Relaxation Time Parameter Research Articles

A time-relaxation reduced order model for the turbulent channel flow

Regularized reduced order models (Reg-ROMs) are stabilization strategies that leverage spatial filtering to alleviate the spurious numerical oscillations generally displayed by the classical Galerkin ROM (G-ROM) in under-resolved numerical simulations of turbulent flows. In this paper, we propose a new Reg-ROM, the time-relaxation ROM (TR-ROM), which filters the marginally resolved scales. We compare the new TR-ROM with the two other Reg-ROMs in current use, i.e., the Leray ROM (L-ROM) and the evolve-filter-relax ROM (EFR-ROM) and one eddy viscosity model, the mixing-length model, in the numerical simulation of the turbulent channel flow at Reτ=180 and Reτ=395 in both the reproduction and the predictive regimes. For each Reg-ROM, we investigate two different filters: (i) the differential filter (DF), and (ii) the higher-order algebraic filter (HOAF). In our numerical investigation, we monitor the Reg-ROM performance with respect to the ROM dimension, N, and the filter order. We also perform sensitivity studies of the three Reg-ROMs with respect to the time interval, relaxation parameter, and filter radius. The numerical results yield the following conclusions: (i) All three Reg-ROMs are significantly more accurate than the G-ROM. (ii) All three Reg-ROMs are more accurate than the ROM projection in terms of Reynolds stresses. (iii) With the optimal parameter values, the new TR-ROM yields more accurate results than the L-ROM and the EFR-ROM in all tests. (iv) The new TR-ROM is more accurate than the mixing-length ROM. (v) For most N values, DF yields the most accurate results for all three Reg-ROMs. (vi) The optimal parameters trained in the reproduction regime are also optimal for the predictive regime for most N values, demonstrating the Reg-ROM predictive capabilities. (vii) All three Reg-ROMs are sensitive to the filter order and the filter radius, and the EFR-ROM and the TR-ROM are sensitive to the relaxation parameter. (viii) The optimal range for the filter radius and the effect of relaxation parameter are similar for the two Reτ values.

Physics-informed neural networks for weakly compressible flows using Galerkin–Boltzmann formulation

In this work, we study the Galerkin–Boltzmann formulation within a physics-informed neural network (PINN) framework to solve flow problems in weakly compressible regimes. The Galerkin–Boltzmann equations are discretized with second-order Hermite polynomials in microscopic velocity space, which leads to a first-order conservation law with six equations. Reducing the output dimension makes this equation system particularly well suited for PINNs compared with the widely used D2Q9 lattice Boltzmann velocity space discretizations. We created two distinct neural networks to overcome the scale disparity between the equilibrium and non-equilibrium states in collision terms of the equations. We test the accuracy and performance of the formulation with benchmark problems and solutions for forward and inverse problems with limited data. We compared our approach with the incompressible Navier–Stokes equation and the D2Q9 formulation. We show that the Galerkin–Boltzmann formulation results in similar L2 errors in velocity predictions in a comparable training time with the Navier–Stokes equation and lower training time than the D2Q9 formulation. We also solve forward and inverse problems for a flow over a square, try to capture an accurate boundary layer, and infer the relaxation time parameter using available data from a high-fidelity solver. Our findings show the potential of utilizing the Galerkin–Boltzmann formulation in PINN for weakly compressible flow problems.

Role of chemical processes and porous media in thermal transport of Casson nanofluid flow: A study with Riga plates

A Riga plate is an electro-magnetic instrument working with anodes and magnets on plates. The Riga plate has numerous advantages in geophysical sciences, the field of engineering, sensors,and astrophysics.The present work investigated the transitory Electromagnetohydrodynamic radiative squeezing unsteady motion of Casson nanofluid through a parallel channel impacted by the Riga plate with endothermic/exothermic chemical processes and porous media. The PDEs transform into non-linear ODEs using the appropriate similarity transformations. The RKF-45 method and Shooting techniques are utilized to compute the solutions to these non-linear ODEs and related boundary conditions. The consequences of non-dimensional parameters on the corresponding profiles are illustrated graphically. And also studied some significant engineering coefficients. The primary findings of the present study are a rise in the thermal relaxation time parameter, temperature increases for the exothermic chemical reaction case, and opposite behavior in the endothermic chemical reaction case. Enhancement in activation energy parameter, the temperature drops for exothermic and increases for the endothermic case. The value of the modified Hartmann number rises, the velocity profile is also increased in the lower plate and the opposite behavior in the upper plate. Increase in Biot number, temperature decreases in the exothermic case and increases in the endothermic case.

