Difference Method Research Articles

Stability and failure probability analysis of super-large irregularly shaped deep excavation in coastal area considering spatial variability in soil properties

ABSTRACT The objective of this paper is to investigate the effects of spatial variability in coastal silty soil properties on the stability and failure probability of deep excavation. A super-large irregularly shaped deep excavation in the coastal area in Wenzhou, China, is considered. A numerical model is established based on the random field theory, finite difference method and Monte-Carlo simulation method. Focusing on the friction angle and cohesion, the effects of horizontal and vertical correlation distances and variation coefficients on excavation stability are systematically studied. Meanwhile, the reliability evaluation approach is also applied to systematically examine the impact of the correlation distance on the surface settlement and horizontal displacement of pile. The results show that the greater correlation distance leads to a larger dispersion degree of the ground settlement curve and the displacement curve of the diaphragm wall around. The influence of the horizontal correlation distance on land settlement is more significant. The horizontal and vertical displacements of the pile top are less affected by the correlation distance. Compared with the deterministic analysis, the random analysis results considering the soil spatial variability produce larger displacement.

Non-linear Dynamics and Control of COVID-19 in India Revisited : Evidence of Synergistic, Antagonistic and Threshold Effects

Abstract Various researchers have investigated the COVID-19 pandemic dynamics since 2020 focusing on various aspects of the epidemics. However, the non-linear dynamics of this epidemic is still not well understood. India having the largest population in the world with wide cultural, genomics, and immunity diversity is being considered a suitable case for present investigation to generate the crucial information of non-linear phenomena during the first two waves of the epidemics. An SIRD model is suggested, integrating varying transmission, recovery, and mortality rates over time to explore the nonlinear behavior of the epidemic in India. The time-dependent transmission, recovery, and mortality are calculated using the finite difference method with the aid of actual data released by the Indian government, for the periods before and during the lockdown phases. The novel results generated from the model show evidence of synergistic, antagonistic, and threshold effects and the role of various measures in controlling these epidemic trends.

Adaptive Sequential Three-way Decisions for Dynamic Time Warping

Dynamic time warping (DTW) algorithm is widely used in diversified applications due to its excellent anti-deformation and anti-interference in measuring time-series based similarity. However, the high time complexity of DTW restrains the applicability of real-time case. The existing DTW acceleration studies suffer from a loss of accuracy. How to accelerate computation while maintaining satisfying computational accuracy remains challenging. Motivated by sequential three-way decisions, this paper develops a novel model with adaptive sequential three-way decisions for dynamic time warping (AS3-DTW). Firstly, we systematically summarize distance differences under the context of adjacent tripartite search spaces for DTW, and propose five patterns of granularity adjustments of the search spaces. Furthermore, we present the corresponding calculation method of DTW adjacent tripartite search spaces distances difference. Finally, we construct a novel dynamism on adaptively adjusting time warping by combining sequence-based multi-granularity with sequential three-way decisions. Experimental results show that AS3-DTW effectively achieves promising trade-off between computational speed and accuracy on multiple UCR datasets when compared with the state-of-the-art algorithms.

A novel meshless method for numerical simulation of fractured-vuggy reservoirs

This paper proposes a novel meshless numerical simulation method for fractured-vuggy reservoirs. Initially, model discretization involves extracting fracture and vug feature nodes along the contours of the reservoir bodies and in alignment with fracture orientations, tailored to the characteristics of the fractured-vuggy oil deposit. Subsequently, a connection element model is established within the influence domain. Based on the seepage equations of the connection system, a computational method for the parameters of the connection elements (connection transmissibility and connection volume) is defined. In addition, a sequential method is employed to solve for the pressure and saturation, achieving rapid prediction of the reservoir's production dynamics. On this basis, an automatic history matching algorithm is utilized for real-time fitting of oil–water dynamic indicators, inverting the characteristic parameters of the connection element model, and quantitatively characterizing the injection–production connection elements. The research findings indicate that the method is capable of rapidly fitting and predicting the dynamics of oil reservoir production. Furthermore, conceptual model examples have substantiated that it achieves comparable computational efficiency and superior computational accuracy when compared to the traditional finite difference (volume) method under the same nodal conditions. Additionally, the node arrangement for fractures and vugs is comparatively flexible, and it can ensure the integrity of the flow paths with a limited number of nodes to enhance predictive accuracy. Therefore, this method can effectively meet the rapid prediction requirements for fractured-vuggy reservoirs and also provides a novel meshless computational approach for the numerical simulation of such reservoirs.

