Reaction Coefficient Research Articles

Determination of output composition in reaction-advection-diffusion systems on network reactors

We consider reaction-transport processes in open reactors in which systems of first order reactions involving a number of gas species and solid catalysts can occur at localized active regions. Reaction products flow out of the reactor into vacuum conditions and are collected at an exit boundary. The output composition problem (OCP) is to determine the composition (molar fractions) of the collected gas after the reactor is fully emptied. We provide a solution to this problem in the form of a boundary-value problem for a system of time-independent partial differential equations. We then consider network-like reactors, which can be approximated by a network consisting of a collection of nodes and 1-dimensional branches, with reactions taking place at nodes. For these, the OCP can be solved in a simple and effective way, giving explicit formulas for the output composition as a function of the reaction coefficients and parameters associated with the geometric configuration of the system. The possibility of determining reaction coefficients from experimentally obtained output composition is shown in the case of one chemically active node.

Gas-Phase Kinetic Investigation of the OH-Initiated Oxidation of a Series of Methyl-Butenols under Simulated Atmospheric Conditions.

Five biogenic unsaturated alcohols have been investigated under simulated atmospheric conditions regarding their gas-phase OH reactivity. The gas-phase rate coefficients of OH radicals with 2-methyl-3-buten-2-ol (k1), 3-methyl-2-buten-1-ol (k2), 3-methyl-3-buten-1-ol (k3), 2-methyl-3-buten-1-ol (k4), and 3-methyl-3-buten-2-ol (k5) at 298 ± 2 K and 1000 ± 10 mbar total pressure of synthetic air were determined under low- and high-NOx conditions using the relative kinetic technique. The present work provides for the first time the rate coefficients of gas-phase reactions of hydroxyl radicals with 2-methyl-3-buten-1-ol and 3-methyl-3-buten-2-ol. The following rate constants were measured (in 10-11 cm3 molecule-1 s-1): k1 = 6.32 ± 0.49, k2 = 14.55 ± 0.93, k3 = 10.04 ± 0.78, k4 = 5.31 ± 0.37, and k5 = 11.71 ± 1.29. No significant differences in the measured rate coefficients were obtained when either 365 nm photolysis of CH3ONO in the presence of NO or 254 nm photolysis of H2O2 was used as a source of OH radicals. Reactivity toward other classes of related compounds such as alkenes and saturated alcohols is discussed. A comparison of the structure-activity relationship (SAR) estimates derived from the available accepted methodologies with experimental data available for unsaturated alcohols is provided. Atmospheric lifetimes for the investigated series of alkenols with respect to the main atmospheric oxidants are given and discussed.

Numerical Simulation Study Considering Discontinuous Longitudinal Joints in Soft Soil under Symmetric Loading

In shield tunneling, the joint is one of the most vulnerable parts of the segmental lining. Opening of the joint reduces the overall stiffness of the ring, leading to structural damage and issues such as water leakage. Currently, the Winkler method is commonly used to calculate structural deformation, simplifying the interaction between segments and soil as radial and tangential Winkler springs. However, when introducing connection springs or reduction factors to simulate the joint stiffness of segments, the challenge lies in determining the reduction coefficient and the stiffness of the springs. Currently, the hyperstatic reflection method cannot simulate the discontinuity effect at the connection of the tunnel segments, while the state space method overlooks the nonlinear interaction between the tunnel and the soil. Therefore, this paper proposes a numerical simulation method considering the interaction between the tunnel and the soil, which is subjected to compression rather than tension, and the discontinuity of the joints between the segments. The model structure and external load are symmetrical, resulting in symmetrical calculation results. This method is based on the soft soil layers and shield tunnel structures of the Shanghai Metro, and the applicability of the model is verified through deformation calculations using three-dimensional laser scanning point clouds of sections from the Shanghai Metro Line 5. When the subgrade reaction coefficient is 5000 kN/m3, the model can effectively simulate the deformation of operational tunnels. By adjusting the bending stiffness of individual connection springs, we investigate the influence of bending stiffness reduction on the bending moment, radial displacement, and rotational displacement of the ring. The results indicate that a decrease in joint bending stiffness significantly affects the mechanical response of the ring, and the extent and degree of this influence are correlated with the joint position and the magnitude of joint bending stiffness.