Scaling Effects of the Weissenberg Number in Electrokinetic Oldroyd-B Fluid Flow Within a Microchannel.

This study attempts to extend previous research on electrokinetic turbulence (EKT) in Oldroyd-B fluid by investigating the relationship between the Weissenberg number ( ) and the second-order velocity structure function ( ) under applied electric fields. Inspired by Sasmal's demonstration in Sasmal (2022) of how heterogeneous zeta potentials induce turbulence above a critical , we develop a mathematical framework linking to turbulent phenomena. Our analysis incorporates recent findings on AC (Zhao & Wang, 2017) and DC (Zhao & Wang 2019) EKT, which have defined scaling laws for velocity and scalar structure functions in the forced cascade region. Our finding shows that and , for a length scale , and , where is a velocity fluctuations quantity and denotes the time relaxation parameter. This work establishes a positive correlation between and turbulent flow phenomena through a rigorous analysis of velocity structure functions, thereby offering a mathematical foundation for building the design and optimization of EKT-based microfluidicdevices.

Physics-informed neural networks approach for pollutant dispersion flow caused by magnetic dipole

Abstract Research on the liquid flow and distribution of waste discharge concentration over cylindrical surfaces might lead to the growth of efficient waste management and pollution controlling strategies. In view of this, the pollutant concentration and magnetic dipole impact on the liquid flow through the cylinder with a porous medium are explored in the present analysis. Moreover, Fourier’s and Fick’s laws are considered to explore heat transport features. The governing partial differential equations (PDEs) of the present study are converted into non-dimensional ordinary differential equations (ODEs) utilizing similarity variables. Also, the current study proposes a novel implementation of neural networks based on physics knowledge for the liquid flow past a cylinder. The self-updating weights and bias facilitate the network to satisfy the minimization objective function and provide accurate results. Additionally, the solution obtained by Runge Kutta Fehlberg's fourth-fifth order (RKF-45) method is utilized to validate the physics-informed neural network (PINN) results, presenting mean squared errors from 10-9 to 10-11. Furthermore, it is found that the increase in temperature relaxation time parameter decreases the Nusselt number gradually at the rate of 1 to 5%. An upsurge in the values of the pollutant external source parameter and the pollutant external source variation parameter decreases the concentration profile.

Thermal performance of a hybrid nanofluid flow through a stretchable stationary disk featuring the Cattaneo-Christov heat flux theory

A hybrid nanofluid is comprised of a (Ethylene glycol) base fluid component and (Copper and Aluminium oxide) nanoparticles, and the nanoparticles are scattered inside the Ethylene glycol. Integrating nanoparticles into a base fluid (Ethylene glycol) can significantly enhance its thermal conductivity, which in turn can boost the base fluid's rate of heat transfer. In addition, the dynamics of viscous fluid together with nanoparticles is quite interesting and has a large of applications in the industrial sector. The current predominately predictive modeling investigates the flow of the hybrid nanofluid via a stretchable stationary disk in the presence of heat source/sink. A progressive modification in he energy equation is done by utilizing the Cattaneo-Christov heat flux expressions. This theory provides predictions for the features of the thermal relaxation time of the liquid on the boundary layer flow. Further, the study focuses on the features of the Lorentz force resulting from the applied of a magnetic field perpendicular to the disk. The similarity approach is used to obtained the dimensionless ordinary differential equations.The bvp4c approach in Matlab is utilized as a numerical method for the solution. All the solutions are obtained through graphical form. According to the results, the thermal profile is reduced by adjusting the thermal relaxation time parameter. Motion of the hybrid nanofluid slows down by enlarging the magnetic force parameter. Additionally, the effect of the heat source significantly increases the thermal profile. It is noted that the temperature field is enhanced in the case of a larger Lorentz force. Moreover, the increase in volume fraction concentration intensifies the thermal distribution, but the velocity is diminished due to the effect of viscosity.

