Flow Problems Research Articles

Heat and mass transfer analysis of non‐miscible couple stress and micropolar fluids flow through a porous saturated channel

AbstractThis study examines the flow rate, Bejan number transportation, concentration distribution and thermal characteristics of an immiscible couple stress‐ micropolar fluids within a porous channel. The authors focus on the effects of heat radiation and an angled magnetic field on the thermal dispersion, concentration distribution and entropy formation of two different types of incompressible immiscible micropolar and couple stress fluids inside a porous channel. Here, the static walls of the channel are isothermal, and the pressure gradient in the flow domain's entrance zone is constant. In this flow problem, we tried to simulate thermal radiation in the energy equation by applying Rosseland's diffusion approximation. To solve the problem, the authors have used no‐slip conditions at the channel's immovable walls, a continuity of temperature profile, shear stresses, thermal flux, linear velocity, and micro‐rotational velocity over the fluid‐fluid interface. The equations that govern the flow of immiscible fluids are solved using a well‐defined methodology and both the temperature and flow field are then evaluated using a closed‐form solution. The mathematical results of the thermal distribution and flow velocity are used to derive the Bejan number distribution and the entropy generation number. Graphical discussions are used to illustrate the impact of different emerging factors on the model's flow and thermal properties, which describe the major impact of the proposed model. These variables involve the micropolarity parameter, Reynolds number, inclination angle parameter, radiation parameter, and Hartmann number. The outcomes of the present models are corroborated by previously established results available in the literature.

Uncertainty modeling and propagation for groundwater flow: a comparative study of surrogates

We compare sparse grid stochastic collocation and Gaussian process emulation as surrogates for the parameter-to-observation map of a groundwater flow problem related to the Waste Isolation Pilot Plant in Carlsbad, NM. The goal is the computation of the probability distribution of a contaminant particle travel time resulting from uncertain knowledge about the transmissivity field. The latter is modelled as a lognormal random field which is fitted by restricted maximum likelihood estimation and universal kriging to observational data as well as geological information including site-specific trend regression functions obtained from technical documentation. The resulting random transmissivity field leads to a random groundwater flow and particle transport problem which is solved realization-wise using a mixed finite element discretization. Computational surrogates, once constructed, allow sampling the quantities of interest in the uncertainty analysis at substantially reduced computational cost. Special emphasis is placed on explaining the differences between the two surrogates in terms of computational realization and interpretation of the results. Numerical experiments are given for illustration.

Optimization of Interconnected Natural Gas and Power Systems Using Mathematical Programs with Complementarity Constraints

The demand for thermal power generation from natural gas has increased globally due to its cleaner burning properties compared to other fossil fuels. Optimizing the gas flow through the network to meet this demand is challenging due to the nonconvex Weymouth equation constraining gas flow and nodal pressures in pipelines. Traditional methods for addressing this nonconvexity lead to significant approximation errors or high operational costs. This study poses the Weymouth constraint as a Mathematical Programming with Complementarity Constraints (MPCC) for an optimal gas flow problem. The complementarity constraints reformulate the discontinuous sign function using binary-behaving continuous variables. This MPCC-based approach avoids solving mixed-integer programming problems while enhancing the accuracy of conventional linear and second-order approximations. Testing the approach on various interconnected systems, including Colombia’s national gas transportation grid, demonstrated significant reductions in Weymouth approximation errors, thereby supporting effective optimization for interconnected networks.

Unsteady flow of nanofluid over a sheet of variable thickness with nonlinear kinematics

