Successive Linearization Method Research Articles

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

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

Mixed convective viscous dissipative flow of Casson hybrid nanofluid with variable thermal conductivity at the stagnation zone of a rotating sphere

AbstractMixed convection flows across the revolving bodies have eminent applications in science and technology, such as fibre coating, polymer deposition, centrifugal blood pumps, rotatory machinery, and so forth. In the current work, magnetohydrodynamic (MHD) flow and heat transfer characteristics of Casson hybrid nanofluid (Ag/MgO as nanoparticles) over the rotating sphere at the stagnation zone are being studied. Moreover, an analysis of heat transmission is conducted by considering the influence of thermal radiation, temperature‐dependent thermal conductivity, magnetic field, and viscous dissipation. The relevant partial differential equations are reformed into ordinary differential equations by appropriate transformations, which are solved using the successive linearization method (SLM). The thermal field, velocity components in x and z directions, heat transfer rate, and skin friction coefficient are computed for various physical quantities like rotation parameter mixed convection parameter, radiation parameter, Eckert number, Casson parameter, magnetic parameter, variable thermal conductivity parameter, and so forth. The current findings align well with the literature in a limiting sense. Thermal enhancement in hybrid nanofluid is observed for the viscous dissipation parameter (Ec), thermal conductivity parameter (), and radiation parameter (Rd). The degree of heat transfer rises from 12.8% to 20% when the Casson parameter's value () increases. Also, a decrease of approximately 33% is depicted between the peak values of the velocity magnitude with an increase in rotation parameter.

Numerical Study for MHD Flow of an Oldroyd-B Fluid Over a Stretching Sheet in the Presence of Thermal Radiation with Soret and Dufour Effects

This paper investigates the impact of Soret and Dufour's MHD flow of an Oldroyd-B fluid over a stretching sheet in the presence of thermal radiation. By a similarity transformation, the controlling partial differential equations are transformed into a system of nonlinear ordinary differential equations. Using the successive linearization method (SLM), the linear system is solved. A determination and discussion of the impacts of specific fluid parameters on the temperature, concentration distribution, and velocity are presented. As the magnetic field increases, we observe that the temperature and concentration profiles rise, while the velocity profile falls. In addition, increases in the Dufour and Soret levels will also result in an improvement in the temperature and concentration distribution. The validity of the acquired results is tested by comparing them to previously published works, with particular attention paid to the accuracy and convergence of the solution.

Modeling the hydromagnetic transient three-dimensional stagnation point flow of a couple stress Casson fluid over a bi-directional stretching sheet

A numerical study is performed to examine the magnetohydrodynamic effects on the transient three-dimensional stagnation point flow of a Casson fluid along a bi-directional stretching sheet. The physical model of the flow includes a sheet which is stretched in both the tangential directions and is thus called “bi-directional stretching”. The heat transfer mechanism includes the influences of space- and time-dependent non-uniform heat generation/absorption, as well as dissipation due to viscosity. The mathematical modeling of the problem involves the constitution of a set of coupled nonlinear boundary layer equations, together with suitable boundary conditions. The mathematical model thus developed is then subjected to suitable similarity transformations to arrive at a set of ordinary differential equations, which were then treated with the successive linearization method (SLM) to obtain approximate solutions for the velocity and temperature fields. A parametric study is carried out, and the results are discussed and presented graphically to analyze the behavior of the primary and secondary velocity distributions, as well as fluid temperature, along with significant physical quantities such as skin friction and Nusselt number for various values of the nondimensional parameters. Multiple quadratic regression analysis is also carried out to investigate the significance of parameters and to estimate the skin-friction and heat transfer coefficients.

Determining a parabolic system by boundary observation of its non-negative solutions with biological applications

In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions represent certain probability densities in different contexts. We innovate the successive linearisation method by further developing a high-order variation scheme which can both ensure the positivity of the solutions and effectively tackle the nonlinear inverse problem. This enables us to establish several novel unique identifiability results for the inverse problem in a rather general setup. For a theoretical perspective, our study addresses an important topic in partial differential equation (PDE) analysis on how to characterise the function spaces generated by the products of non-positive solutions of parabolic PDEs. As a typical and practically interesting application, we apply our general results to inverse problems for ecological population models, where the positive solutions signify the population densities.

