Showing papers in "International Journal of Applied and Computational Mathematics in 2021"

Two-Phase Darcy-Forchheimer Flow of Dusty Hybrid Nanofluid with Viscous Dissipation Over a Cylinder

Abstract: The current article concerns with the flow of an incompressible dusty hybrid nanofluid over a stretching cylinder by considering Darcy–Forchheimer porous medium and viscous dissipation. Heat transfer and momentum behavior of water-based fluid with suspended nanoparticles (copper and Titania) is scrutinized in this study. The two-phase model which handles the particle phase and the fluid phase is accounted in this study. The modelled equations are reduced to a set of non-linear ordinary differential equations (ODEs) using suitable similarity variables. Later, these reduced equations are solved by adopting the Runge–Kutta Fehlberg-45(RKF-45) technique along with shooting scheme. The graphs are plotted to examine the impact of various dimensionless parameters on velocity and thermal profiles for both dust and fluid phases. For engineering apprehensions, the coefficient of skin friction and Nusselt number are also calculated and scrutinized through graphs. The outcomes reveal that, increase in mass concentration of particles improves the heat transfer but declines velocity gradient. The increase in velocity interaction parameter of the fluid reduces the velocity gradient of fluid phase but increases the velocity of the dust phase. Finally, increasing values of curvature parameter improves the velocity and temperature of both the phases.

Heat and Mass Transfer Assessment of Magnetic Hybrid Nanofluid Flow via Bidirectional Porous Surface with Volumetric Heat Generation

Abstract: The theme of this article is to assess the impact of MHD flow of SWCNT + Ag + H2O hybrid nanofluid via a bidirectional porous stretchable sheet having volumetric heat generation and chemical reaction of higher order. The governing equations of the flow problem for working fluid are tackled by with RKF-4th and 5th order technique. The features of heat transfer, mass diffusion and fluid flow are depicted in the range of power law index number, $$1 \le n \le 6$$ ; Hartmann number, $$0.1 \le Ha \le 0.6$$ ; internal heat generation, $$0.1 \le H \le 2.2$$ ; chemical reaction, $$0.5 \le \Omega \le 4$$ ; chemical reaction order ( $$1 \le q \le 9$$ ) and nanoparticles volume fractions varies from 2 to 10%, and remaining parameters are fixed. The upshots of the current problem illustrate that with increase in volume fraction of hybrid nanofluid, thermal field function increases, while both velocity functions declined. Moreover, Nusselt number function is reduced with increase in volumetric heat generation and increases with order of chemical reaction for $$n = 1$$ and $$n = 2$$ .

Investigation of Micropolar Hybrid Nanofluid (Iron Oxide–Molybdenum Disulfide) Flow Across a Sinusoidal Cylinder in Presence of Magnetic Field

Abstract: The purpose of this paper is to investigate the micropolar nanofluid flow across a sinusoidal cylinder in presence of the magnetic field. The base fluid is an equal mixture of ethylene glycol and water; also,ithybridized by iron oxide (Fe3O4) andMolybdenum disulfide (MoS2) nanoparticles.In this study, equations are transformed from PDEs to ODEs and solved by Rung-Kutta fifth-order. After solving the equations, it can be seen that various nondimension parameters are involved (e.g.micro-polar parameter, nanoparticle volume fraction, shape factor, and magnetic field parameter), therefore a sensitivity analysis is applied to investigate the effect ofinvolvedparameters. Besides, variation of Nusselt number and skin friction coefficient are studied.Further analysis showed that Nusselt number is an increasing function of volume fraction and increment in the magnetic field leads to higherskin friction coefficient.Also, whenmicro-gyrationis zero the microelements in the vicinity of the wall are unable to rotate, and by increasing micro-gyration parameters these microelements meet rotation.As a novelty, the hybrid Micropolar nanofluid suspends in mixture fluid flow in sinusoidal cylinder geometry have been investigated. The magnetic force and rotational velocity have been considered.

