Fundamental Conservation Laws Research Articles

Cylinder-piston application for surge prevention and energy efficiency in an industrial compression unit

Compressions are prevalent in industrial applications and are notable for their substantial energy consumption. Therefore, the simulation and analysis of the compression process are essential for maintenance and energy conservation efforts. These systems are prone to potentially unstable surge conditions, necessitating the use of traditional anti-surge valves that result in considerable energy losses. Ensuring the near-optimal operation of these systems is critical to minimizing energy consumption.In this article, a conceptual framework for a cylinder-piston mechanism is delineated, intended for design and operation as an active surge control system. Additionally, a modular quasi-one-dimensional model is articulated for the transient simulation of an industrial compression system, which integrates models for both the anti-surge and active control systems. The manuscript presents a novel design, featured by a cylinder-piston system integrated with a robust controller, posited as a potential alternative to traditional anti-surge systems. The effectiveness of this design in expanding the operational envelope of the compression system and surge prevention is rigorously examined. Moreover, a thermodynamic model, grounded in the fundamental laws of mass, momentum, and energy conservation, is applied to each component of the system. Furthermore, the manuscript explores the benefits of the innovative design in achieving a marked decrease in energy wastage. Simulation results from a test scenario reveals that the implementation of the cylinder-piston design, as opposed to the conventional anti-surge system, can diminish energy losses and associated pollutant emissions by approximately 33 percent.

A Physical Insight into Computational Fluid Dynamics and Heat Transfer

Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the physical processes. This article represents a derivative-free approach for the mathematical modelling. The proposed approach for CFD and numerical heat transfer is based on the conservation and phenomenological laws, and physical constraints on the minimum problem-dependent spatial and temporal scales (for example, on the average free path of molecules and the average time of their collisions for gases). This leads to the derivative-free governing equations (the discontinuum approximation) that are very convenient for numerical simulation. The theoretical analysis of governing equations describing the fundamental conservation laws in the continuum and discontinuum approximations is given. The article demonstrates the derivative-free approach based on the correctly defined macroparameters (pressure, temperature, density, etc.) for the mathematical description of physical and chemical processes. This eliminates the finite-difference, finite-volume, finite-element or other approximations of the governing equations from the computational algorithms.

Multiphysics simulation of freezing and thawing granular media using material point method

In this paper, a fully coupled thermo-hydro-mechanical material point method, applicable to liquid-saturated porous systems undergoing large deformations and phase transitions, is presented. A mathematical framework was established based on multiphasic mixture theory and fundamental physical conservation laws, rather than using phenomenological or semi-empirical equations. A fractional-step-based semi-implicit solution scheme was proposed to solve the coupled formulations within the framework of the generalized interpolation material point method. The proposed method was validated using several benchmark examples, including the talik closure and thaw consolidation. Its performance in simulating climate-driven large deformation problems was further demonstrated by simulating the settlement of a rigid footing on thawing ground. This paper presents an innovative and rigorous framework for predicting the impact of climate change on engineering practices.

Enhancing wildfire propagation model predictions using aerial swarm-based real-time wind measurements: A conceptual framework

The dynamic behaviour of wildfires is mainly influenced by weather, fuel, and topography. Based on fundamental conservation laws involving numerous physical processes and large scales, atmospheric models require substantial computational resources. Therefore, coupling wildfire and atmospheric models is impractical for high resolutions. Instead, a static atmospheric wind field is typically input into the wildfire model, either as boundary conditions on the control surface or distributed over the control volume. Wildfire propagation models may be (i) data-driven; (ii)theoretical; or (iii)mechanistic surrogates. Data-driven models are beyond the scope of this paper. Theoretical models are based on conservation laws (species, energy, mass, momentum) and are, therefore, computationally intensive; e.g. the Fire Dynamics Simulator (FDS). Mechanistic surrogate models do not closely follow fire dynamics laws, but related laws observed to make predictions more efficiently with sufficient accuracy; e.g. FARSITE, and FDS with the Level Set model (FDS-LS). Whether theoretical or mechanistic surrogate, these wildfire models may be coupled with or decoupled from wind models (e.g. Navier-Stokes equations). Only coupled models account for the effect of the fire on the wind field. In this paper, a series of simulations of wildfire propagation on grassland are performed using FDS-LS to study the impact of the fire-induced wind on the fire propagation dynamics. Results show that coupling leads to higher Rates of Spread (RoS), closer to those reported from field experiments, with increasing wind speeds and higher terrain slopes strengthening this trend. Aiming to capture the fire–wind interaction without the hefty cost of solving Navier-Stokes equations, a conceptual framework is proposed: 1) a swarm of unmanned aerial vehicles measure wind velocities at flight height; 2) the wind field is constructed with the acquired data; 3) the high-altitude wind field is mapped to near-surface, and 4) the near-surface wind field is fed into the wildfire model periodically. A series of simulations are performed using an in-house decoupled physics-based reduced-order fire propagation model (FireProM-F) enhanced by wind field “measurements”. In this proof of concept, wind velocities are not measured but extracted from physics-based Large Eddy Simulations taken as ground truth. Unsurprisingly, higher measurement frequencies lead to more accurate and realistic predictions of the propagating fire front. An initial attempt is made to study the effect of wind measurement uncertainty on the model predictions by adding Gaussian noise. Preliminary results show that higher noise leads to the fire front displaying more irregular shapes and slower propagation.

