocity profile enhances due to Darcy parameter in both channel walls. The temperature profile for hybrid nanofluid increases for Brinkman number. Low concentration profile is claimed for activation energy parameter. Current results incorporate the applications in thermal engineering, nuclear systems, roller pumps, heat transfer devices, chemical engineering, etc.

Numerical investigation of unsteady MHD immiscible Casson micropolar and Jeffery fluid in a horizontal channel with heat transfer using MCB-DQM approach

The dynamics of immiscible Casson micropolar and Jeffery fluid flow offer new possibilities for enhancing momentum and heat transfer efficiencies. Motivated by numerous applications of immiscible fluid flows in natural and industrial systems, the current work presents a numerical investigation of unsteady, incompressible, magnetohydrodynamic (MHD) flow involving two immiscible fluids, namely, Casson micropolar and Jeffery fluid, in a horizontal channel. The flow, driven by a uniform pressure gradient, assumes no-slip conditions at the channel walls and a continuous, nondeformable interface between the immiscible fluids. The well-established rapid converging modified cubic B-spline differential quadrature method (MCB-DQM) is applied to solve the partial differential equations governing the flow. The impact of crucial fluid parameters comprising the Casson micropolar fluid parameter, Jeffery fluid parameter, thermal, magnetic, and various other fluid parameters on temperature, microrotation, and velocity profile is illustrated graphically. Notably, the parameters of each fluid influence the profiles in both fluid zones. The flow dynamics are significantly affected by viscous dissipation, Lorentz force, fluid–wall interactions, and interfacial conditions. Key parameters such as time, Jeffery fluid, Casson micropolar, ion slip and Hall parameters, Reynolds number, Eckert number, the ratio of viscosities, the ratio of densities, and pressure gradient show significant impacts on the velocity, microrotation, and temperature profiles. However, reverse or mixed behavior is observed for other parameters. The novelty of current work lies in modeling the unsteady, immiscible, MHD flow of Casson micropolar and Jeffery fluid and proposing a numerical solution by deploying the MCB-DQM method. The findings have potential applications in various industrial and engineering processes, such as the design of oil extraction, optimizing processes in the food processing and cosmetics industry, and developing effective strategies for environment conservation.

Flow field prediction in bed configurations: A parametric spatio-temporal convolutional autoencoder approach

The use of deep learning methods for modeling fluid flow has drawn a lot of attention in the past few years. Here we present a data-driven reduced-order model (ROM) for predicting flow fields in a bed configuration of hot particles. The ROM consists of a parametric spatio-temporal convolutional autoencoder. The neural network architecture comprises two main components. The first part resolves the spatial and temporal dependencies present in the input sequence, while the second part of the architecture is responsible for predicting the solution at the subsequent timestep based on the information gathered from the preceding part. We also propose the utilization of a post-processing non-trainable output layer following the decoding path to incorporate the physical knowledge, e.g. no-slip condition, into the prediction. The ROM is evaluated by comparing its predicted solution with the high-fidelity counterpart. In addition, proper orthogonal decomposition (POD) is employed to systematically analyze and compare the dominant structures present in both sets of solutions. The assessment of the ROM for a bed configuration with variable particle temperature showed accurate results at a fraction of the computational cost required by traditional numerical simulation methods.