Artificial Neural Network Modeling in the Presence of Uncertainty for Predicting Hydrogenation Degree in Continuous Nitrile Butadiene Rubber Processing

The transition from batch to continuous production in the catalytic hydrogenation of nitrile butadiene rubber (NBR) into hydrogenated NBR (HNBR) marks a significant advance for applications under demanding conditions. This study introduces a continuous process utilizing a static mixer (SM) reactor, which notably achieves a hydrogenation conversion rate exceeding 97%. We thoroughly review a mechanistic model of the SM reactor to elucidate the internal dynamics governing the hydrogenation process and address the inherent uncertainties in key parameters such as the Peclet number (Pe), dimensionless time (θτ), reaction coefficient (R), and flow rate coefficient (q). A comprehensive dataset generated from varied parameter values serves as the basis for training an artificial neural network (ANN), which is then compared against traditional models including linear regression, decision tree, and random forest in terms of efficacy. Our results clearly demonstrate the ANN’s superiority in predicting the degree of hydrogenation, achieving the lowest root mean squared error (RMSE) of 3.69 compared to 21.90 for linear regression, 4.94 for decision tree, and 7.51 for random forest. The ANN’s robust capability for modeling complex nonlinear relationships and dynamics significantly enhances decision-making, planning, and optimization of the reactor, reducing computational demands and operational costs. In other words, this approach allows users to rely on a single ML-based model instead of multiple mechanistic models for reflecting the effects of possible uncertainties. Additionally, a feature importance study validates the critical impact of time and element number on the hydrogenation process, further supporting the ANN’s predictive accuracy. These findings underscore the potential of ML-based models in streamlining and enhancing the efficiency of chemical production processes.

Studies of the diluent, temperature and pressure effect on the lower and upper flammability limits of ammonia in air

Ammonia safety and environmental protection research forms the basis for its role as a clean energy carrier. In this work, an experimental study was conducted in this work to analyze the effect of different inhibitors (nitrogen, argon and water vapor) on the flammability limits (FLs) of ammonia at elevated temperatures and pressures. In addition, the influence of diluents on the compositions and flame temperature changes was evaluated, and the temperature sensitivity coefficients of the elementary reactions and the ROP of free radicals and partial products at the FL concentrations were analyzed. The findings indicated that water vapor provided the strongest flame retardant effect on ammonia in three inhibitors. Within a certain temperature and pressure range, the FLs of ammonia in ammonia/diluent/air can be predicted using the extended Le Chatelier equation. The flame temperature decreased at the lower flammability limit (LFL) concentrations and increased at the upper flammability limit (UFL) concentrations of ammonia with increasing initial pressure. As the initial temperature increases, the flame temperature decreases during ammonia combustion. The influence of ammonia concentration on flame temperature is greater than that of diluents dilution. The elementary reactions H+O2<=>O+OH (R1) and NH2+NO<=>NNH+OH (R82) were the primary reactions that increased the flame temperature at the FL ammonia concentrations in ammonia/diluent/air. Conversely, NH2+NO<=>N2+H2O (R80) and H+O2(+M)<=>HO2(+M)(R15) were the main reactions that decreased the flame temperature. H, OH and NH2 radicals played a crucial role in the combustion reaction process at ammonia FL concentrations. At the LFL concentrations of ammonia, the molar fraction of the OH radical showed the greatest variation, while at the UFL concentrations of ammonia it was NH2 radical. The elementary reaction NH3+OH<=>NH2+H2O (R158) was the primary reaction that consumed OH radical and promoted the formation of NH2 radical. Free radical concentrations decreased with increasing pressure and temperature, while the change rate of free radical ROP accelerated with increasing pressure. In addition to nitrogen and water, the partial products were mainly nitric oxide at the LFL concentrations, while at the UFL concentrations were mainly hydrogen.