Kirchhoff's law-based velocity-controlled motion models to predict real-time cutting forces in minimally invasive surgeries

A theoretical framework, united by a “system effect” is formulated to model the cutting/haptic force evolution at the cutting edge of a surgical cutting instrument during its penetration into soft biological tissue in minimally invasive surgery. Other cutting process responses, including tissue fracture force, friction force, and damping, are predicted by the model as well. The model is based on a velocity-controlled formulation of the corresponding equations of motion, derived for a surgical cutting instrument and tissue based on Kirchhoff's fundamental energy conservation law. It provides nearly zero residues (absolute errors) in the equations of motion balances. In addition, concurrent closing relationships for the fracture force, friction coefficient, friction force, process damping, strain rate function (a constitutive tissue model), and their implementation within the proposed theoretical framework are established. The advantage of the method is its ability to make precise real-time predictions of the aperiodic fluctuating evolutions of the cutting forces and the other process responses. It allows for the robust modeling of the interactions between a medical instrument and a nonlinear viscoelastic tissue under any physically feasible working conditions. The cutting process model was partially qualitatively verified through numerical simulations and by comparing the computed cutting forces with experimentally measured values during robotic uniaxial biopsy needle constant velocity insertion into artificial gel tissue, obtained from previous experimental research. The comparison has shown a qualitatively similar adequate trend in the evolution of the experimentally measured and numerically predicted cutting forces during insertion of the needle.

Study of mass and heat transfer for peristaltic transport of cross nanofluid through a curved channel

AbstractNanoparticles have significant applications in drug delivery systems, heat exchanges, treatment of several diseases and chemical reactions. The Cross non‐Newtonian nanofluid model for heat and mass transfer inspection with diethylene glycol‐based fluid is highlighted in this study. The magnesium aluminate nanoparticles are used to evaluate nanofluid characteristics. The current investigation explores the numerical results for magnetohydrodynamics (MHD) peristaltic movement of Cross‐nanofluid via a curved channel under the influences of thermal radiation, heat sink/source and Joule heating. The effects of viscous dissipation, thermophoretic, variable thermal conductivity and Brownian diffusion coefficients in the presence of mass and thermal convection are also taken into consideration. Flow problem is modeled using fundamental conservation laws, and the resulting nonlinear partial differential equations (PDEs) are reduced to a system of nonlinear ordinary differential equations (ODEs) by employing long wavelength and a small Reynolds number approximations. Simplified systems of ODEs are addressed by adopting numerical technique via the NDSolve built‐in command in Mathematica. Furthermore, graphical presentations explain the behavior of relevant flow parameters. Results indicate that better values of the magnetic number and the thermophoresis parameter increase the rate of mass transfer. Results indicate that the nanofluid's temperature increases by improving values of the Brinkman number and falls with the thermal radiation parameter. It is also stated that the nanofluid's velocity reduces near the lower wall for greater values of Hartman number. Moreover, heat transfer rate improves for larger values of the heat generation parameter and curvature parameter.