Cattaneo-Christov fluxes for nonlinear mixed convective entropy generated Reiner-Rivlin material flow

Thermal and solutal transportation processes involve in tremendous useful applications related to heat exchanger, scientific, micro-electronic device technologies and industry sectors like nuclear reactors cooling, marine engineering, nanotechnology, thin-film technology, biomedical applications and thermal conduction in soft tissue. In view of such useful applications the Cattaneo-Christov analysis for nonlinear mixed convective Reiner-Rivlin material flow in presence of constant applied magnetic field is considered. Heat source, magnetohydrodynamics and radiation are incorporated in energy equation. Cattaneo-Christov flux is employed to discuss the thermal and mass transport characteristics. Entropy calculation in radiating flow is discussed. The proposed non-linear systems are transformed into dimensionless ordinary systems through appropriate transformation. Non-linear ordinary expressions are computed for convergent series solutions through Optimal homotopy analysis technique (OHAM). Graphical interpretations for quantities under interest against pertinent variables are explored. Large magnetic parameter has opposite impact for entropy and fluid flow. An increase of temperature through thermal relaxation time parameter is noticed. Velocity has same trend for both mixed convection and Reiner-Rivlin fluid variables. Reduction in concentration is seen for solutal relaxation time parameter. Temperature enhancement is witnessed in presence of heat generation. Entropy rate enhancement for radiation is observed. Decrease in concentration is noticed for reaction. Entropy rate increases against diffusion variable is enhanced.

Magnetic resonance (MR) evaluation of deep venous thrombosis of 338 discharged viral pneumonia patients.

Viral pneumonia (VP) often leads to the development of deep vein thrombosis (DVT) in hospitalized patients. The aim of the study was to investigate the incidence of DVT in discharged patients with VP, and whether new and old DVT differ in transverse relaxation time. In this prospective cohort study in Wuhan, China, 338 consecutive discharged VP patients from February 2021 to March 2023 who underwent T2 weighted Sampling Perfection with Application Optimized Contrast Evolution (SPACE) were recruited to detect DVT. T2 mapping and T2* mapping were performed for the patients with DVT detected by magnetic resonance imaging (MRI). The minimum, maximum, mean of T2 time and T2* time of DVT were recorded as T2min, T2max, T2mean, T2*min, T2*max, and T2*mean, respectively. Clinical data and laboratory findings were compared between new and old DVT cases, which were defined based on the examination results before and after discharge. A Mann-Whitney test was used to compare transverse relaxation time parameters between new and old DVT. Twelve percent of VP patients (40/338) developed new DVT after discharge. Thirty-three out of 104 DVTs did not resolve after discharge. Compared with patients with new DVT, patients with old DVT were older (67 vs. 59 years, P=0.003); and had a higher proportion of bedridden time >72 hours (72.7% vs. 37.0%, P<0.001). Patients with old DVT had a lower lymphocyte count (0.67×109/L vs. 0.97×109/L, P=0.01), higher C-reactive protein (59 vs. 35 mg/L, P=0.019), and higher levels of D-dimer (6.7 vs. 0.9 µg/mL, P<0.001) than patients with new DVT. Patients with old DVT received more invasive mechanical ventilation (30.3% vs. 7.4%, P<0.001) and had a higher proportion of acute respiratory distress syndrome (75.8% vs. 51.9%, P<0.001), and a higher proportion of cardiac injury (39.4% vs. 14.8%, P=0.033) than patients with new DVT. T2min, T2max, T2mean, and T2*max of new DVT were significantly greater than old DVT (17.6±10.4 vs. 13.2±5.9 ms, 94.9±44.9 vs. 42.3±23.6 ms, 46.8±24.0 vs. 25.0±12.6 ms, 22.5±12.4 vs. 10.7±3.5 ms, P<0.05 for all). There was no significant difference in T2*min or T2*mean between new and old DVT (3.2±0.4 vs. 3.1±0.4 ms, 8.2±4.9 vs. 5.5±1.5 ms, P>0.05 for both). T2 weighted SPACE magnetic resonance (MR) is valuable in the follow-up of thrombosis of discharged VP patients. T2 mapping distinguishes between new and old DVT.