Random Responses of Shield Tunnel to New Tunnel Undercrossing Considering Spatial Variability of Soil Elastic Modulus

This paper investigates the effect of spatial variability of soil elastic modulus on the longitudinal responses of the existing shield tunnel to the new tunnel undercrossing using a random two-stage analysis method (RTSAM). The Timoshenko–Winkler-based deterministic method considering longitudinal variation in the subgrade reaction coefficient and the random field of the soil elastic modulus discretized by the Karhunen–Loeve expansion method are combined to establish the RTSAM. Then, the proposed RTSAM is applied to carry out a random analysis based on an actual engineering case. Results show that the increases in the scale of fluctuation and the coefficient of variation of the soil elastic modulus lead to higher variabilities of tunnel responses. A decreasing pillar depth and mean value of the soil elastic modulus and an increasing skew angle strengthen the effect of the spatial variability of the soil elastic modulus on tunnel responses. The variabilities of tunnel responses under the random field of the soil elastic modulus are overestimated by the Euler–Bernoulli beam model. The results of this study provide references for the uncertainty analysis of the new tunneling-induced responses of the existing tunnel under the random field of soil properties.

Highly Selective Electroreduction of Nitrobenzene to Aniline by Co-Doped 1T-MoS2.

The selective electrocatalytic reduction of nitrobenzene (NB) to aniline demands a desirable cathodic catalyst to overcome the challenges of the competing hydrogen evolution reaction (HER), a higher overpotential, and a lower selectivity. Here, we deposit Co-doped 1T MoS2 on Ti mesh by the solvothermal method with different doping percentages of Co as x % Co-MoS2 (where x = 3, 5, 8, 10, and 12%). Because of the lowest overpotential, lower charge-transfer resistance, strong suppression of the competing HER, and higher electrochemical surface area, 8% Co-MoS2 achieves 94% selectivity of aniline with 54% faradaic efficiency. The reduction process follows first-order dynamics with a reaction coefficient of 0.5 h-1. Besides, 8% Co-MoS2 is highly stable and retains 81% selectivity even after 8 cycles. Mechanistic studies showed that the selective and exothermic adsorption of the nitro group at x % Co-MoS2 leads to a higher rate of NB reduction and higher selectivity of aniline. The aniline product is successfully removed from the solution by polymerization at FTO. This study signifies the impact of doping metal atoms in tuning the electronic arrangement of 1T-MoS2 for the facilitation of organic transformations.

Analysis of the influence of the metal wheel radial stiffness on traction characteristics

BACKGROUND: The traction characteristic of a wheel mover depends both on its type and rigidity properties, and on the physico-mechanical soil properties. The combined use of the discrete element method to describe the soil and the finite element method to model the wheel makes it possible to specify and expand the existing empirical models of the interaction of the mover with the ground. The application of this method will reduce the amount of full-scale testing required to verify the interaction model. AIMS: Development the traction characteristic of a metal wheel by varying its design parameters. METHODS: To develop a mathematical model of a metal wheel and determine traction characteristics, numerical methods of discrete and finite elements are used. RESULTS: In this paper, a metal wheel mathematical model with ability to vary the thickness of the elastic sidewall was developed. Radial stiffness characteristics were obtained for three wheel samples. The developed mathematical model of the interaction of a wheel mover with a ground is based on the application of discrete and finite element methods. In this paper, a proportional controller was used to application of forces to the wheel mover. The dependences of the longitudinal reaction coefficient on the slip coefficient were obtained and a comparative analysis of the radial stiffness influence on traction characteristics was carried out. CONCLUSIONS: The combined application of the discrete and finite element methods will make it possible to determine the traction characteristics of the movers of various designs when interacting with a deformable soil and to evaluate the influence of its design parameters on it.

Investigating the influence of excavating a tunnel undercrossing an existing tunnel at zero distance.