Fluid–rigid body coupling simulations with the passively moving solid model based on a physically consistent particle method

Fluid–rigid body interaction is a significant topic in research on particle methods. This study developed a fluid–rigid body coupling method based on a physically consistent particle method, i.e., the moving particle hydrodynamics (MPH) method, incorporating the passively moving solid (PMS) model. When the discrete particle system satisfies the fundamental laws of physics, i.e., mass conservation, linear and angular momentum conservation, and the second law of thermodynamics, the method is asserted physically consistent, and this feature is important for robust dynamic calculations. The PMS model is a pioneering approach that is practical for particle methods in which fluid and rigid-body particles are initially calculated as a fluid. Then, only rigid-body particles are modified to restore the initial shape by applying rigid-body constraints. Thus, combining the MPH method and the PMS model realizes a fluid–rigid body coupling method that satisfies fundamental physical laws. The proposed method was first verified via the fundamental rigid body and fluid–rigid body coupling problems: the Dzhanibekov effect on a T-shaped rigid body, a floating rectangular solid, a floating cylinder, and water entry of a two-dimensional cylinder. Second, the proposed method was validated via calculating a cylinder rolling on a liquid film as a fluid–rigid body coupling problem with rotation. By using a potential-based surface tension model, the computed results showed reasonable agreement with the experimental data obtained in this study. Overall, it was confirmed that the proposed method is a promising fluid–rigid body coupling approach, in which the surface tension and wettability can be considered as well.

Modeling of heat and mass transfer in the discontinuum approximation

The article presents a theoretical analysis of the governing equations expressing the fundamental conservation laws in the continuum and discontinuum approximations, and methods for solving problems of hydrodynamics as one of the most important subfields of continuum mechanics. This article is an attempt to more accurately describe physicochemical macro-processes. It is shown that the most suitable equations for computer modeling are the conservation laws under natural constraints on the minimum spatial and time scales, i.e., equations without partial derivatives and constraints on the solution smoothness. Using the continuity and thermal conductivity equations, a phenomenological method for constructing and numerically solving the governing equations is presented, and comparison with the traditional approach is given.

DESTRUCTION OF ROCKS BY EXPLOSION DURING OIL TRANSPORTATION

When oil and gas wells are ready for operation, when drilling is carried out at the bottom of the well to establish contact with the formation, it is considered that the degree of crushing of the rocks is proportional to the speed of application of the load. As a result of the stresses created by them, the degree of fragmentation is higher. In the article, it is proposed to take into account the quality of crushing of the necessary rock by using some empirical coefficients in the calculation formulas. The dynamics of the rock dispersion process is studied on the basis of the hydrodynamic hypothesis. Here, the solution of the system of differential equations is given based on the fundamental laws of conservation of mass, energy and momentum. Based on the strength properties of mountain rocks, broken lines are found in the continuum of the whole environment, which determines the final effect of rock crushing. However, the accepted assumptions about the incompressibility of the rock and the transfer of the explosive impulse to the immediate environment significantly reduce the practical value of the results. It should be noted that in the immediate area directly adjacent to the load, the mountain rock is under uneven volume compression. In this case, the largest tangential stresses occur mainly in planes oriented at an angle of 450 to the radial direction. Thanks to this, a system of spiral sliding lines breaks the rock into small blocks. Outside this zone, a system of radial cracks is formed as a result of the expansion of the massif. When the pressure in the gas cavity decreases and the mass moves back in the direction of the load, tangential cracks appear. The combination of the volume compression zone and the reach zone constitutes the controlled crushing area. When the compression wave reaches the bare surface, it becomes a stress wave. As this wave travels from the surface to the load, it forms a system of jump cracks. The high explosive effect of explosive gases with sufficient explosion energy causes the release of such shattered rock. Obviously, this concept is very important for the development of the theory of explosive disintegration of mountain rocks. Because there is no unequivocal relationship between the nature of the dissolution of the rock and the acoustic hardness. One of the first to clearly describe the mechanism of shock wave formation and its transformation into a more explosive and seismic wave when detonation reaches the boundary of the charge cavity. In rocks, shock waves are formed during the entire time of expansion of the gas cavity. It explains in detail the mechanism of cracking phenomena by considering the cracks as a source of multiple reflections of the stress wave. Keywords: rock strength, constant material, scale effect, rocks, destruction probability, fractured, robustness theory, microcrack, mineral, experience constant, density of defects, displacement, compression.