Computational Investigation of Stefan Blowing Effect on Flow of Second-Grade Fluid Over a Curved Stretching Sheet

Abstract: Non-Newtonian fluids have extensive range of applications in the field of industries like plastics processing, manufacturing of electronic devices, lubrication flows, medicine and medical equipment. Stimulated from these applications, a theoretical analysis is carried out to scrutinize the flow of a second-grade liquid over a curved stretching sheet with the impact of Stefan blowing condition, thermophoresis and Brownian motion. The modelled governing equations for momentum, thermal and concentration are deduced to a system of ordinary differential equations by introducing suitable similarity transformations. These reduced equations are solved using Runge–Kutta–Fehlberg fourth fifth order method (RKF-45) by adopting shooting technique. The solutions for the flow, heat and mass transference features are found numerically and presented with the help of graphical illustrations. Results reveal that, curvature and Stefan blowing parameters have propensity to rise the heat transfer. Further, second grade fluid shows high rate of mass and heat transfer features when related to Newtonian fluid for upsurge in values of Brownian motion parameter.

Convective Flow of Second Grade Fluid Over a Curved Stretching Sheet with Dufour and Soret Effects

Abstract: The present study investigates the flow of a second-grade liquid over a curved stretching sheet with the Soret, magnetic and Dufour effects. In addition, the Newtonian heating effect is taken into account in this simulation. The framed equations are transformed to a set of nonlinear ordinary differential equations using suitable similarity variables, and then numerically solved using Runge–Kutta–Fehlberg's fourth fifth order approach and the shooting technique. The impact of dimensionless factors on the flow, thermal, and concentration fields are interpreted and explained in detail by using suitable graphs. The increase in the Newtonian heating parameter increases the heat transfer coefficient which increases the heat transfer of both second grade and Newtonian fluids. Furthermore, Newtonian liquid is significantly influenced by Newtonian heating parameter and exhibits enhanced heat transfer. The concentration profile of Newtonian fluid is significantly influenced by Soret and Dufour numbers and rises quicker than the non-Newtonian fluid.

Investigation of Cattaneo–Christov Double Diffusions Theory in Bioconvective Slip Flow of Radiated Magneto-Cross-Nanomaterial Over Stretching Cylinder/Plate with Activation Energy

Abstract: The present exploration examines the Cattaneo–Christov double diffusions theory in magneto-Cross nanomaterial flow conveying gyrotactic microorganisms over an extending horizontal cylinder/plate under the aspects of velocity slippage, and activation energy with chemically reacting features. The phenomena of thermophoresis, Brownian movement, and thermal radiation are also incorporated. Utilization of the adopted similarity transformations makes it convenient to transform our governing nonlinear higher-order coupled PDEs into ODEs which are further solved numerically by adopting well-known MATLAB function bvp4c. The quantitative outcomes of emerging thermo-physical and geometrical parameters on the associated non-dimensional profiles of interest are anatomized via requisite graphs and numerically erected tabular forms. It is detected that fluid velocity components decline due to upgraded magnetic field and velocity slippage parameter. When thermal time relaxation parameter varies from 0.0 to 0.9, Nusselt number augments about $$22.02\%$$ for cylindrical surface and about $$23.61\%$$ for plate surface. Likewise, with the same variations in thermal time relaxation parameter Sherwood number increases about $$17.32\%$$ for cylindrical surface and about $$18.24\%$$ for plate surface. Moreover, comparative exploration of the emerging flow features over a flat plate, and cylindrical surface is reported. It is visualized that flat plate offers less temperature than cylindrical surface when flow occurs. The results would offer primary guidance for many industrial, biological, medical and ecological challenges, for instance, bio-fuel, bio-diesel, ethanol, biological tissues, bio-fertilizers, bio-micro-systems, reproduction, infection, and marine life ecosystems, etc.

Soliton Solutions of (2 + 1) Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational sine − cosine and sinh − cosh Method

Abstract: In this research, our main motivation is to find the novel analytical solutions of $$(2+1)$$ dimensional Heisenberg ferromagnetic spin equation, which describes the nonlinear dynamics of the ferromagnetic materials by using the extended rational $$sine-cosine$$ and $$sinh-cosh$$ methods. The considered PDE is converted to an ODE by applying a wave transformation, and then the solutions of the ODE are supposed to be in the rational forms of trigonometric functions. After substituting the solutions to the ODE and doing some basic calculations, a system of algebraic equations is derived. So, finding the solutions of the PDE turns into a problem of solving an algebraic system of equations. The unknown coefficients in the solutions that are in the rational form are found by solving the obtained system. The methods are powerful and can be applied to find exact solutions to lots of PDEs in mathematical physics.