In urban areas with limited underground space, the new tunnel construction introduces additional loads and displacements to existing tunnels, raising serious safety concerns. These concerns become particularly pronounced in the case of closely undercrossing excavation at zero-distance. The conventional elastic foundation beam model, which assumes constant reaction coefficients for the subgrade, fails to account for foundation loss. In this study, the existing tunnel is modeled as an Euler-Bernoulli beam supported by the Pasternak elastic foundation, and the foundation loss caused by zero-distance undercrossing excavations is considered. Furthermore, an analytical solution is proposed to evaluate the mechanical response in segments, by establishing governing differential equations and boundary conditions for the excavation and neutral zones, and underpinning loads are also considered. The analytical solution is validated in two case studies. Finally, a parametric analysis is performed to explore the influence of various parameters on the mechanical response of the existing tunnel.

Weaknesses and Strengths of the Winkler Method in Designing Foundations

The reaction between the foundation and the soil below it is one of the important issues in civil engineering, and this factor has a significant effect on the behavior of the structure. In this article, first, the basic principles of this method and the simplifications introduced in it are introduced, and then the concept of the most important input parameter of this model, the substrate reaction coefficient, determination relationships, and factors affecting it are discussed. The main goal of this article is to understand the concept of the Winkler method and the bed reaction coefficient so that engineers can choose this model with full knowledge of its weaknesses and strengths and the theories used in it. Also, by studying the factors affecting the bed reaction coefficient, it is possible to estimate More realistic values should be provided so that the results of this method are more correct and accurate.

Thermal and solutal transport by Cattaneo-Christov model for the magnetohydrodynamic Williamson fluid with joule heating and heat source/sink

This article scrutinizes the 2-dimensional and boundary layer flow of magnetohydrodynamic Williamson fluid flowing on a stretchable surface with variable viscosity. The thermal and solutal rates are examined through the Cattaneo-Christov model with Joule heating, heat source/sink, and chemical reaction. The authors are motivated to conduct this study because of its practical and scientific significance in various processes, including polymer processing, textile industries, food industries, solar energy, biomedical science, wind turbine blades, oil spill clean-up, metal rolling, and forging. With the mentioned assumptions, the partial differential equations are achieved by using the basic governing laws, including momentum law, energy law, and concentration law. This non-linear system of equations is transmuted into ordinary differential equations by taking similarity transformations. The main novelty behind the conduction of this work is the numerical technique, namely the ‘Adams-Milne (Predictor-Corrector)’ method along with the Runge-Kutta technique on Matlab software, which has not previously been studied by any researcher in the literature. The analytical solution of the determined equations is not possible due to their highly non-linear nature; therefore the multistep numerical method namely the ‘Adams-Milne (Predictor-Corrector)’ method, along with the Runge-Kutta technique is used to determine the numerical results. The outcomes are noted due to numerous parameters for velocity, temperature, and concentration profiles. The explanation of graphical and numerical results is discussed here. The graphical impression of the Williamson parameter reveals that the velocity and temperature curves diminish for higher inputs of this parameter. The movement of fluid shows the declining behavior for the Hartmann number and viscosity parameter. The solutal and thermal findings due to Cattaneo-Christov heat and mass relaxation coefficients mark the reducing behaviour in respective field. The rise in reaction coefficient decreases the mass distribution. The analyses of comparison of results are also presented here.

Dimensionless Reaction Coefficients for Embedded Piled Raft Foundations in Soft Clays under Vertical Loads

Dimensionless Reaction Coefficients for Embedded Piled Raft Foundations in Soft Clays under Vertical Loads

A scaling rule for power output of salt hydrate tablets for thermochemical energy storage