Completeness of atomic structure representations

In this paper, we address the challenge of obtaining a comprehensive and symmetric representation of point particle groups, such as atoms in a molecule, which is crucial in physics and theoretical chemistry. The problem has become even more important with the widespread adoption of machine-learning techniques in science, as it underpins the capacity of models to accurately reproduce physical relationships while being consistent with fundamental symmetries and conservation laws. However, some of the descriptors that are commonly used to represent point clouds— notably those based on discretized correlations of the neighbor density that power most of the existing ML models of matter at the atomic scale—are unable to distinguish between special arrangements of particles in three dimensions. This makes it impossible to machine learn their properties. Atom-density correlations are provably complete in the limit in which they simultaneously describe the mutual relationship between all atoms, which is impractical. We present a novel approach to construct descriptors of finite correlations based on the relative arrangement of particle triplets, which can be employed to create symmetry-adapted models with universal approximation capabilities, and have the resolution of the neighbor discretization as the sole convergence parameter. Our strategy is demonstrated on a class of atomic arrangements that are specifically built to defy a broad class of conventional symmetric descriptors, showing its potential for addressing their limitations.

Coupled heat and mass transfer mathematical study for lubricated non-Newtonian nanomaterial conveying oblique stagnation point flow: A comparison of viscous and viscoelastic nanofluid model

Abstract The lubrication phenomenon plays a novel role in the chemical industries, manufacturing processes, extrusion systems, thermal engineering, petroleum industries, soil sciences, etc. Owing to such motivated applications, the aim of the current work is to predict the assessment of heat and mass transfer analysis for non-Newtonian nanomaterial impinging over a lubricated surface. The flow is subject to the oblique stagnation point framework. The lubricated phenomenon is observed due to viscoelastic nanofluid. The impacts of chemical reaction are also endorsed. The fundamental conservation laws are utilized to model the flow problem and similarity transformation are used to transform the governing system of partial differential equations into ordinary differential equations. A thin layer of power law lubricant is used to enhance the lubrication features. The numerical object assessment regarding the simulation process is captured by implementing the Keller Box scheme. The physical characterization endorsing the thermal fluctuation with flow parameters is inspected.

Matematyczne modele hydromechaniki przepływu wielofazowego o zmiennej masie

The paper discusses the mathematical model of hydromechanics of multiphase flows with varying mass. A multiphase flow is considered a continuum consisting of a set of a large number of different groups of particles. The derivation of motion equations and similarity criteria are given taking into account both the externally attached (or detached) mass and phase transitions within the medium. The equations of mass, momentum and energy transfer for individual phases and the medium as a whole are derived based on fundamental conservation laws. It was demonstrated that in the absence of sources (or flow-offs) of mass, momentum and energy, the known equations of single- and multi-phase flow hydromechanics follow as a special case from the obtained systems of motion equations and similarity criteria. The obtained motion equations are valid for the description of an ingredient of mixture and the medium as a whole, regardless of their physical and mechanical properties. Thermodynamic and rheological state equations, as well as expressions for heat flow, interfacial mass forces phase transitions, and heat exchange between phases can be used to close them. The implemented models make it possible to simulate both the stationary distribution of parameters along the wellbore during production and non-stationary processes that occur, for example, when the pump shaft speed changes during oil production. The developed approaches were implemented in the DataFlow software tool for analysis of the hydrodynamics of multiphase hydrocarbon flows, taking into account heat exchange with the rocks surrounding the well, and phase transitions in the fluid. Using the software package, test calculations were carried out to demonstrate the performance of the proposed and implemented models.

Mass balance of generation, retention, and production for the Wolfcamp-sourced hydrocarbon in the Permian Delaware Basin: Insight on remaining recoverable resource and expulsion efficiency

Detailed quantification of basin-wide hydrocarbon (HC) masses from generation to production is necessary for a quantitative petroleum system analysis, and ultimately, for accurate resource estimation. Such quantified HC masses must be balanced following the fundamental laws of mass conservation. Mass balance is particularly important for unconventional-conventional petroleum systems in which expulsion efficiency (EE) is a critical parameter defining HCs in place, within the source rock (SR) interval and outside. This study performs an HC mass balance assessment aiming primarily to obtain insights on the remaining recoverable and EE, applied to the Wolfcamp Formation (Fm) in the Permian Delaware Basin. Calculated generated HC volumes from the Wolfcamp Fm based on the assumed 3D geologic model and p90/50/10 SR properties are 878/2107/4514 billion barrels of oil equivalent (BBOE). The mass balance is performed with three calculation scenarios: (1) inversion of EE (based on the United States Geological Survey [USGS]-estimated remaining recoverable HC in the Wolfcamp Fm), (2) forward calculation with multiple assumed EE, and (3) HC expulsion simulation. The mass balance with the inversion of EE indicates that the p90/50/10 of 58%/62%/69% overall EE is required for the Wolfcamp Fm to achieve the USGS-estimated remaining recoverable HC of 35/78/140 BBOE. Both mass balance with forward calculation and expulsion simulation predict overall lower p90/50/10 EE of 50% and 30%/56%/75%, respectively, thus resulting in higher than the USGS-estimated remaining recoverable HC in the Wolfcamp Fm in most scenarios. All of the mass balance calculations are also consistent with the interpretation of Wolfcamp unconventional play as a self-sourced play. This workflow is an efficient tool for taking a quantitative look at the petroleum system, especially related to the possibilities of generated HC distribution in the system. The calculated mass balance can serve as a reference in modeling unconventional systems and resources.