Effects of New Nonlinear Curvature Models and Non-Local Elasticity on Buckling investigation of FG Tapered Nano-Beams Locating on Elastic Foundations

New nonlinear curvature models are proposed to show their effects on the compressive critical buckling load on functionally graded (FG) tapered nano-beams locating on elastic foundations in the presence of non-local elasticity. Fourth and fifth orders finite difference methods (bvp4c and bvp5c) are applied on the governing differential equation which is a highly non-linear, due to curvature and has variable coefficients, due to properties. Dimensional analyses have been applied on the governing system together with the problem conditions to produce their dimensionless forms. For different considered parameters, the critical buckling load is computed using the eigenvalue theorem. The effects of nonlinear curvature, variable Young modulus, variable moment inertia and foundation parameters are studied and displayed in tables and figures. The stability and convergence of the present solution are tested using more than one strategy as: comparison with available results, comparison between bvp4c and bvp5c with different mesh intervals and tolerances of truncation errors. These comparisons show that, the new curvature model affects the critical buckling with different ratios depending on variability of properties and foundation parameters. The new results show that the nonlinear curvature model reduces the critical buckling load in comparison with the classical linear model, which, leads to decreasing in factor of safety in design of structures. The new results show that the design of structures will be influenced with the new reduction of the compressive critical buckling load, since it may affect the factor of safety in design of structures. The new results can lead, generally, to more reduction of critical buckling load for large or small input parameters and it will affect other critical values such that frequencies. The introduced Tables and Figures of the present problem with comparisons of previously exact, analytical and numerical works establish the higher accuracy and stability of current findings using bvp4c or bvp5c with preferable of the later. This study is related to some practical applications such as aeronautical and structural engineering.

Experimental and numerical studies on ground failure and soil erosion caused by bursting of buried water pipeline

Pressurized water pipelines buried in an urban environment are prone to bursting failures, threatening public safety and traffic convenience. The limited studies in literature just focused on soil fluidization while few studies considered ground failure, shear strain, soil erosion and the influence of leakage locations during pipe bursts. In this study, extensive experimental tests along with a finite difference method – discrete element method (FDM-DEM) solid–fluid coupling analysis were conducted to investigate these issues. It was disclosed that the failure development during pipe bursts can be divided into three stages, i.e., seepage diffusion, erosion cavity expansion, and soil fluidization. By digital image correlation (DIC) analysis of the experimental results, a wedge-shaped displacement zone in ground was identified, with peak shear strain near its boundaries. Moreover, it was revealed that leakage locations affected the expansion origin of erosion cavity; as the burial depths increased, the ground heave range increased linearly; the maximum water outflow distance was closely related to the internal pressures of buried pipeline, which could be modeled by a square root formula based on turbulent jet theory. Mesoscopic analyses revealed that finer particles were more susceptible to erosion during pipe bursts because of the low possibility of forming strong connections with surrounding particles. The findings yielded from this study can enhance the understanding of pipe bursts and help professionals mitigate potential damage.

3-D P-wave velocity structure of the upper mantle beneath eastern Indonesia from body wave tomography

Eastern Indonesia's tectonic setting is well known for its complexity and intense seismic activity. Controlled by several major and minor plates, including the Eurasian, Australian, and Pacific plates, this region is famous for its U-shaped subduction system beneath the Banda Arc. To better understand the architecture of the underlying structure in this region, we performed body-wave travel time tomography using ten years of catalog data provided by the Indonesian Agency for Meteorology, Climatology, and Geophysics. We utilize 9729 events in total, from which 46,446 P-wave arrival times were extracted. We used a double difference method to relocate the initial event catalog, which produced a pattern of seismicity consistent with a curved subduction system. Our tomographic model reveals a high velocity band between 90 and 240 km depth in the upper mantle, which is interpreted to be a concave dipping lithospheric slab that is parallel to the present-day Banda arc. Our results also show that lithosphere subducting from the north and south starts to collide at a depth of 300–350 km and becomes shallower further east. Apparent discontinuities in the high velocity band and a corresponding lack of seismicity supports the presence of a slab tear to the west of Seram. A dipping high velocity structure that is present from south to north beneath the island of Timor represents a subducting slab that dips more steeply beyond a depth of 150–200 km, which appears consistent with slab roll-back. Our tomographic model also shows evidence of back arc thrusting to the north of Sumbawa and Flores Islands in the form of a south-dipping higher velocity band at shallow depth. Furthermore, our tomographic models also reveal the possible presence of underthrust continental forearc in the form of a thin higher velocity anomaly that connects the backarc thrust and northward dipping lithosphere slab in the Timor area. Finally, a zone of low velocity above the higher velocity slab is clearly seen beneath Seram Island at a depth of ~100 km and may represent a partial melting zone.