Dynamics of Fourier's and Fick's laws on the convectively heated oscillatory sheet under Arrhenius kinetics: The finite-difference technique

The significance of chemical reaction with activation energy and convective boundary conditions on the fluid flow via an oscillatory stretchy surface in the presence of permeable media and radiation is analyzed in this study. This inspection presents Fourier and Fick's laws-based equations for heat, mass transport, and liquid flow through an oscillating stretchy sheet. Understanding these dynamics aids in the optimisation of catalytic reaction settings, where gradients greatly influence reaction rates in concentration and temperature. The governing differential equations of the current study are modelled and changed into their non-dimensional form by employing suitable similarity variables. The finite difference method (FDM) is also used to numerically solve the obtained dimensionless equations. The influence of many factors on the several profiles is portrayed with graphical representations. The outcome of the unsteadiness and porosity parameters on the velocity profile with time coordinate is depicted. The increase in the radiation parameter and Biot number upsurges the thermal profile. The temperature reduces as the unsteadiness parameter and temperature relaxation time parameter grow. The upsurge in the activation energy parameter intensifies the mass transport. The rise in concentration relaxation time parameter diminishes the concentration profile.

Enhanced detection of damaged myocardium and risk stratification in hypertrophic cardiomyopathy using integrated [68Ga]Ga-FAPI-04 PET/CMR imaging.

This study aims to explore the correlation between PET and CMR in integrated [68Ga]Ga-FAPI-04 PET/CMR multimodal imaging and its value in the diagnosis and risk assessment of hypertrophic cardiomyopathy (HCM). This study included 20 HCM patients and 11 age- and gender-matched controls. PET analysis evaluated left ventricular (LV) [68Ga]Ga-FAPI-04 uptake, including SUVmax, TBR, cardiac fibroblast activity (CFA) and volume (CFV), and total SUV of the 16 segments. CMR tissue characterization parameters included cardiac function, myocardial thickness, late gadolinium enhancement (LGE), relaxation time, extracellular volume (ECV), and peak strain parameters. The 5-year sudden cardiac death (SCD) risk score and the 2-year and 5-year atrial fibrillation (AF) risk scores were calculated for each patient. The study analyzed differences between HCM patients and controls, the correlation between [68Ga]Ga-FAPI-04 PET and concurrent CMR imaging results, and the predictive value of PET/CMR. The FAPI uptake, myocardial mass, myocardial thickness, and T1/T2 mapping values were significantly higher in HCM patients compared to controls. Twenty HCM patients and their 320 myocardial segments were discussed. Increased [68Ga]Ga-FAPI-04 uptake in the left ventricular wall was observed in 95% (19/20) of the patients, covering 48.8% (156/320) of the segments. On concurrent CMR, 80% (16/20) of the patients showed LGE, including 95 (29.7%) segments. The FAPI(+)LGE(+) segments exhibited the highest myocardial PET uptake, greatest thickness, longest T1/T2 native values, largest ECV value and the greatest loss of myocardial strain capacity (P < 0.05). There was a significant correlation between FAPI uptake and CMR parameters (P < 0.05). Higher [68Ga]Ga-FAPI-04 uptake showed a positive correlation with SCD and AF risk scores (P < 0.05). The number of LGE(+) segments, mapping parameters, and ECV values in CMR also had prognostic significance. Combining PET with CMR aided in further risk stratification of HCM. [68Ga]Ga-FAPI-04 PET/CMR multimodal imaging has potential value in the detection of damaged myocardial lesions and risk assessment of HCM patients. [68Ga]Ga-FAPI-04 PET can detect more affected myocardium compared to CMR, and segments with abnormalities in both PET and CMR show more severe myocardial damage.