Salt hydrates are thermochemical materials capable of storing and releasing heat through reversible reaction with water vapor. In a heat battery, salt hydrate tablets of millimeter size are necessary to ensure a sufficient permeability of the packed bed. A profound understanding of the hydration process of these tablets is required to improve their kinetic performance. In this study we show that the hydration timescale of salt tablets is transport limited and that it depends primarily on the porosity and on the driving force (Δp). From gravimetric measurements done on SrBr2·6H2O and CaC2O4 we derived the intrinsic reaction and effective diffusion coefficients (k and Deff) and found that they validate a front-diffusion limited hydration hypothesis. In particular, the obtained Deff values (0.8–4.5 mm2 s−1) only depend on the tablets' porosities. Based on these parameters, we calculated the second Damköhler number (DaII) and proved that many other hydration reactions are diffusion limited. In the case of identical structures, the power output is therefore controlled only by the driving force. Its variation could be predicted by calculation of a so-called power scaling factor (Λ) for a selection of salts. This power scaling factor depends on the enthalpy (ΔH) and entropy (ΔS) of the reaction. For a temperature output of 40 °C and at 12 mbar most hydration reactions fall in the interval 0<Λ<30 and Λ exceeds 30 only in very few cases. This parameter establishes therefore another important constraint to the selection of the most ideal salt. Suitable strategies to circumvent the diffusion limitation will lead to the development of next generation salt hydrate tablets for thermochemical energy storage.

Investigation on deformation behavior and bearing capacity of a segmental ring based on the horizontal convergence

AbstractIn this study, a refined numerical model, which contains the detailed geometric construction of the longitudinal joints, is established to investigate the bearing performance of the segmental ring based on the horizontal convergence. Firstly, the model is verified by comparing it with the reported results of a documented full‐scale model test. Then, according to the load‐structure method, this numerical model is employed to investigate the deformation behavior and bearing capacity of the segmental ring. Moreover, the effects of the coefficient of lateral pressure and subgrade reaction are extensively taken into consideration through comprehensive numerical analyses. According to the numerical results, a bilinear model is proposed to describe the relation between the convergent displacement and the stratum pressure, which could be used to preliminarily estimate the convergence after the completion of tunnel construction. Otherwise, the development of structural defects, such as the joint opening and the water leakage, has close association with the horizontal convergence. Therefore, a simple evaluation method for tunnel structure safety assessment is proposed using horizontal convergence deformation as an indicator to predict the tunnel service state. Since this indicator is easy to obtain during the tunnel operation, it is convenient for the engineers to assess the bearing capacity of the segmental ring and the service state of the tunnel structure quickly.

Arrhenius activation energy and thermal radiation effects on oscillatory heat-mass transfer of Darcy Forchheimer nanofluid along heat generating cone

The main goal of present research is to illustrate the frequency and amplitude behavior of heat and mass transfer of Darcy Forchheimer nanofluid flow with Arrhenius activation energy and thermal radiation effects. The impact of heat generation and chemical reaction on Darcy Forchheimer nanofluid along vertical porous cone is investigated to improve heating durability of thermodynamic systems in this research. The governing mathematical model is moderated in suitable format to construct physical coefficients. The oscillating stokes and primitive coefficients are used to differentiate the model into oscillating and steady forms. The Gaussian elimination and implicit finite difference techniques are used to address the numerical findings. To construct pertinent algorithm in FORTRAN system, the primitive-type variables are used on steady and oscillating models with first law of thermodynamics, nanoparticles and heat generation. The results under defined conditions are reported in numerical and graphical sequence through Tec-plot 360. It is found that the amplitude of surface temperature increases as heat generation increases because heat generation improves the excessive thermal transport. It is depicted that the Darcy-Forchheimer porous material decreases the fluid temperature. It is found that amplitude of mass transfer increases as activation energy and chemical reaction coefficient increases. The oscillating frequency of heat and mass transfer increases as Prandtl number increases. The current mechanism of mass and heat transfer of nanofluid has several uses in mineralogy, cutting tools, lubricating oils, machining operations, heat exchangers, coating sheets, petroleum drilling and cooling of metallic cones.

Improved Approach for ab Initio Calculations of Rate Coefficients for Secondary Reactions in Acrylate Free-Radical Polymerization.