Micropolar flow and heat transfer within a permeable channel using the successive linearization method

Abstract This research investigates the flow of micropolar fluid and heat transfer through a permeable channel using the successive linearization method (SLM). The study considers parameters such as coupling, spin-gradient viscosity, and micro-inertia density. The partial differential equations involved are transformed into a system of ordinary differential equations using similarity variables. The resulting nonlinear equations are solved using the SLM technique, and their accuracy and computational efficiency are validated through comparative analysis with previous results. The study shows that increasing the parameters of coupling and spin-gradient viscosity has a positive impact on fluid flow, microrotation, heat transfer, and mass transport, as demonstrated by the increased dimensionless profiles. Conversely, an increase in the micro-inertia density parameter leads to a reduction in these profiles. This decrease can be attributed to the increase in the micro-inertia effect of fluid flow and heat transfer, resulting in a decrease in convection and a change in the flow pattern in the channel. Additionally, higher Reynolds numbers are associated with decreases in velocity, microrotation, temperature, and concentration distribution. This implies a reduction in fluid flow intensity, weaker heat transfer, and decreased mass transport. However, an increased Peclet number results in increased fluid temperature and concentration profiles, indicating enhanced thermal convection and mass transport. These findings have significant implications for applications involving micropolar fluids, such as lubrication systems, blood flow, microchannels, and filtration systems.

MHD Boundary Layer Flow due to an Exponentially Stretching Surface Through Porous Medium with Radiation Effect and Chemical Reaction

In this study, the numerical solutions for an exponentially stretching sheet with radiation effects, chemical reaction and a heat sink is obtained for the problem of MHD boundary layer flow. By using similarity transformation, the PDEs ruling system is converted into an ODEs system. The resulting nonlinear equations governing the flow problem are numerically solved by a successive linearization method (SLM) using MATLAB software. The significance of this paper is to show and compare the results of solving velocity, temperature, and concentration equations in the existence of changes through SLM for presenting it as appropriate and accurate method for solving nonlinear differential equations. Tables with the numerical data are created for comparison and displayed graphically. Analysis and studies of the effects of different parameters are conducted. The numerical values for the local skin friction coefficient, local Sherwood number, and local Nusselt number are tabulated and explained. The study demonstrates that different parameters have a substantial impact on the fluid flow profiles. It was noted that the concentration patterns were impacted by the reaction rate parameter. In addition, it was found that as the magnetic and radiation parameters increase in value, the local heat transfer rate at the surface decreases.

Analyses of entropy generation and Hall influence in the Cattaneo–Christov double diffusive radiative Non-Darcy flow of a Casson nanofluid within rotating disks

The present research work interprets the entropy generation in the magnetohydrodynamic multiple slip flow of Casson nanofluid initiated due to stretching and coaxially rotating surfaces of two disks inside a non-Darcy porous medium under the dominance of the diacritic Hall current and heat generation. The energy field is explored by incorporating the consequences of distinctive thermal radiation, viscous dissipation, and Joule heating. The present study overcomes the barrier of heat and mass transport by annexing Cattaneo–Christov double diffusion effects. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with multiple slip boundary conditions. A compatible similarity transformation comprised in the current study is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via dispensing the successive linearization method. The present article deals with an in-depth exploration of diagnostic flow parameters’ attributes against the flow field and efficient physical quantities with the help of distinctive graphs and tables. As per regression analysis, the maximum relative error for the regression model on the skin friction coefficient in the radial direction ranging from .0097236 to .017225% is less than that of the other physical quantities. Besides, augmenting the thermophoretic diffusion boosts diluting the concentration of nanoparticles.