The transport of heat in an unsteady flow of nanofluid has been discussed in this paper. The flow is maintained over a non-flat, variably porous, and moving sheet in the present simulation. Moreover, the sheet has both constant temperature and nanoparticle concentration at its surface. Unsteadiness in all field variables (i.e. the flow, temperature, and nanoparticles concentration) has been produced by the time-dependent quantities, specified at the surface of the sheet (i.e. kinematics of sheet). The well-known Buongiorno model of nanofluid has been undertaken in the present studies. Furthermore, the simulation includes the particular cases of uniform and linear (polynomial & algebraic functions) stretching/shrinking and injection/suction velocities. Besides that observations of the same nature have been recorded for the non-flat sheet. The boundary layer form of the governing PDEs has been utilized to evaluate the exact status of field variables in the flow domain. Appropriate conditions are imposed by considering the geometry of the flow problem. The problem at hand is simplified by introducing a new set of functions for the field variables because of boundary inputs. After this treatment, the system of boundary value ODEs, which contains several dimensionless numbers (parameters), has appeared, and the problem is solved numerically for various values of parameters, involved in it. More precisely, effects of unsteadiness, wall roughness, surface deformation parameters, Prandtl, Schmidt, thermophoretic, and Brownian motion numbers have been seen on profiles of four field variables. Besides that, the numerical results are also obtained for the skin friction coefficient, Nusselt, and Sherwood numbers. The present modelled problem and its solution are compared with classical models of that particular nature and with their solutions.

Numerical analysis for Cattaneo-Christov heat flux on convective viscous non-Newtonian fluid flow through porous medium with nonuniform heat source

This work investigates the Ohmic heating, nonuniform heat generation, and Hall effects with Cattaneo-Christov model (CCM) on flow and heat transfer of power-low non-Newtonian fluids (NNFs) past stretching surface embedded in a porous medium. Runge-Kutta method is used to solve non-linear ODEs numerically using a shooting procedure. We study non-Newtonian fluids for power law values of 0.7 and 1.2, respectively. Innovation of this work lies in studying the effect of Hall currents in presence of buoyancy force and an irregular heat source on slip flow of NNFs moving through Darcy porous medium. Varying velocities, surface frictional forces, and Nusselt numbers are examined. Resulting entropy is also examined using computational flow problem investigation. Model-simulated results suggested that various factors play critical role in constructing thermal systems. It is asserted that Hall parameter, mixed convection parameter, Biot numbers, and thermal relaxation time improve heat transference rates by directly affecting fluid molecules temperature.

Molecular dynamics simulation of wax micro-structure characteristics in the oil-water emulsion

As a key issue in the flow assurance of wax-containing crude oils, the microscopic mechanism of wax deposition in multiphase pipelines is still unclear. Based on macroscopic experimental data, two forms of crystallized wax have been found under an oil-water emulsion, including adsorbed wax on the interface of water droplets and suspended wax in the bulk oil phase, which are the important factors influencing wax deposition. However, the micro-formation mechanism of the adsorbed & suspended wax is not elucidated. In this work, molecular dynamics simulations are used to investigate the micro-structure characteristics of the adsorbed & suspended wax in the oil-water emulsion containing surfactant Span60. A method is proposed to quantitatively calculate the distributions of the adsorbed & suspended wax and the percentage of wax adsorption area at the oil-water interface. The results indicate that surfactant with the hydrophilic end will insert into the water phase and the trailing hydrophobic end stretching will point to the oil phase during co-crystallizing with wax molecules. Meanwhile, the interface tension is further reduced by tilting the adsorbed wax tail chain to enhance the adsorption stability. Based on the complicated influence of surfactants on wax adsorption, the quantitative distribution characteristics of the adsorbed & suspended wax in the oil-water emulsion are complex under different wax carbon numbers and surfactant/wax contents. This microscopic investigation of wax distribution in oil-water emulsion can support the establishment of better strategies for solving the wax deposition problem in multiphase flow.

Iterative schemes for coupled flow and transport in porous media -- Convergence and truncation errors

Nonlinearities of coupled flow and transport problems for partially saturated porous media are solved with explicit iterative L-schemes. Their behavior is analyzed with the aid of the computational orders of convergence. This approach allows highlighting the influence of the truncation errors in the numerical schemes on the convergence of the iterations. Further, by using manufactured exact solutions, error-based orders of convergence of the iterative schemes are assessed and the convergence of the numerical solutions is demonstrated numerically through grid-convergence tests.