Passive control of bio-convective flow on Eyring–Powell nanofluid over a slippery surface with activation energy and magnetic impact

The current communication deliberates the consequences of the Darcy–Forchheimer flow of Eyring–Powell nanofluid past a slippery surface containing activation energy and motile microorganisms. The flow is influenced by the consequences of Brownian motion, thermal radiation, the Cattaneo–Christov heat-mass flux theory, and thermophoresis. The framed flow models are transformed into ordinary derivative equations by adopting appropriate conversion variables. The transformed equations are numerically tackled by using the bvp4c scheme in MATLAB. The study is remarkable for its comprehensive analysis of the interplay of several flow factors, such as the Forchheimer number, Richardson number, bioconvection Rayleigh number, radiation, thermophoresis, Brownian motion, thermal and mass relaxation time parameters. The outcomes are visualized through tables and diagrams, which provide significant insights into the intricate physical mechanisms involved in this multifaceted subject. Evidently, the velocity profile declines when there is a rise in the buoyancy ratio parameter and the opposite trend is obtained for the Richardson number. The temperature grows when there is a larger magnitude of the thermophoresis parameter and it reduces for greater values of the time relaxation parameter. The activation energy and mass relaxation parameters enhance the concentration profile. The microbe density increases when enhancing the quantity of Peclet number and it declines for bioconvection Lewis number.

Об идентификации характеристик неоднородных вязкоупругих тел в рамках модели дробного порядка

Nowadays, the development of models of viscoelastic materials with complex inhomogeneous structure is one of the hottest problems of continuum mechanics. Along with classical models, fractional-differential models of viscoelasticity have become increasingly popular. In this paper, we present a model for describing steady-state oscillations of inhomogeneous viscoelastic bodies in terms of fractional-order differential operators. Taking into account the fractional order of the model operators, the corresponding form of the complex module describing the material properties is constructed. The module includes four characteristics: instantaneous and long-term elastic moduli (in the case of material inhomogeneity, they are the functions of coordinates), relaxation time and fractionality parameter. The properties of the complex module are studied, and the ranges of the model parameters, at which the rheological properties are most pronounced, are identified. A general formulation of the inverse problem (IP) on the identification of function-parameters of the model based on the acoustic sounding data is proposed. In the framework of this formulation, the inverse problems for specific objects , namely, an inhomogeneous rod and a round plate, are considered. In both model problems, the influence of the fractionalization parameter on the amplitude-frequency characteristics is analyzed. It has been found that in the vicinity of viscoelastic resonances the fractionality parameter affects the parameters of the oscillatory process most significantly, which is typical for such problems. A solution to the nonlinear IPs under consideration is constructed based on the linearization method, which also serve as basis for the iterative processes supplemented with the elements of the projection approach. This allows one to determine corrections to the required functions in the specified classes of functions using regularization. For both IPs, a series of computational experiments were carried out. The analysis of the experimental results made it possible to formulate recommendations for the selection of optimal sensing modes.

What is the physical origin of the gradient flow structure of variational fracture models?

We investigate a physical characterization of the gradient flow structure of variational fracture models for brittle materials: a Griffith-type fracture model and an irreversible fracture phase field model. We derive the Griffith-type fracture model by assuming that the fracture energy in Griffith's theory is an increasing function of the crack tip velocity. Such a velocity dependence of the fracture energy is typically observed in polymers. We also prove an energy dissipation identity of the Griffith-type fracture model, in other words, its gradient flow structure. On the other hand, the irreversible fracture phase field model is derived as a unidirectional gradient flow of a regularized total energy. We have considered the time relaxation parameter a mathematical approximation parameter, which we should choose as small as possible. In this research, however, we reveal the physical origin of the gradient flow structure of the fracture phase field model (F-PFM) and show that the small time relaxation parameter is characterized as the rate of velocity dependence of the fracture energy. It is verified by comparing the energy dissipation properties of those two models and by analysing a travelling wave solution of the irreversible F-PFM. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Impact of chemical reaction on the Cattaneo–Christov heat flux model for viscoelastic flow over an exponentially stretching sheet

In this article, the numerical solutions for the heat transfer flow of an upper-convected Maxwell fluid across an exponentially stretched sheet with a chemical reaction on the Cattaneo–Christov heat flux model have been investigated. Using similarity transformation, the controlling system of nonlinear partial differential equations was transformed into a system of ordinary differential equations. The resulting converted equations were solved numerically by a successive linearization method with the help of MATLAB software. A graphic representation was created to analyze the physical insights of the relevant flow characteristics. The findings were presented in the form of velocity, temperature, and concentration profiles. As the relaxation time parameter varied, the local Nusselt number increased. The thermal relaxation time was shown to have an inverse relationship with fluid temperature. Furthermore, the concentration boundary layer becomes thinner as the levels of the reaction rate parameter increase. The results of this model can be applicable in biological fluids and industrial situations. Excellent agreement exists between the analysis's findings and those of the previous studies.