Solution of boundary eigenvalue problems and IBVP involving a system of PDEs using the successive linearization method

AbstractThe paper illustrates a numerical technique to solve a system of three partial differential equations that govern the problem of Rayleigh‐Bénard‐Brinkman convection in a two‐dimensional porous rectangular box. As a result of linear and weakly nonlinear stability analyses of the system a boundary eigenvalue problem (BEVP) and an initial boundary value problem (IBVP) arise. Spatial information on the periodicity of the convection cells is first used in the system of PDEs to make it possible for the successive linearization method (SLM) to be applied. The resulting much‐simplified versions of BEVP and the IVP are then solved by direct and time multi‐stepping versions of SLM, respectively. The SLM solution of the BEVP is compared with that obtained through MATLAB routine bvp4c and the multi‐stepping‐SLM solution of the IVP is validated with that of the Runge‐Kutta‐Fehlberg (RKF45) method (using MATLAB routine ode45). The present numerical technique is found to have quadratic convergence for any desired accuracy.

THE CONVECTIVE FLOW OF MAXWELL FLUID DRIVEN BY TWO ROTATING AND SPINNING DISKS

The present work addresses the axisymmetric flow of Maxwell fluid between two stretchable and rotating disks with porous regime. The influence of velocity slip and convective heat transfer are considered to govern the flow. The energy equation is modeled using Cattaneo-Christov heat flux model. The resulting mass, momentum and energy PDE’s are converted to ODE’s by using the Von Karman similarity transformations. Successive linearization method is implemented for numerical solution. The tangential velocity of the fluid increases with the rotating speed of the disks. The enhancement in the convective heat transfer of lower disc results in the rise of temperature profiles whereas temperature falls with the rise in Biot number of the upper disk.

Two-stage stochastic decentralized low-carbon economic dispatch of integrated electricity-gas networks

To achieve low-carbon operation optimization of integrated electricity gas network (IEGN) system with uncertainty, a two-stage stochastic decentralized low-carbon economic scheduling model and its solution method for multi-region interconnection is proposed. Firstly, an IEGN operation cost model considering the stepped carbon emission cost and the benefits of P2G's participation in carbon market transactions is constructed, considering demand-side management (DSM) with user satisfaction and degree of regulation. Secondly, multi-region interconnection is served to overcome single-region space-time limitations with the multi-energy flow, regional decoupling is realized by copying multi-region IEGN boundary nodes, and the scenario method is used to quantify the output uncertainty of IEGN. Hence, a two-stage stochastic optimal scheduling model of multi-region IEGN is established. Then, an improved successive linearization method is proposed for the non-convex transformation. Considering the decentralized autonomy and information privacy of different decision-makers, a decentralized optimization model is established, and the synchronous alternating direction multiplier method (synchronous-ADMM) based on nested improved successive linearization is introduced for the iterative solution. Finally, the feasibility and superiority of the proposed model and algorithm are verified by comparing and analyzing the simulation results of multi-region IEGN under different scenarios and scheduling strategies.

Regression analysis and features of negative activation energy for MHD nanofluid flow model: A comparative study

This article elucidates the impact of activation energy on magnetohydrodynamic (MHD) stagnation point nanofluid flow over a slippery surface in a porous regime with thermophoretic and Brownian diffusions. Negative activation energy is scarce in practice, but the impact of negative activation energy could not be neglected as it is noticed in chemical processes. The rate of some Arrhenius-compliant reactions is retarded by increasing the temperature and is therefore associated with negative activation energies, such as exothermic binding of urea or water. In some processes, the temperature dependence of the pressure-induced unfolding and the urea-induced unfolding of proteins at ambient pressure give negative activation energies. The present mathematical model is solved with successive linearization method (a spectral technique). A comparison of results is made for negative and positive values of activation energy. Apart from it, the quadratic multiple regression model is discussed briefly and explained with bar diagrams. It is observed that with rise in unsteadiness parameter from 0 to 1 (taking positive activation energy), skin friction and Sherwood number are increased by 9.36% and 19% respectively, and Nusselt number is decreased by 26%. However, for negative activation energy, 9.36% and 112% enhancement is observed in skin friction and Sherwood number, respectively.

Features of activation energy for a flow with microrotation near stagnation region and unbounded domain : a spectral simulation

This article is motivated to find the impact of various flow controlling parameters such as viscous dissipation, negative and positive values of activation energy on MHD stagnation point micropolar nanofluid flow over a surface. However, negative activation energy is scarce in practice, but the impact of negative values of activation energy could not be neglected as seen in chemical processes. The present mathematical model is solved with successive linearization method (a spectral technique). The velocity, angular velocity, temperature and concentration profiles are drawn by varying flow controlling parameters. The bar diagrams for skin friction, Nusselt number, Sherwood number and couple stress are also displayed. Results indicate that the activation energy boosts the concentration profile up. The negative values of activation energy have higher impact on concentration curves compared to positive values. Arrhenius function decays as activation energy enlarges. This eventually promotes the generative chemical reaction due to which concentration rises. By varying thermophoretic parameter from 0.1 to 0.3, 88.65% and 8.34% enhancement is captured in heat transfer and mass transfer respectively.