A numerical inquiry of the MHD radiative thin film nanofluid flow and heat transfer augmentation for Ni and Ta nanoparticles of different shapes dispersed in C 12 H 26–C 15 H 32 over an unsteady, curved stretching surface

Thin films are a versatile technology used in various industries, including light-emitting diodes, magnetic recording media, electronic device manufacturing, and optical coating. They are crucial for studying quantum phenomena, superlattices, and multiferroic materials. Their small size allows for better thermal transport studies due to the combination of thin film flow and nanoparticles. Therefore, this study aims to investigate thin film flow and heat transfer with the effects of thermal radiations, magnetic field, and velocity slip in association with tantalum ( Ta ) and nickel ( Ni ) nanoparticles that emerged in kerosene oil ( C 12 H 26 − C 15 H 32 ) toward a curved stretching surface. A review of the pertinent literature indicates that no research has previously been done on the present problem of an unsteady thin film flow across a curved stretching surface. The problem under consideration is modeled by choosing the curvilinear coordinate system. The controlling nonlinear system of partial differential equations is transformed into the system of ordinary differential equations by using an appropriate similarity transformation and then solved numerically using the BVP 4 C technique in MATLAB . The impact of significant physical parameters on velocity, temperature, skin friction, and Nusselt numbers are depicted through graphs and radar charts. The investigation highlights the significant influence of magnetohydrodynamics ( MHD ) , thermal radiation, volumetric fraction, and velocity slip on the enhancement of nanofluid temperature. It is also noted that cylindrical-shaped Ta nanoparticles exhibited the maximum velocity, while blade-shaped Ni nanoparticles showed the lowest. Moreover, the maximum and minimum temperatures were observed for blade-shaped Ni nanoparticles and cylindrical Ta nanoparticles, respectively. Additionally, the maximum and minimum values of skin friction are found for cylindrical Ni nanoparticles and blade-shaped Ta nanoparticles, respectively. Similarly, the maximum and minimum Nusselt numbers are recorded for cylindrical Ta nanoparticles and blade-shaped Ni nanoparticles, respectively.

Exact exploration of time fractional-based magnetized flow of a generalized second grade fluid through an oscillating rectangular duct

To model several engineering and physical models, the approach of the fractional derivative is highly anticipated. As compared to the ordinary derivatives, the fractional derivatives with more flexibility can estimate the data due to the involvement of the fractional-order derivatives. Due to these advantages of the fractional approach, this study communicates with the determination of the fractional-based exact outcomes of an oscillatory rectangular duct problem of a generalized second-grade fluid. The approach of the fractional operator is involved in the relationship of the constitutive equations. For cosine oscillation of the rectangular duct, exact results of the magnetized unsteady flow problem are evaluated through the technique of Laplace transform with double finite Fourier sine transform. This study concludes that the velocity field exhibits escalating behavior relative to the improved fractional parameter. Moreover, the magnetic parameter with increasing values declines the flow field while the accelerating values of the fluid parameter enhance the velocity field.

The effects of energy accommodation of reflected gas molecules on flow structures during expired spacecraft reentry

To study the influence of energy accommodation of scattering gas molecules on flow fields during large expired spacecraft reentry, a more elaborated gas-surface interaction model, compared with full Maxwellian diffuse model, is employed in implicit algorithms based on Boltzmann model equation. The characteristic distributions around cylinder at different fluid regimes are accordingly obtained by implicit algorithms, Navier-Stokes solver and DSMC ((Direct Simulation Monte Carlo) method. And the consistency of these results is verified. It is confirmed that present algorithms are capable of solving external flow problems covering various fluid regimes. Then the simulation results see that under current conditions set in the paper, pressure and temperature are proportional to wall activation (ω=Tw/T∞, Tw is surface temperature, T∞ denotes as free stream temperature), but their amplitudes alter with ω at different fluid regimes. As for the effects of energy accommodation coefficients (αe), both pressure and temperature profiles vary in a linear way with αe. However, the variation ranges of these parameters are diverse with regard to different fluid regimes. These observations are favor to the construction of efficient forecasting software, which could predict the flight path of large defunct spacecraft. In this forecasting software, the external ballistics computations and aerothermodynamic simulations are synchronously carried out.