Optimizing heat transfer with nano additives: A mathematical approach

This study is carried out to investigate heat transfer of hybrid nanofluid between two concentric cylinders using the fractional Maxwell model. The fractional model is solved numerically; fractional derivatives are integrated using the L1 algorithm of Caputo derivative and the integer order derivatives are discretized using the Crank–Nicolson numerical method. The findings show that skin friction decreases when the relaxation time parameter increases. The thermal performance of the working fluid increased up to 5% when hybrid nanoparticles were suspended to it.

Quantitative derivation of a two-phase porous media system from the one-velocity Baer–Nunziato and Kapila systems

We derive a novel two-phase flow system in porous media as a relaxation limit of compressible multi-fluid systems. Considering a one-velocity Baer–Nunziato system with friction forces, we first justify its pressure-relaxation limit toward a Kapila model in a uniform manner with respect to the time-relaxation parameter associated with the friction forces. Then, we show that the diffusely rescaled solutions of the damped Kapila system converge to the solutions of the new two-phase porous media system as the time-relaxation parameter tends to zero. In addition, we also prove the convergence of the Baer–Nunziato system to the same two-phase porous media system as both relaxation parameters tend to zero. For each relaxation limit, we exhibit sharp rates of convergence in a critical regularity setting. Our proof is based on an elaborate low-frequency and high-frequency analysis via the Littlewood–Paley decomposition and includes three main ingredients: a refined spectral analysis of the linearized problem to determine the frequency threshold explicitly in terms of the time-relaxation parameter, the introduction of an effective flux in the low-frequency region to overcome the loss of parameters due to the overdamping phenomenon, and renormalized energy estimates in the high-frequency region to cancel higher-order nonlinear terms. To justify the convergence rates, we discover several auxiliary unknowns allowing us to recover crucial O(ε) bounds.

Unsteady MHD oblique stagnation point slip flow of maxwell fluid over an oscillating–stretching cylinder with Cattaneo–Christov double diffusion model

The unsteady oblique stagnation point slip flow of a Maxwell fluid over an oscillating–stretching cylinder with convective heat transfer is investigated. The evaluation of this phenomenon is facilitated by employing the Cattaneo–Christov double diffusion model. According to the oblique stagnation point flow characteristics, an ordinary differential equation about pressure is derived, and pressure terms can be corrected by solving this equation. The equations are subjected to the similarity transformation, resulting in a set of dimensionless equations. The homotopy analysis method (HAM) is subsequently utilized to obtain their solutions. The effects of various parameters on the velocity, temperature, and concentration are analyzed. It is observed that slip boundary conditions accelerate fluid flow by reducing resistance. Elevating the Schmidt number means a reduction in the mass diffusion, leading to a diminished concentration. The temperature distributions of different thermal relaxation time parameters intersect at a thermal equilibrium point. Moreover, three-dimensional plots depicting the evolution of velocity and temperature over time demonstrate excellent agreement with the flow behavior and boundary conditions. They contribute to the comprehension and prediction of time-dependent flow and heat transfer phenomena.