Application of Successive Linearisation Method on Mixed Convection Boundary Layer Flow of Nanofluid from an Exponentially Stretching Surface with Magnetic Field Effect

The this paper, we investigate the heat and mass transfer in MHD nanofluid flow from an exponentially stretching surface numerically. The partial governing equations are transformed into a system of ordinary differential equations and then solved using a Successive Linearisation Method (SLM). The velocity, temperature and concentration profiles are shown graphically for various flow parameters and the physical quantities such as Skin-friction, Nusselt and Sherwood numbers are computed for different values of governing parameters. It is was observed from results that the SLM provides highly numerical solution and converges rapidly for nonlinear differential equations. It is concluded that an increase in the value of magnetic field parameter reduces the velocity field while the opposite trend is observed for temperature and concentration distributions. An increase in the value of nanoparticle volume fractions enhances the velocity field and the temperature distributions while the concentration distribution reduces.

Numerical solution for MHD flow and heat transfer of Maxwell fluid over a stretching sheet

In this article, the numerical solutions for the flow of heat transfer for an incompressible Maxwell fluid on a stretching sheet channel are presented in this study. By applying appropriate transformations, the system of governing partial differential equations is transformed into a system of ordinary differential equations. A successive linearization method (SLM) is used to describe and solve the resulting nonlinear equations numerically using MATLAB software. The main goal of this paper is to compare the results of solving the velocity and temperature equations in the presence of β1 changes through SLM for introducing it as a precise and appropriate method for solving nonlinear differential equations. Tables with the numerical results are created for comparison. This contrast is important because it shows how precisely the successive linearization method can resolve a set of nonlinear differential equations. Non-Newtonian parameters on the flow field, like mixed convection, Hartman, Deborah, and Prandtl numbers, are explored and illustrated graphically. Apart from that, a great deal of agreement has been seen between the current results and the published data that have been evaluated and compared in a limited way.

Numerical simulation and regression analysis of MHD dissipative and radiative flow of a Casson nanofluid with Hall effects

The magnetohydrodynamic (MHD) flow of Casson nanofluid has several applications in engineering and medical processes. The present research work is performed to examine the unsteady viscous dissipative and radiative flow of a Casson nanofluid over a stretching sheet under the influence of a transverse magnetic field with a view to highlight the impact of Hall current. The mathematical model comprising of nonlinear coupled PDE is transformed into a set of coupled ODEs using appropriate similarity transformation. The reduced mathematical model in a similar form is then solved by adopting the successive linearization method (SLM). The residual analysis is used to validate the solutions. A parametric study is performed to inquire about the impacts of Hall current, nonlinear thermal radiation, viscous dissipation, and other pertinent flow parameters such as temperature ratio, Brownian movement, thermophoresis on the nanofluid velocities, temperature, and concentration. The effects of pertinent flow parameters are also examined on the skin-friction coefficients, Nusselt number, and Sherwood number. A quadratic regression analysis is presented to estimate the skin-friction coefficient and Nusselt number for different values of effecting parameters. Results reveal that the increasing values of Casson parameter decrease the fluid velocity and temperature, whereas a converse trend is detected in concentration profile, rate of heat transfer and mass transfer.

Non‐linear steady‐state data reconciliation: Theoretical perspective and practical scenarios

AbstractData reconciliation (DR) is one of the primary error handling methods to reduce measurement errors in industries that may otherwise cause misleading information about the plant. In this article, the mathematical aspects of measurement errors and their treatment by DR are discussed in detail. The flaws in the existing DR methods have been identified and re‐investigated. More importantly, the feasibility and health check‐up of the DR problem have been discussed. The primary objective of the work is to develop a DR code based on the observations made in the present study, which involves DR solutions by both successive linearization (SL) and sequential quadratic programming (SQP) schemes. Benchmarking of the code with standard cases showed its wider suitability in solving DR problems. The algebraic SL method was found suitable for proper data health check‐ups and reliable solutions, whereas SQP was robust. The developed code was tested successfully for a chemical plant as well.