Combined Effect of Radiation and Inclined MHD Flow of a Micropolar Fluid Over a Porous Stretching/Shrinking Sheet with Mass Transpiration

Abstract: The present investigation is focused on the study of a micropolar flow in a porous medium subject to inclined magnetic field, mass transpiration and internal radiation. The analytical solutions of the flow and temperature fields were derived in closed forms for the first time here by using similarity transformations. The transformed velocity, microrotation and temperature fields were plotted and analyzed for a number of relative dimensionless parameters, while skin friction coefficient and Nusselt number were also calculated and discussed. The results showed that the micropolar flow may accelerate or decelerate depending on the effect of porous medium, the mass transpiration, the radiation and the inclined applied magnetic field. Moreover, heat transfer may enhanced or diminished depending on the same phenomena. The present analytical results are anticipated to be of great significance regarding the effect of important MHD and heat transfer parameters on micropolar fluids and they can be used in a variety of industrial applications.

Generalized Lucas Polynomial Sequence Treatment of Fractional Pantograph Differential Equation

Abstract: This paper deals with the implementation and presentation of numerical solutions of fractional pantograph differential equations (FPDEs) using generalized Lucas polynomials (GLPs) The derivation of our proposed algorithms is built on introducing an operational matrix of derivatives (OMDs) of the GLPs and after that employing it to convert the problem into an algebraic system of equations whose solution can be found through some suitable algorithms such as Gauss elimination and Newton–Raphson methods Finally, by providing various illustrative examples, including comparisons with the results obtained by some other existing literature methods, the efficiency and applicability of our proposed algorithms are demonstrated

Analysis of Time-Fractional $$\phi ^{4}$$ ϕ 4 -Equation with Singular and Non-Singular Kernels

Abstract: In this article, we investigate the nonlinear time-fractional $$\phi ^{4}$$ -equation under Caputo, Caputo-Fabrizio, and Atangana-Baleanu in Caputo’s sense. The modified double Laplace decomposition method is applied to study the proposed model under the aforementioned operators. The suggested approach is the combination of double Laplace and decomposition methods. It is observed that, the obtained series solutions of the system with considered fractional derivatives converges to the exact solution. A numerical example is presented with corresponding numerical simulations to demonstrate and validate the efficiency of the proposed technique. The error analysis of the considered equation with all considered operators is presented in the form of the tables. The physical behaviors of the obtained solutions with different fractional orders are discussed in detail.

Aligned Magnetic and Bioconvection Effects on Tangent Hyperbolic Nanofluid Flow Across Faster/Slower Stretching Wedge with Activation Energy: Finite Element Simulation

Abstract: The underlying work includes the time-dependent flow and improved thermal transport for tangent hyperbolic nanofluids across an extending wedge. Self-motile microorganisms are suspended in the fluid to avoid agglomeration of tiny particles. Moreover, magnetic field, heat source, convectively heated boundary, and activation energy are considered. Mathematical formulation based on usual laws of conservation is non dimensionalized with emerging parameters through implementation of similarity transform to yield a corresponding set of ordinary partial differential equations. In the face of convective non linearity, a finite element discretization is harnessed to be coded and run on Matlab platform. The parametric calculation are carried out for faster and slower wedge. The rising strength of wedge angle, unsteadiness, and material law index recede the velocity distribution. The distribution of temperature upgrades directly against growing of Hartman number, thermophoresis, Biot number, material law index, and Brownian motion parameters. The concentration profile of nanoparticles decrease against Lewis number and activation energy, but it rises directly with higher input of activation energy. The computational results obtained through Matlab code blocks are corroborated with the existing literature and found to be a tolerable correlation.

Fractal Fractional Operator Method on HER2+ Breast Cancer Dynamics

Abstract: In this paper, an in vitro model of HER2+ breast cancer cells dynamics resulting from various dosages and timings of paclitaxel and trastuzumab combination regimens is considered. Since, the combined in vitro results and development of dynamics of drug synergy has a potential to evaluate and improve standard of care, then combination therapies in timings of paclitaxel and trastuzumab combination regimens, thus, HER2+ breast cancer cells dynamics are extended to a system of fractal fractional partial differential equations in order to enable one to capture the dynamics of the deadly breast cancer in terms of combination of the two therapies. Moreover, the well-posedness of solutions is presented and the extended dynamics are analysed to that effect. Since it is not that easy to obtain the analytic solution a novel numerical method based on fractal fractional derivatives is design, implemented and the results with respect to the stability conditions are presented.