Secondary reactions in radical polymerization pose a challenge when creating kinetic models for predicting polymer structures. Despite the high impact of these reactions in the polymer structure, their effects are difficult to isolate and measure to produce kinetic data. To this end, we used solvation-corrected M06-2X/6-311+G(d,p) ab initio calculations to predict a complete and consistent data set of intrinsic rate coefficients of the secondary reactions in acrylate radical polymerization, including backbiting, β-scission, radical migration, macromonomer propagation, mid-chain radical propagation, chain transfer to monomer and chain transfer to polymer. Two new approaches towards computationally predicting rate coefficients for secondary reactions are proposed: (i) explicit accounting for all possible enantiomers for reactions involving optically active centers; (ii) imposing reduced flexibility if the reaction center is in the middle of the polymer chain. The accuracy and reliability of the ab initio predictions were benchmarked against experimental data via kinetic Monte Carlo simulations under three sufficiently different experimental conditions: a high-frequency modulated polymerization process in the transient regime, a low-frequency modulated process in the sliding regime at both low and high temperatures and a degradation process in the absence of free monomers. The complete and consistent ab initio data set compiled in this work predicts a good agreement when benchmarked via kMC simulations against experimental data, which is a technique never used before for computational chemistry. The simulation results show that these two newly proposed approaches are promising for bridging the gap between experimental and computational chemistry methods in polymer reaction engineering.

Atmospheric chemistry of trifluorodicarbonyls initiated by Cl atoms: Reactivity trends, mechanism, and acid formation yields

Rate coefficients of the gas-phase reactions of Cl atoms with a series of fluorinated diketones (FDKs): CF3C(O)CH2C(O)CH3 (TFP), CF3C(O)CH2C(O)CH2CH3 (TFH) and CF3C(O)CH2C(O)CH(CH3)2 (TFMH), have been measured at (298 ± 2) K and under atmospheric pressure. The experiments were performed using the relative-rate method with a GC-FID detection system. From different determinations and references used, the following rate coefficients were obtained (in cm3/(molecule·sec)): k4(TFP + Cl) = (1.75 ± 0.21) × 10−10, k5(TFH + Cl) = (2.05 ± 0.23) × 10−10, k6(TFMH + Cl) = (2.71 ± 0.34) × 10−10. Reactivity trends of FDKs were discussed and Free Energy Relationships analysis was developed. The expression lgkOH = 1.68 lgkCl + 5.71 was obtained for the reactivity of the studied FDKs together with similar unsaturated VOCs with Cl and OH radicals Additionally, acetic acid (CH3C(O)OH) and trifluoroacetic acid (CF3C(O)OH) were positively identified and quantified as degradation products using in situ FTIR spectroscopy. According to the identified products, atmospheric chemical mechanisms were proposed. The atmospheric implications of the studied reactions were assessed by the estimation of the tropospheric lifetimes of TFP, TFH, and TFMH concerning their reaction with Cl atoms to be 48, 41, and 31 hours, respectively. The relatively short residence in the atmosphere of the fluorocarbons studied will have a local/regional impact with restricted transport. Global warming potential (GWP(20yr)) calculated for the studied fluoro diketones were 0.014, 0.003 and 0.001 for TFP, TFH and TFMH, respectively with a negligible contribution to the greenhouse effect.

Influence of updated isoprene oxidation mechanisms on the formation of intermediate and secondary products in MCM v3.3.1