Computational Treatment of Magnetohydrodynamic Micropolar Fluid Flow Through Porous Medium Over an Exponentially Stretching Sheet with Heat Sink and Chemical Reaction Effects

The purpose of this research is to look into the magnetohydrodynamic boundary layer flow of Maxwell fluid across an exponentially stretching sheet with chemical reaction, and radiation impacts, that involves a heat sink. The PDE governing equation is converted to an ODE governing system. A Successive Linearization Method is then used to solve the system numerically. Graphically, the numerical outputs of, temperature, concentration profiles, and velocity are displayed. The results of several parameters are explored and examined. The numerical outcomes for the skin friction coefficient, local Nusselt number, Deborah number, local Sherwood number, and porosity are reported and analyzed. Based on the results, many characteristics have a considerable effect on fluid flow profiles. The reaction rate parameter had a significant impact on the concentration profile and the thickness of the boundary layer dropped as the reaction rate parameter was increased. The analyses’ findings were compared to those of previous studies and found to be in great agreement.

Quadratic convection in a power-law fluid with activation energy and suction/injection effects

Current research demonstrates the effects of activation energy and quadratic convection on the non-Newtonian power-law fluid flow through an inclined permeable plate. In addition, the fluid’s heat transfer is carefully investigated while taking convective boundary conditions and thermal radiation into account. Also, mass transfer between the flow and the inclined plate was investigated for binary chemical reactions. By appropriate transformations, governing fluid flow equations are changed into the dimensionless form. Numerical solution of this system of equations is obtained by both the local non-similarity method and the successive linearisation method. The effect of emerging parameters on the flow and physical quantities are examined with Biot number ( B i ), activation energy coefficient ( E ), the chemical reaction parameter ( M ), quadratic convection parameters ( α 1 , α 2 ), inclination angle ( Ω ), the suction/injection parameter ( f w ) and the radiation parameter ( R d ). Further, the rate of mass and heat transfer are compared for all the instances of linear and quadratic convective flows. Power-law fluids concentration is increased with activation energy, while it diminishes with chemical reaction. The thickness of thermal boundary layer is considerably enhanced by both Biot number and radiation parameters. The thermal and solutal rates are increasing functions of quadratic convection parameters.

Application of Successive Linearization Method on Steady Radial Flow of Nanofluids Between Inclined Plane Walls

The present work purveys the heat transfer enhancement in the steady two-dimensional viscous incompressible radial flow of Au-Water and Ag-Water nanofluids in the presence of MHD effect between the stationary convergent/divergent channel walls which are permitted to stretch or shrink. A uniform magnetic field is applied. The governing partial differential equations of the present physics and their appropriate boundary conditions are initially cast into dimensionless forms to reduce into the ordinary differential equations. The resulting equations thus formed are then solved by adopting the Successive Linearization Method (SLM) to get the accurate numerical solution. Solution errors and residual norms are analyzed to elaborate the convergence and accuracy of the numerical solution. The behavior of thermal conductivity of both types of nanofluids is examined for converging channel and diverging channel cases under the uniform magnetic field effect. The present results are validated with favorable comparisons with previously published results as the current investigations’ unique cases. A parametric study of the governing parameters, namely the magnetic field strength parameter, Reynolds number, angle of inclination, and the stretching parameter on the non-dimensional velocity and temperature, is conducted. Analysis discloses that the profiles of the flow are largely impacted by the physical parameters. It is noticed that the magnetic parameter deploys an enhancing influence on fluid velocity profile as well as heat transfer rate, and the effect of the magnetic field is less pronounced on Au-water nanofluid than that of the Ag-water nanofluid. The fluid velocity increases as the values of Re increase for both the nanofluids in the convergent channel and decreases in the case of the divergent channel. Fluid temperature increases as Re increases for the divergent channel. The velocity of both the nanofluids increases as the angle of inclination of the plates increases.