Modeling the Dynamics of COVID-19 in Nigeria

Abstract: To understand the dynamics of COVID-19 in Nigeria, a mathematical model which incorporates the key compartments and parameters regarding COVID-19 in Nigeria is formulated. The basic reproduction number is obtained which is then used to analyze the stability of the disease-free equilibrium solution of the model. The model is calibrated using data obtained from Nigeria Centre for Disease Control and key parameters of the model are estimated. Sensitivity analysis is carried out to investigate the influence of the parameters in curtailing the disease. Using Pontryagin’s maximum principle, time-dependent intervention strategies are optimized in order to suppress the transmission of the virus. Numerical simulations are then used to explore various optimal control solutions involving single and multiple controls. Our results suggest that strict intervention effort is required for quick suppression of the disease.

The Space–Time Coupled Fractional Cattaneo–Friedrich Maxwell Model with Caputo Derivatives

Abstract: In the current article, we have thoroughly investigated the collective impact of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid (Cattaneo–Friedrich Maxwell-CFM model) over a permeable surface embedded in a porous medium. Here we have utilized the Caputo time-fractional derivatives and mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s and Fick’s laws) are being used to fractionalize the presented model. The effects of radiative heat flux, Ohmic dissipation, and internal absorption are presented through generalized Fourier’s law while Fick’s law or mass transfer equation offers the effects of first order chemically reactive species. The finite element method and finite difference method are being utilized to numerically solve the nonlinear coupled differential equations. It is established, through compression of numerical and analytical solutions, that the presented model is convergent. Further, error analysis of the subject model is also carried out. Moreover, for better illustration of results, we have also offered a graphical and tabular presentation of impacts of the parameters of interest on velocity, temperature, concentration profile, local skin friction coefficient, and heat and mass transfer. It is evident from the obtained results that velocity near and away from the surface increases with the enhancement of fractional derivative parameter whereas an opposite trend is observed in the case of temperature. Furthermore, it is noticed that temperature shows a decreasing behavior for the value $${\Lambda }_{\theta }<2$$ and $${\Lambda }_{\phi }<2$$ , on the other hand entirely opposite trend is witnessed for $${\Lambda }_{\theta }\ge 3$$ and $${\Lambda }_{\phi }\ge 3$$ . From an engineering perspective, we have acquired comprehensive outcomes such that the heat transfer offers an increasing trend in the case of TR and thermal fractional parameter $$\beta_{1}$$ . Additionally, the chemical reaction parameter and Sc significantly contribute towards the mass transfer rate. Since, in literature, one cannot refer to such results with non-integer Caputo fractional derivatives thus the results obtained through the current assessment hold significance for future research avenues. Moreover, the numerical inferences of the subject study may contribute to an advanced thermal processing method in the food industry to swiftly increase the temperature for cooking or sterilization drives.

Soliton Solutions of Deformed Nonlinear Schrödinger Equations Using Ansatz Method

Abstract: In this paper, the deformation of nonlinear Schrodinger (NLS) type equations, the so-called Camassa–Holm NLS (CH-NLS) equation and Camassa–Holm derivative NLS (CH-DNLS) equation are investigated to obtain the solitary waves solutions. These deformed equations are recently constructed using the Lagrangian deformation and loop algebra splittings. The solitary wave ansatz method is used to obtain the exact soliton solutions of these equations. The behaviours of solitons solutions are presented by 3D and 2D graphs.

Numerical Analysis of Couple Stress Nanofluid in Temperature Dependent Viscosity and Thermal Conductivity

Abstract: This communication reports on an innovative study of two-dimensional couple stress fluid 3 with effect of viscosity and conductivity. We proposed a new model based on temperature dependent variable thermal conductivity on kinetic theory. Our model assumes that thermal conductivity is a decreasing function of temperature rather than an increasing function. The effect of the three key parameters, viscosity, thermal conductivity and couple stress parameter are analyzed. The coupled non-linear system is further validated numerically using the spectral quasilinearization method. The method is found to be accurate and convergent. Increasing the temperature dependent parameter for viscosity is shown to reduce the heat mass transfer rates at the surface. Increasing thermal conductivity and the couple stress parameter increased the heat mass transfer rates on the boundary surface