In this study, we developed an observation based photochemical box model with the measurement data collected at a suburban site (i.e., the Xianghe, XH site) of the Beijing-Tianjin-Hebei (BTH) region and the latest version of the Master Chemical Mechanism (MCM v3.3.1), which newly incorporated 498 reaction for the additional 155 species with the oxidation of isoprene by the OH radical. The influence of updated isoprene degradation on the radical budgets, formation of intermediate and secondary products by comparing the simulation results in the original version (MCM v3.2) was firstly analyzed to estimate whether the updates of precursors could influence the model performance on its evolution pathways and related products. The results demonstrated that though the input of isoprene could significantly decrease or increase the concentrations of OH and HO2 radicals in the model simulation, respectively, the difference in the simulated concentrations of these radicals with isoprene oxidation before and after the updates was not statistically significant. For intermediate products, the simulated concentrations of formaldehyde and methacrolein (MACR) did not significantly alter before and after the updates, while the abundance of methyl vinyl ketone (MVK) reduced obviously (the maximum reduction of 31%) due to lower reaction coefficient between ISOPBO2 and NO and the lower branching ratios caused by the newly added pathways involving CISOPA and TISOPA in the updated scheme. On the other hand, the simulation concentrations of acrolein (ACR), glyoxal (Gly) and methylglyoxal (Mgly) increased significantly after the model updates. The dominant pathway for the increment of ACR was the decomposition of CH2CHCH2O produced by PE4E2CO, while those of Gly and Mgly were associated with radicals of C537O and PACLOOA that were both from the new intermediate radical of CISOPC. In addition, 39 isoprene oxidation products among the 155 new added species were identified to partition in the formation of secondary organic aerosol (SOA), which were coupled in the gas-particle partitioning module to optimize the formation of SOA, contributing 1.15 μg m−3 to the increase of SOA mean concentration. The updates of isoprene degradation further resulted in the significant change for its sensitivity in SOA formation, making it as the secondary important SOA precursor at the XH site. Last but not the least, the influence on photochemical ozone formation related to updates of isoprene degradation was ignorable. Overall, the above results confirmed the insufficient description of the degradation of precursors indeed limited the simulation of the intermediate and secondary products, highlighting the needs of exploring and parameterizing the precursor degradation processes for better understanding of their behaviors and SOA formation in the atmosphere.

Mixed convection flow in a square lid-driven cavity subject to inclined magnetic field with highly accurate wavelet-homotopy solutions

Numerical studies of flow in square enclosures attain great interest due to their wide applications in engineering, such as in the meteorology, navigation, mechanology and mining, etc. In this paper, the solutions are obtained to the square lid driven cavity describing classical mixed convection in the presence of an inclined magnetic field, chemical radiation and heat absorption/generation. The problem is mathematically reduced into Navier-Stokes equations. The Coiflet wavelet homotopy approach, a newly suggested computational technique, is then used to solve these nonlinear partial differential equations with their non-homogeneous boundary conditions. The numerical solutions for streamlines, isotherms, iso-concentrations contours, Nusselt number are carefully determined. The solutions so obtained are analyzed through various plots to demonstrate the effects of several physical parameters such as Reynolds numbers (Re), Richardson number (Ri), Grashof number (Gr), Hartman number (Ha), thermal radiation parameter (NR), chemical reaction coefficient (K), heat generation/absorption coefficient (Qh), the angle of inclination of magnetic field (γ), slipping parameter (λ) and Schmidt number (Sc) and their physical insights are also reported. Rigid comparison of with previous studies shows excellent computational effectiveness of newly proposed method. Additionally, according to the results, our recently proposed approach has superior characteristics and strong nonlinear processing capabilities, which render it more appropriate than the Coiflet wavelet analysis method and the traditional homotopy analysis method for tackling complex nonlinear problems.

Analytical solution for buried pipeline deformation induced by normal and reverse fault considering structural joint influence

AbstractPrevious studies take less account of analytical solution analysis for buried pipeline under the action of active fault. Furthermore, current theoretical studies of fault‐pipeline interactions generally treat the structure as continuous pipeline, with less attention given to the effect of joints. This paper provides an analytical method to estimate the deformation and internal force of jointed pipelines under normal and reverse fault. By introducing the simplified soil deformation model and error function, the soil greenfield deformation curves under the influence of normal and reverse fault are obtained. Considering the interaction between the pipeline structure and the disturbed soil, the two‐parameter Pasternak foundation model is adopted to analyze the forces on pipeline infinitesimal elements. Then, the mechanical response of the jointed pipeline structure due to the fault additional load is solved by finite difference method. The accuracy of the presented analytical solution is verified by comparisons with observed data of model test and 3D numerical simulation results. Finally, the parametric analyses are performed to estimate the influence for the characteristics of the foundation, fault and joint, including subgrade shear stiffness, subgrade reaction coefficient, fault dip, joint rotational stiffness, joint spacing, and intersection of fault and pipeline.