Numerical analysis of the axisymmetric lattice Boltzmann method for steady and oscillatory flows in periodic geometries

Compared to more typical computational fluid dynamics techniques, the lattice Boltzmann method (LBM) is relatively new and unexplored. In recent years, axisymmetric LBM formulations, which can simulate flow in rotationally symmetric 3D geometries, have been published. Here we verify a novel axisymmetric LBM implementation using numerical criteria. Hagen–Poiseuille and Womersley flow are considered within a straight tube where analytic solutions are available. With this, we establish sufficient accuracy of the approximated flow and study the effects of changing simulation parameters (e.g. Reynolds number, Womersley number) and spatial/temporal parameters (e.g. relaxation time, mesh nodes, time steps). Furthermore, steady and oscillatory flows within a periodically-varying, longitudinally asymmetric geometry are considered. Analytic solutions are not available in these cases; however, the validity of the axisymmetric LBM for curved boundaries is ensured through convergence, mesh independence and qualitative observations. Guaranteeing reasonable flow field determination for the aformentioned geometry is relevant to a larger problem where particulate suspension is pumped back and forth through a membrane of axisymmetric micropores. In these circumstances, experiments have induced directed particle transport even though there is no net flow of the carrier fluid. Hence, our work aims to improve current numerical simulations of these flow problems to better understand the factors that facilitate particle transport.

Assessment of Stroke Patients' Muscle Strength Following a Combination of Mirror Therapy and ROM (Range of Motion) Exercises Based on Self-Care Theory

Background: When blood flow problems kill off some brain cells, the result is a neurological deficiency known as a stroke. There have been 507 reported cases of stroke in East Java, while the overall stroke prevalence in Indonesia has jumped from 7% to 10.9% (Riskesdas, 2020). The researchers at RSI Darus Syifa's Surabaya set out to determine how much of an impact self-care theory-based mirror therapy and range-of-motion exercises had on the muscular strength of stroke patients admitted to the inpatient unit. Methods: A true experimental with a pretest-posttest control group design was utilised in this type of research. One hundred and ten stroke patients made up the study's population. There were a total of 34 participants in this study, with 17 serving as control subjects and 17 as interventionists. Sampling was based on probability sampling using simple random sampling. The Medical Research Council (MRC) scale was utilised by the device to measure muscular strength. Mann-Whitney and the Wilcoxon Signet Rank Test were used to examine the collected data. Results: In the inpatient ward of the Darus Syifa Surabaya Hospital, stroke patients who undergo a combination of mirror therapy and range of motion exercises based on self-care theory show a significant improvement in muscle strength, according to the Mann-Whitney test (p < 0.05). Conclusion: The study found that stroke patients' muscle strength improved with a combination of mirror therapy and range of motion exercises grounded in self-care theory.

A modified continuum surface force (M-CSF) model for two-phase flow problems in smoothed particle hydrodynamics

ABSTRACT This work proposes a modified interfacial tension model based on the continuum surface force (M-CSF) in the context of smoothed particle hydrodynamics. This correction aims to enhance computational stability, improve force evaluation precision, and increase symmetry around the interface. Several two-phase flow benchmarks are solved using both the conventional and proposed CSF models, and the results are compared with each other and with the available literature. The results indicate that the modified model can efficiently increase the force evaluation accuracy in the pressure field at the interface. For instance, the relative error in pressure calculation using the proposed and conventional CSF models is 0.05% and 3.5%, respectively, when compared to the analytical solution, with both models having the same particle resolutions for the droplet deformation problem. In predicting the critical surface tension for hydrodynamic instabilities, such as the Rayleigh-Taylor instability, the M-CSF methodology exhibits much better alignment with existing theories, showing less than 5% deviation, while conventionally used CSF models can deviate up to 15% for the same problem. These findings confirm the superiority of the proposed methodology in evaluating interfacial forces, even in complex hydrodynamic instabilities.

A Bayesian Approach To Locally Varying Regularization In Optical Flow Velocimetry

A recent method for determining accurate, dense velocity fields from a pair of particle images is to solve the optical flow problem, but the ill-posed inverse problem of optical flow velocimetry (OFV) generally entails minimizing a weighted sum of two terms--fidelity and regularization--and the weights in the sum are parameters that require manual tuning based on the flow properties and particle images. This tuning of the weighting parameters makes the experimental applicability of the method much more challenging as the calculated velocity field has demonstrated sensitivity to the value of the weights. This work proposes a hierarchical model for the weighting parameters in the framework of maximum a posteriori (MAP)-based Bayesian optimization approaches. The resulting method is tested on three different synthetic datasets and on experimental particle images. The method is found to be capable of self-adjusting the local weights of the optimization process in real-time while simultaneously determining the velocity field, leading to a more accurate estimate of the velocity field without requiring any dataset-specific manual tuning of parameters.