Numerical treatment for radiative hybrid nanofluid flow over a stretching sheet

Artificial neural networks (ANNs) have brought a huge transformation to the machine learning regime by furnishing unparalleled abilities for modeling intricate phenomena and coping with a variety of challenges. In the oneiric field of ANNs, the essential approach for training ANNs is backpropagation. However, optimization is crucial when handling the complex fluid flow phenomenon through backpropagation. The current article implements the Levenberg Marquardt Technique with ANN backpropagation (LMT-BP-ANN) to investigate the radiative flow of a hybrid nanofluid (RHNF) addressing a Cattaneo-Christov flux system past a stretching sheet (SS). Fe2O3 with single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) hybrid nanofluid is considered. The base fluid is ethylene glycol. Physical parameters of nanofluidic system, including the magnetic parameter M, the solid volume fractions φ1 and φ2, the velocity slip parameter λ, the relaxation time parameter Ω, the Biot number ϒ, and the thermal radiation parameter Gr are evaluated through appropriate variations that effectively accomplish the dynamics of the fluid model. These are utilized to create the dataset for LMT-BP-ANNs using the renowned deterministic Adam's numerical technique in Mathematica software. In MATLAB software, 70 % of data is kept for preparing, 15 % for checking, and 15 % for validating the neural network. The performance plot, regression graphs, and error histograms are constructed to demonstrate the suggested LMT-BP neural network scheme's high efficiency, efficacy, and exactness. When ANN performs, a mean squared error (MSE) of order 10−11 is observed. The observed R squared value is 1. As the magnetic parameter estimate grows, the fluid velocity declines, although the thermal profile shows increasing behavior. As the velocity slip parameter increases, the velocity of the fluid drops. Key findings of this study are anticipated to have a noteworthy bearing on sectors that require local refrigeration and heating by contravention.

MHD Maxwell dusty fluid in thermally stratified radiative flow with temperature-dependent thermal conductivity and Cattaneo-Christov model

It might be very important for the polymer processing industries to comprehend how Maxwell fluids behave on a stretched cylinder. Optimizing the extrusion and drawing processes can ensure the desired product qualities while avoiding faults. The objective of this study is heat transfer analysis on a Maxwell dusty fluid flow cylindrical surface with the Cattaneo-Christov concept. We immerse the cylinder in porous media, with a two-dimensional fluid regulating the flow. Our mathematical model further considers the effects of variable thermal conductivity, radiation, viscous and joule heating, magnetic field, thermal stratification, and slip velocity. Based on the presumptions, partial differential equations (PDE's) have been used to evolve the mathematical model. Using similarity transformations, the PDE's for heat and momentum for both phases are transformed into highly nonlinear ODE's.The numerical results have been obtained on these ordinary differential equations by using the RKF-45 method. This issue's main characteristic is that it examines the scenario's liquid and dust phases throughout. Results are given both visually and tabularly for the major parameters over a velocity, temperature, skin friction coefficient, and Nusselt number. When we compared our method to a previously published paper, we discovered a decent match. The findings, which were obtained for our system, show that the velocity and thermal gradient of both the phases of fluid and dust behave in an opposite trend in favor of rising Maxwell parameter, where the curvature parameter makes the rise in the same manner. Furthermore, the thermal transport profiles for both phases decline for the rising thermal time relaxation parameter.

Flow of magnetohydrodynamic blood-based hybrid nanofluids with double diffusion in the presence of Riga plate for heat optimization and drug applications

In a recent study, researchers investigated the flow behavior of Casson Hybrid nanofluids (HNFs) combination of single and multi-walled carbon nanotubes (SWCNTs), (MWCNTs) on a Riga plate for drug delivery applications. The study found that the Casson HNFs exhibited non-Newtonian behavior on the Riga plate, with the presence of nanoparticles causing an increase in viscosity and shear-thinning behavior. This rheological behavior is favorable for drug delivery applications as it improves the stability and dispersion of drug particles in the fluid. The similarity equations of the flow problem are easily tackled with the homotopy analysis method (HAM) built on fundamental homotopy mapping. In high-speed flows, Riga actuators are expected to achieve the requirements, since HNF is enhanced by modified Hartmann numbers. As the Eckert number, heat generation/absorption parameter, and thermal relaxation time parameter decrease the temperature, thermal transport increases. Furthermore, with the increments in paramount parameters, the skin friction coefficient and heat transfer rate are remarkably meliorated under higher modified Hartmann number. Furthermore, the study also found that the Casson Hybrid nanofluids showed enhanced heat transfer properties on the Riga plate, which is beneficial for localized drug delivery applications that require precise temperature control.