Hybrid Lattice Boltzmann Approach for Simulation of High-Speed Flows

A lattice Boltzmann approach utilizing hybrid lattices for accurate simulation of high-speed transonic (TS) flows is presented in this study. Single-layer lattice models, such as D3Q19, are computationally efficient with low numerical dissipation, but are limited to simulate weakly compressible flows within subsonic Mach regime. Multilayer lattice models, such as D3Q33, are capable of simulating thermal and high-speed compressible flows in TS Mach regime, but suffer from a higher numerical dissipation and higher computational cost. To take full advantages of these two types of lattices, a simulation domain is divided into two regions, high-subsonic (HS) flow regions to be solved by single-layer lattices and TS flow regions to be solved by multilayer lattices. The interface connecting the HS and TS flow regions are represented by double-sided surfels to realize smooth flow transition and ensure satisfaction of fundamental conservation laws. The hybrid lattice Boltzmann approach is stable and robust, and it allows multiple HS/TS flow regions with arbitrary shapes. Extensive validation studies demonstrate that the proposed approach is capable of obtaining accurate aerodynamic prediction of flows with a wide range of Mach numbers, and preserving the low numerical dissipation advantage of single-layer lattices in aeroacoustic computations.

Real-Time GW-Ehrenfest-Fan-Migdal Method for Nonequilibrium 2D Materials.

Quantum simulations of photoexcited low-dimensional systems are pivotal for understanding how to functionalize and integrate novel two-dimensional (2D) materials in next-generation optoelectronic devices. First-principles predictions are extremely challenging due to the simultaneous interplay of light-matter, electron-electron, and electron-nuclear interactions. We here present an advanced ab initio many-body method that accounts for quantum coherence and non-Markovian effects while treating electrons and nuclei on equal footing, thereby preserving fundamental conservation laws like the total energy. The impact of this advancement is demonstrated through real-time simulations of the complex multivalley dynamics in a molybdenum disulfide (MoS2) monolayer pumped above gap. Within a single framework, we provide a parameter-free description of the coherent-to-incoherent crossover, elucidating the role of microscopic and collective excitations in the dephasing and thermalization processes.

Mathematical Model of the Working Processes of the Gas Cap of a Piston Pump Installed in the Discharge Line

A mathematical model of the working processes occurring in the gas cap has been developed on the basic fundamental laws of conservation of energy, mass and motion, and the equation of state, both taking into account the change in the mass of the gas due to phase transitions and the solubility of the gas in the liquid, and without taking them into account with a dividing element. In addition, there was developed a mathematical model of the liquid flow from the gas cap through a pipeline of constant cross section. It was found from the results of a numerical experiment that to reduce the feed irregularity, it is necessary to increase the length of the pipeline and the crankshaft revolutions, in addition to the known ratio of the volume of gas in the cap to the working volume of the pump; an increase in discharge pressure and an increase in the diameter of the connecting pipeline increases the feed irregularity.

Nonsimilar forced convection analysis of maxwell nanofluid flow over an exponentially stretching sheet with convective boundary conditions