A high-order fully Lagrangian particle level-set method for dynamic surfaces

We present a fully Lagrangian particle level-set method based on high-order polynomial regression. This enables meshfree simulations of dynamic surfaces, relaxing the need for particle-mesh interpolation. Instead, we perform level-set redistancing directly on irregularly distributed particles by polynomial regression in a Newton-Lagrange basis on a set of unisolvent nodes. We demonstrate that the resulting particle closest-point (PCP) redistancing achieves high-order accuracy for 2D and 3D geometries discretized on irregular particle distributions and has better robustness against particle distortion than regression in a monomial basis. Further, we show convergence in classic level-set benchmark cases involving ill-conditioned particle distributions, and we present an example application to multi-phase flow problems involving oscillating and dividing droplets.

Mathematical analysis of heat and mass transfer efficiency of bioconvective Casson nanofluid flow through conical gap among the rotating surfaces under the influences of thermal radiation and activation energy

In the current proceeding, the flow of incompressible non-Newtonian nanofluid called Casson nanofluid is considered. A conical gap occurred among the rotating disc and the cone filled with the fluid flow. Heat and mass transport through this nanofluid is done by the convection mode of heat transfer. The impacts of microorganisms, chemical processes, thermal radiation, minimal amount of energy, and magnetic field are also considered in the mathematical model of flow problem. The Casson nano-fluid governing equations are interpreted in cylindrical coordinates. By implementing proper similarity transformations, the modeling PDEs of energy, momentum, concentration, and microorganism density are transformed into non-linear ODEs. A set of non-linear ODEs that deals with the distributions of temperature, velocity, concentration, and motile microorganisms produced by this technique. MATLAB in-built ‘bvp4c‘ technique is utilized to solve these equations. Findings are displayed graphically and elaborated theoretically. The primary goal of this work is to examine the effects during the rotation of the disc and cone as well as the impacts of other variables on the rotation. The nano-fluid temperature and radial velocity are found to be negatively impacted by the rotation parameter whereas azimuthal velocity is positively impacted. The parametric values are taken as 0.1<Nb<0.7, 0.1<λ<0.4, 1.0<Pr<2.50.1<M<0.4, 1.0<Rb<4.0, 0.1<Nr<0.4, 0.1<Sc<3.0, 0.1<Nt<0.4 for the purpose of generating modified results. From published and current results noted that rotation parameter effects impacted the transfer rate of the nanofluid.

On one analytical solution to the problem of flow around a tandem from two profiles by a flow of ideal incompressible fluid

On one analytical solution to the problem of flow around a tandem from two profiles by a flow of ideal incompressible fluid

Enhancing hydrodynamic forces through miniaturized control of square cylinders using the lattice Boltzmann method

This study investigates the influence of small control cylinders on the fluid dynamics around a square cylinder using the Lattice Boltzmann Method (LBM). Varying the gaps (L) between the main and control cylinders from 0 to 6, four distinct flow regimes are identified: the solo body regime (SBR), shear layer reattachment (SLR), suppressed fully developed flow (SFDF), and intermittent shedding (IS). The presence of control cylinders results in significant reductions in flow-induced forces, with drag coefficient (CD) and root mean square values of drag and lift coefficients (CDrms and CLrms) decreasing by approximately 31%, 90%, and 81%, respectively. The SFDF flow regime exhibits the lowest fluid forces compared to other regimes. The effects of tiny control cylinders on the fluid flow characteristics of a square cylinder are examined using the Lattice Boltzmann Method (LBM) in this research work. The gaps (L) between the main and control cylinders are varied in the range from 0 to 6. The size of each control cylinder is equal to one-fifth of the primary cylinder. According to the findings, there are four distinct flow regimes as the gap spacing varies: solo body regime (SBR), shear layer reattachment (SLR), suppressed fully developed flow (SFDF), and intermittent shedding (IS) for gap spacing ranges 0 ≤ L ≤ 0.2, 0.3 ≤ L ≤ 0.9, 1 ≤ L ≤ 3, and 3.2 ≤ L ≤ 6, respectively. Additionally, it has been noted that the amplitude of variable lift force is reduced when the gap separation between the main and control cylinders is increased. When compared to solo cylinder values, it is found that the presence of small control cylinders in the flow field results in a considerable reduction of flow-induced forces. The SFDF flow regime was determined to have the lowest fluid forces compared to the other flow regimes studied. Our findings highlight the efficacy of small control cylinders in mitigating flow-induced forces and controlling flow characteristics. The LBM proves to be a valuable computational technique for such fluid flow problems.