Partial abrasion modeling and variable load characteristics analysis for high-speed load sensing electro-hydrostatic actuator pump of aircraft

The load-sensing electro-hydrostatic actuator (LS-EHA) allows to reduce the thermal output and enhance the dynamic characteristics of the more electric aircraft (MEA). In addition, the forecasting of the LS-EHA is crucial for its efficient functioning. This study proposes a novel model for the analysis of overturning and wear characterization of the slipper, while focusing on the partial abrasion. The transient thermoelastic hydrodynamic (TEHD) lubricating analysis of the slipper pair is solved by an analytical model along with the finite difference method. In the proposed partial abrasion model, the non-uniformity of the oil film thickness and the partial abrasion contour for the slipper bottom surface are considered through the discrete friction area approach in order to reach a higher precision. Afterward, the overturning behavior characteristics of the slipper and the variation law in its overturning behavior under different rotation speeds, load delivery pressures, and swashplate angles are analyzed. The obtained results demonstrate that the lubricating oil film field is unevenly distributed, and the overturning behavior of the slipper has certain variable load characteristics. Finally, the effectiveness and precision of the proposed partial abrasion model are validated through comparative simulation experiments and analysis.

A numerical framework for modeling evaporation and combustion of isolated, spherically-symmetric, multi-component fuel droplets

This paper presents a comprehensive numerical framework for simulating the evaporation and combustion of isolated, spherically-symmetric, multi-component fuel droplets. The framework incorporates a detailed description of chemical reactions in the gaseous phase and is capable of modeling pure evaporation, autoignition, and hot-wire ignition scenarios.The transport equations for mass, species, and energy are solved in both the liquid (droplet) and gaseous (surrounding atmosphere) phases. Diffusion in the liquid phase is described using the Stefan-Maxwell theory, while in the gaseous phase, both molecular and thermal diffusion are considered. The model also includes the thermophoretic effect for carbonaceous particles and accounts for gas radiation through various models, ranging from optically-thin approximations to more complex methods like the P1 and discrete ordinate methods. Non-gray radiative effects are handled using the Weighted-Sum-of-Gray-Gases Model (WSGGM). Liquid/gas interface conditions are evaluated by imposing flux continuity of mass and energy, along with thermodynamic equilibrium for species. Deviations from ideal thermodynamic behavior in the liquid droplet are managed by incorporating a suitable activity coefficient or by using a proper cubic equation of state. Additionally, the presence of supporting fibers is modeled using a simplified one-dimensional approach. The transport equations are solved using the method of lines, with spatial discretization performed via the finite difference method on a body-fitted grid. The resulting system of Differential-Algebraic Equations (DAEs) is then solved using a fully-coupled approach.Thanks to its generality in terms of kinetic and thermodynamic descriptions and the reduced computational time, the proposed framework offers significant potential for advancing our understanding of the complex combustion processes of multi-component liquid fuels and for enhancing the planning and execution of experiments involving isolated fuel droplets.

Thermodynamic behavior of high-power inductively coupled plasma quartz tube wall

High-power inductively coupled plasmas are commonly used in planetary entry simulations and are increasingly being used in electric propulsion applications. However, during the operation of the system, the walls of the quartz tube will crack and melt. Its thermodynamic behavior is key to ensuring the safe and reliable operation of the system, which is directly related to the distribution of thermal energy within the discharge volume. In this paper, the temperature and stress distribution of the quartz tube wall of an inductively coupled plasma generator at 27 kW-85 kW are described. A numerical simulation model was established to depict the interaction between the plasma and the quartz tube wall. In the field of experimental research, the temperature of the outer wall of the quartz tube was obtained by using a thermal imager, and a non-uniform B-spline difference method was proposed to fit the outer wall temperature of the quartz tube to eliminate the influence of the induction coil. It is found that the numerical simulation and experimental results show that the temperature is stable region, temperature rise area, temperature drop zone, and the high temperature region of the quartz tube wall is located in the coil area, and the high stress area is also located in this region. On this basis, the outer wall temperature and thermal stress of quartz tubes under different heat fluxes are studied. When the heat fluxe exceeds 18.6 kW/m2, the stresses in the coil area and downstream of the coil exceed the limit stress. Mechanical failures may occur in areas where the ultimate stresses are exceeded, and these results can provide theoretical data for the optimal design of high-power inductively coupled plasma generators.