AbstractThis proposed work aims to describe nonsimilar forced convection analysis for the flow of Maxwell nanofluids. The forced flow is commenced due to the stretching surface (SS) at an exponential rate. Heat and mass transmission is tackled with convective and zero mass flux at the surface. The fundamental laws of conservation governing the present flow problem are expressed mathematically in the form of a nonlinear partial differential system. The differential system is then remodeled into a system of nonlinear dimensionless partial differential equations (PDEs) under the implementation of suitable nonsimilar transformations. The resulting nonsimilar system is analytically approximated by applying local nonsimilarity (LNS) and then using the finite‐difference based bvp4c algorithm, it is numerically simulated to ascertain the influences of the various parameters—including the; Deborah number, Biot number, Schmidt number, Brownian diffusion parameter, Prandtl number, and thermophoresis diffusion parameters, on velocity and temperature. The reduced Nusselt numbers and the conduct of velocity and thermal distribution for varying parameters are illustrated graphically. The reduction of the boundary layer (BL) thickness is measured because‐of the Biot number while an increase is observed with an elevation in Deborah number. The velocity configuration is reduced with expanding Deborah number. It is remarked that as the values of the thermophoresis and Brownian motion parameter rise, the thermal BL thickness expands, and at the surface, the temperature gradient demises. An excellent comparison is noticed between present works with the already published article. The novelty of this article is that most of realworld BL flow problems are nonsimilar in nature, while many research have neglected this fact and treated the problem as similar. Therefore, we talked about the Maxwell problem's nonsimilar analysis here. The author's observations indicate that the analysis of the topic under discussion has not yet been declared in published literature.

Fundamental solutions and conservation laws for conformable time fractional partial differential equation

In this paper, the connections between fundamental solutions and Lie symmetry groups for a class of conformable time fractional partial differential equations (PDEs) with variable coefficient are investigated for the first time. The group-invariant solutions to the considered equations are constructed by means of symmetry group method. Then, the corresponding fundamental solutions for these PDEs are established by taking the inverse Laplace transform of the group invariant solutions. In addition, some examples are introduced to illustrate the effectiveness of this approach. Furthermore, the conservation laws of these fractional PDEs are obtained making use of new Noether theorem.

Developing a method of accounting for the existence of local surface heat exchange in rods of variable cross-section

The load-bearing elements of a number of strategic equipment are of limited length and variable cross-section. Most of them are exposed to certain types of heat sources. In order to ensure the reliable operation of this equipment, it is necessary to know the temperature field along the length of the variable cross-section rod. In this paper, a computational algorithm and a method for determining the temperature field along the length of a rod with a limited length and variable cross-section are proposed. They are based on the fundamental laws of conservation of energy. The nonlinearity of the process is due to nonlinear dependencies of the areas of the variable cross-section on the coordinate. The radius of the cross-section of the rod decreases linearly along the entire length, starting from the left end. The side surface of the first and third discrete elements of the rod is heat-insulated. Convective heat exchange with the environment takes place on the side surface of the second discrete element of the rod. The cross-sectional area of the left end of the rod is under the heat flow with a constant intensity, and a heat flow with different intensities is supplied to the right end, wherein the heat transfer coefficient is considered constant. For this task, you must first determine the law of temperature distribution along the length of the rod. In addition, if one end is rigidly fixed and the other end is free, the elongation must be calculated depending on the available heat sources, the physical and geometric characteristics of the rod, taking into account the presence of insulation. In case of pinching of both ends of the investigated rod, the value of axial compressive force is calculated taking into account the addition of real factors. The distribution of all components of the strain, stress, and displacement field is also defined

Activation energy and convective heat transfer effects on the radiative Williamson nanofluid flow over a radially stretching surface containing Joule heating and viscous dissipation

This article recognizes the time-dependent axisymmetric flow of a non-Newtonian Williamson fluid caused by a radially stretching surface in the presence of nanoparticles in the porous medium. The combined impacts of Joule heating and viscous dissipation on the flow profiles are also discussed. Chemical reaction at the surface is implemented. The convective heat transfer model and Brownian motion are also studied for the electrically conducting nanofluid flow. The Williamson nanofluid flow has been modeled using a set of partial differential equations based on the fundamental conservation laws of mechanics. By using nondimensional quantities, these equations are first transformed into ordinary differential equations. The Galerkin weighted residual method is performed to resolve these equations numerically. Visual displays and detailed descriptions of the impacts of relevant variables on the thermal performance, concentration field, and velocity field are provided. It is noticed that the thermal profile enhances as the values of the Brownian motion parameter and temperature ratio parameter increase while declining when the values of the velocity slip parameter increase. The Biot number, activation energy, and unsteadiness parameters have proportional effects on the concentration profile, but the reaction parameter has inversely proportional effects on the concentration profile. Heat transfer rate increases with increasing the Weissenberg number and velocity slip parameter, drops with increasing the thermophoresis and unsteadiness parameters, and the Arrhenius activation energy. Finally, a comparison of the obtained numerical solution for the porous and nonporous medium are also done graphically and discussed in details.