Influence of activation energy and variable thermal conductivity on magneto-convective nonlinear thermo-radiative Casson nanofluid containing motile microorganisms over a sinusoidal surface

The activation energy of convective-radiative nanoliquids with sinusoidal walls has garnered significant academic interest in recent years. This focus arises due to the pivotal applications of nanoparticles in thermal engineering, industrial processes, and medical sciences. This article investigates the magnetohydrodynamic heat transfer characteristics of Casson nanofluids containing microorganisms influenced by an oscillatory surface. The study incorporates temperature-dependent viscosity and utilizes Buongiorno’s mathematical model to account for nonlinear thermal radiation, Brownian motion, and thermophoretic effects from using nanomaterials in Casson fluids. These effects enhance thermal conductivity, improving the heat transportation phenomenon while considering gyrotactic microorganism density distributions. The boundary layer flow problem is formulated using partial differential equations and associated boundary conditions, subsequently numerically simulated using the bvp4c function. The investigation explores the thermal behavior of nanoparticles in the presence of bioconvection phenomena, Lorentz force, chemical reactions, and activation energy. As a result, this model addresses variable thermal conductivity and bioconvection aspects in Casson nanofluids over a sinusoidal surface. Numerically computed results for the Nusselt number, motile density, and Sherwood number provide insights into several essential features. The findings reveal that an increase in the Casson fluid parameter correlates with a decreased velocity profile. The assumptions of variable thermal conductivity and temperature-dependent viscosity prove more effective in raising the temperature of nanoparticles. The nanoparticle concentration profile rises noticeably for smaller Schmidt number Sc values when the activation energy parameter is higher than larger Sc values. Additionally, the presence of microorganisms in Casson nanofluids leads to increased temperatures due to an elevation in the bioconvection Rayleigh number. Moreover, heightened oscillating frequency parameters decrease nanoparticle concentration and microorganism density. Including activation energy and oscillating frequency parameters further enhances the understanding of nanoparticle concentration and microorganism density dynamics, offering valuable contributions to theoretical research and practical applications across multiple interdisciplinary fields.

An all Mach number scheme for visco-resistive magnetically-dominated MHD flows

In this work we present a novel conservative, semi-implicit, finite-volume scheme, designed for the numerical simulation of magnetically-dominated plasma rapidly evolving from a near-equilibrium state into a time-dependent compressible regime. The proposed scheme utilises a well-studied flux vector splitting approach, where the ideal magnetohydrodynamic (MHD) system is partitioned into two sub-systems, one containing all the advective terms and the other containing the rest of the terms, including not only the gas pressure but also magnetic pressure terms. The former is discretised explicitly as part of a standard finite-volume update, while the latter is treated implicitly by means of a nested Picard algorithm. As a result, the algorithm is constrained only by a mild velocity CFL stability condition, rendering it highly suitable for low Mach number flows in both gas and magnetic pressure dominated conditions, and for the incompressible limit of the MHD equations. The visco-resistive dissipative terms are also treated implicitly so that the numerical stability of the algorithm remains dependent only on the fluid velocity, maintaining its efficiency even for visco-resistive dominated problems. The divergence constraint of the magnetic field is handled through either staggered or unstaggered adaptations of the constrained transport methodology, which are both shown to preserve the divergence error up to machine precision levels. The algorithm is validated thoroughly by means of several benchmark problems for high and low Mach number flows, as well as multiple visco-resistive test cases. The scheme is found to perform well for both regimes, providing accurate and computationally efficient results in low Mach number flows in both gas and magnetic pressure dominated scenarios, while also demonstrating excellent shock-capturing capacity. A novel test case is finally introduced to truly demonstrate the all Mach number capabilities of the proposed scheme.