Prediction of adjacent single pile deformation induced by tunnel excavation based on the Pasternak model

The construction of metro tunnels in soft ground would cause significant settlement of the ground surface and deformation of buildings and their foundations in the vicinity of the tunnels. The deformation laws of the pile of the neighbouring structures induced by the tunnel construction have not yet been fully identified. This paper analyzed the impact mechanism of tunnel construction on piles based on the Pasternak model, deduced the calculation methods of additional horizontal displacement and additional internal force of piles, and introduced three solution methods. The computational method results have been validated through numerical simulations using coupling of discrete element method and finite difference method and compared to select laboratory data. The results show that the model accuracy is better when the tunnel axis burial depth is less than the pile bottom burial depth. The analysis shows that the tunnel burial depth significantly influences the displacement distribution of the adjacent single pile, while the impact on the peak displacement is insignificant. The thickness of the elastic layer (C) is inversely related to the maximum horizontal displacement and internal force, but it does not impact the distribution patterns of the displacement and internal force. For thickness of the elastic layer (C), the bending moment’s point is constant at 2 m above and below the tunnel axis, whereas the shear force’s point remains constant at the buried tunnel axis’s depth and 4 m above the tunnel axis.

Numerical methods for scalar field dark energy in tabletop experiments and Lunar Laser Ranging

Numerous tabletop experiments have been dedicated to exploring the manifestations of screened scalar field dark energy, such as symmetron or chameleon fields. Precise theoretical predictions require simulating field configurations within the respective experiments. This paper focuses onto the less-explored environment-dependent dilaton field, which emerges in the strong coupling limit of string theory. Due to its exponential self-coupling, this field can exhibit significantly steeper slopes compared to symmetron and chameleon fields, and the equations of motion can be challenging to solve with standard machine precision. We present the first exact solution for the geometry of a vacuum region between two infinitely extended parallel plates. This solution serves as a benchmark for testing the accuracy of numerical solvers. By reparametrizing the model and transforming the equations of motion, we show how to make the model computable across the entire experimentally accessible parameter space. To simulate the dilaton field in one- and two-mirror geometries, as well as spherical configurations, we introduce a non-uniform finite difference method. Additionally, we provide an algorithm for solving the stationary Schrödinger equation for a fermion in one dimension in the presence of a dilaton field. The algorithms developed here are not limited to the dilaton field, but can be applied to similar scalar-tensor theories as well. We demonstrate such applications at hand of the chameleon and symmetron field. Our computational tools have practical applications in a variety of experimental contexts, including gravity resonance spectroscopy (q Bounce), Lunar Laser Ranging (LLR), and the upcoming Casimir and Non-Newtonian Force Experiment (cannex). A Mathematica implementation of all algorithms is provided.

Prediction of permeability characteristics of mine slurries and sediments using finite-strain framework by optimisation algorithms

Determining the permeability characteristics of mine tailing slurries through laboratory finite-strain consolidation tests is costly due to the extensive testing required. An alternative approach involves back-predicting hydraulic conductivities from settling column test data. This study employed settlement and excess pore pressure data as inputs in optimising the permeability parameters using the finite-strain consolidation (FSC) framework. The proposed approach used the finite difference method to solve the governing equation for FSC in the forward analysis. Two novel variants of the Artificial Bee Colony (ABC) algorithm, namely the Modified Artificial Bee Colony (MABC) and the Hybrid Artificial Bee Colony (HABC) algorithms, were used to back-predict the hydraulic conductivity function parameters from the FSC test data. These models predicted the permeability characteristics using the temporal variation of the settlements for six slurries and excess pore pressure dissipation data for four slurries. The performance of the proposed algorithms along with Hybrid Particle Swarm Optimisation (HPSO) was compared with the conventional optimisation algorithms, viz., PSO, ABC, and Quantum PSO (QPSO). The HABC and HPSO exhibited remarkable stability, consistently converging to identical solution sets across multiple iterations, thereby outperforming other algorithms in this study. Despite its higher time complexity by HABC relative to the other evaluated methods, this complexity is warranted for enhanced robustness. The current study is helpful in brining practical and reliable methodologies for estimating the hydraulic conductivity function from field-scale conductivity (FSC) data, providing critical insights for the safe and efficient management of slurry wastes.

Performance analysis of natural draft power plant cooling tower: Mathematical modeling of cross-flow type, application in capital cities of Iranian provinces

Cooling towers are heat exchangers that reduce the hot water temperature produced by process equipment through heat and mass transfer between water and air stream. This study investigates the performance of cross-flow cooling towers under various geometrical, physical, and environmental conditions. For this purpose, thermodynamic modeling of the cross-flow cooling tower was conducted, and the governing equations were numerically solved using the finite difference method. Unlike previous studies, the effects of water droplet deformation into an elliptical shape during its fall along the cooling tower were also considered. This deformation, which influences the drag coefficient, Reynolds number of the water droplets, droplet surface area, and its cross-section area, along with the incorporation of buoyancy force in the droplet momentum equation, led to an improvement in the results. Consequently, the maximum computational error in this case was reduced to 1.97 %, compared to the scenario where droplet deformation and buoyancy force were neglected. The change in geometrical parameters of the tower in Tehran and Rasht was investigated, revealing that increasing the outlet radius of the tower from 20 m to 22.5 m decreased the outlet water temperature by 1.21 °C and 0.67 °C and increased the thermal efficiency of the tower by 4.94 % and 2.88 % respectively, while increasing the tower height from 100 m to 120 m, only decreased the outlet water temperature by 0.47 °C and 0.26 °C, and increased the thermal efficiency of the tower by 1.89 % and 1.09 % respectively. Additionally, the cooling tower performance was assessed in the centers of different provinces .of Iran. Results showed that with an initial droplet radius of 1 mm and an inlet water temperature of 50 °C, the maximum and minimum temperature reductions occurred in Shahrekord by 20.16 °C and Bandarabbas by 12.37 °C, respectively.

CONTACT INTERACTION OF AN UNDERGROUND PIPELINE WITH SOIL UNDER DYNAMIC IMPACTS

The interaction between a semi-infinite underground pipeline and the surrounding soil during longitudinal seismic wave propagation is examined in the article. The wave travels through the soil with its front perpendicular to the pipeline's axis, and the nonlinear laws of interaction (friction) on the surface of their contact, including the Amonton-Coulomb law, are used to solve related wave problems for the pipeline and soil. The method of characteristics and the finite difference method are sequentially used to solve these problems numerically. The implementation of the law of interaction (friction) processes is shown, depending on the parameters of the wave in soil and the mechanical characteristics of soil. It was determined that a wave in soil that involves the pipeline generates a powerful wave in the pipeline. The amplitude of this wave is many times greater than the amplitude of the wave in soil, and it propagates through the pipeline without attenuation. The dependences of the amplitude of this wave on the parameters of the law of friction, waves in soil, and the mechanical characteristics of soil are determined.

A novel binary data classification algorithm based on the modified reaction-diffusion predator-prey system with Holling-II function.

In this study, we propose a modified reaction-diffusion prey-predator model with a Holling-II function for binary data classification. In the model, we use u and v to represent the densities of prey and predators, respectively. We modify the original equation by substituting the term v with f-v to obtain a stable and clear nonlinear decision surface. By employing a finite difference method for numerical solution of the original model, we conduct various experiments in two-dimensional and three-dimensional spaces to validate the feasibility of the classifier. Additionally, with consideration for wide real applications, we perform classification experiments on electroencephalogram signals, demonstrating the effectiveness and robustness of the classifier in binary data classification.

Modification of the dimensional doma method for linear elliptic equations

Currently, one of the most common methods for the numerical solution of boundary value problems are difference methods (grid method, finite difference method). These methods are well suited for solving problems in regular domains. In areas of complex structure, their use leads to a number of difficulties both in the construction of difference schemes, and in the implementation on a computer. One of the methods to overcome these difficulties is the method of fictitious regions. There are four interrelated directions in the development of the method of fictitious regions: study of various ways to continue the original problems in a fictitious area; obtaining unimprovable estimates in stronger metrics; extension of the class of problems on the application of the method of fictitious areas; construction of effective difference schemes for solving auxiliary problems constructed by the method of fictitious areas. For the first time, the fictitious domain method for the Navier-Stokes equation was studied in the work of A.N. Bugrova, Sh. Smagulov, Smagulov Sh. This article discusses the method of additional areas, which is an analogue of the method of fictitious areas for solving linear boundary value problems, but in the auxiliary problem of this method there is no small perimeter. This method is based on the variational principle of solving linear boundary value problems of elliptic type in an arbitrary region. The existence of a solution is proved by the Galerkin uniqueness method.

A Simplified Calibration Procedure for DEM Simulations of Granular Material Flow

The discrete element method (DEM) has emerged as an essential computational tool in geotechnical engineering for the simulation of granular materials, offering significant advantages over traditional continuum-based methods such as the finite element method (FEM) and the finite difference method (FDM). The DEM’s ability to model particle-level interactions, including contact forces, rotations, and particle breakage, allows for a more precise understanding of granular media behavior under various loading conditions. However, accurate DEM simulations require meticulous calibration of input parameters, such as particle density, stiffness, and friction, to effectively replicate real-world behavior. This study proposes a simplified calibration procedure, intended to be conducted prior to any granular material flow DEM modeling, based on three fundamental physical tests: bulk density, surface friction, and angle of repose. The ability of these tests, conducted on dry quartz sand, to accurately determine DEM micromechanical parameters, was validated through numerical simulation of cylinder tests with varying height-to-radius ratios. The results demonstrated that this calibration approach effectively reduced computational complexity while maintaining high accuracy, with validation errors of 0% to 12%. This research underscores the efficacy of simplified DEM calibration methods in enhancing the predictive reliability of simulations, particularly for sand modeling in geotechnical applications.

Numerical study on the effect of strategically placed multiple diathermal obstructions within a porous enclosure

A novel strategy to reduce the convection heat transfer across a differentially heated, fluid-saturated porous enclosure has been reported in the present investigation. This objective is achieved by sequentially and strategically embedding multiple diathermal obstructions within the enclosure. To describe it in short, the strategy is to identify the location of maximum convection strength and place a single obstruction at that location. This strategy is re-applied to find an updated location of maximum convection strength and placing another single obstruction at that newly updated location. Darcy flow model is used to describe the fluid flow in porous media and solved using Successive Accelerated Replacement scheme using finite difference method. The parameters under study are type of obstructions (horizontal, vertical, right-inclined, left-inclined, straight-crossed and inclined-crossed), number of obstructions (0 < N <10) and modified Rayleigh number (100 < Ra < 2000). The size of obstruction (Z) has been fixed at 0.1. Flow and temperature distribution are plotted using streamlines and isotherms. The strength of convection is quantified using Nusselt number and maximum absolute stream function. It has been found that introducing obstructions within a differentially heated porous enclosure weakens the convection strength developed within it and the maximum reduction can be obtained for inclined-cross obstruction.

Study of hybrid nanofluid flow in a porous medium over an exponentially stretching sheet under Joule heating and thermal radiation: Finite difference

The significant purpose of present investigation of the behavior of a nanofluid's in magneto-hydrodynamics (MHD), mass transfer, Joule heating, and boundary layer transfer characteristics over an exponentially stretching sheet in a porous medium and thermal radiation effects. The article's goal is to look at the fluid flow and heat transmission characteristics from a sheet of hybrid nanoparticles. The partial differential equations (PDEs) that were derived for the mathematical model were converted using the proper similarity transformation into ordinary differential equations (ODEs). The hybrid nanofluid composed of 97 % of ethyl glycol (EG) and the volume concentration of Magnetite (Fe3O4) and Copper(Cu) are ranging from 0.5 % to 2.5 % both respectively. The effects of thermal radiation, stretching rate, Joule heating, porous medium permeability, and nanoparticle volume fraction on the flow and heat transmission properties are investigated by numerical simulations using the finite difference method (FDM). The analysis reveals that the inclusion of nanofluids enhance the thermal conductivity and enhance the heat transfer rate. Additionally, the influence of variable viscosity on the flow behavior and thermal characteristics are examined graphically. The effects of variable viscosity and thermal conductivity are examined, as it has significance in optimizing system under various thermal and magnetic effects. This study offers a pathway to develop more efficient thermal management solutions, by contributing to technological advancement and energy saving. The key findings of present study reveal that the temperature profile rises significantly due to Joule heating effects. The Nusselt number reveal an improvement of about 12 % when the volume fraction of nano particles is increased by 1–4 % indicating the enhancement in heat transfer efficiency. Similarly, the velocity profile was influenced by porous medium permeability as 11 % increase in porosity result a 18 % decrease in velocity profile.By using parametric research, the role of physical parameters in determining the local skin-friction coefficient, temperature, nanoparticle volume percentage, and longitudinal velocity profiles, local Nusselt number, and local Sherwood number are thoroughly examined. A graphic representation of the velocity, temperature, and concentration distribution findings is presented.