Fractional Model and Numerical Algorithms for Predicting COVID-19 with Isolation and Quarantine Strategies

Abstract: In December 2019, a new outbreak in Wuhan, China has attracted world-wide attention, the virus then spread rapidly in most countries of the world, the objective of this paper is to investigate the mathematical modelling and dynamics of a novel coronavirus (COVID-19) with Caputo-Fabrizio fractional derivative in the presence of quarantine and isolation strategies. The existence and uniqueness of the solutions for the fractional model is proved using fixed point iterations, the fractional model are shown to have disease-free and an endemic equilibrium point.We construct a fractional version of the four-steps Adams-Bashforth method as well as the error estimate of this method. We have used this method to determine the numerical scheme of this model and Matlab program to illustrate the evolution of the virus in some countries (Morocco, Qatar, Brazil and Mexico) as well as to support theoretical results. The Least squares fitting is a way to find the best fit curve or line for a set of points, so we apply this method in this paper to construct an algorithm to estimate the parameters of fractional model as well as the fractional order, this model gives an estimate better than that of classical model.

Computational Method for Reaction Diffusion-Model Arising in a Spherical Catalyst

Abstract: In this paper, we consider Lane–Emden problems which have many applications in sciences. Mainly we focus on two special cases of Lane–Emden boundary value problems which models reaction–diffusion equations in a spherical catalyst and spherical biocatalyst. Here we propose a method to obtain approximate solution of these models. The main reason for using this technique is high accuracy and low computational cost compared to some other methods. Numerical results are shown using tables and figures. Accuracy of the computational method is shown by comparing numerical results by analytical methods.

A Fast Convergent Semi-analytic Method for an Electrohydrodynamic Flow in a Circular Cylindrical Conduit

Abstract: A semi-analytical solution of the nonlinear boundary value problem that models the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit is presented. An integral operator expressed in terms of Green’s function is constructed then followed by an application of fixed point theory to generate a highly accurate semi-analytical expression of the fluid velocity for all possible values of relevant parameters. A proof of convergence for the proposed method, based on the contraction mapping principle, is presented. Numerical simulations and comparison with other analytical methods confirm that the proposed approach is convergent, stable, and highly accurate.

On the Frequency-Amplitude Formulation for Nonlinear Oscillators with General Initial Conditions

Abstract: This paper extends the frequency-amplitude formulation to solve nonlinear conservative oscillators with general initial conditions. The obtained result is exactly as that by the Hamiltonian approach. As the solution process is extremely simple, this method can be used for fast insight of periodic properties of a nonlinear vibration system.

A Novel Numerical Approach for Simulating the Nonlinear MHD Jeffery–Hamel Flow Problem

Abstract: The present study is related to the numerical simulation of the well-known Jeffery Hamel blood flow problem of nonlinear form. For the numerical solutions of the designed model, a Bernoulli collocation method is implemented. The method is based on converting the model into a system of a nonlinear algebraic equation which is then solved using a novel iterative technique. To check the perfection and exactness of the proposed schemes, two novel residual error correction methods are illustrated to ensure that the method is effective. The method does not require any extensive computational time while providing good results. Some numerical simulations are provided and a comparison is made with other existing methods from the literature. From these results, it can be seen that the Bernoulli collocation method is effective yet simple in providing accurate results for such a model. The method can be extended in the near future for solving similar other problems with applications in both science and engineering.

A Non-Fourier’s and Non-Fick’s Approach to Study MHD Mixed Convective Copper Water Nanofluid Flow over Flat Plate Subjected to Convective Heating and Zero Wall Mass Flux Condition

Abstract: A theoretical model of MHD mixed convective Cu–water nanofluid boundary layer flow over flat vertical plate has been developed and investigated. As a novelty, firstly, modified Buongiorno’s model is utilized to include the effects of Brownian motion, thermophoresis and volume fraction for nanofluid. Secondly, thermal energy equation and concentration equation are modeled with the help of Cattaneo–Christov theory of heat and mass flux, respectively. Due to this non-Fourier’s and non-Fick’s approach, two parameters namely, thermal relaxation parameter and solutal relaxation parameter were introduced in thermal energy equation and concentration equation, respectively. In addition, the surface of flat plate is subjected to suction, convective heating and zero wall mass flux condition. Authors have used the similarity method and through analysis it is shown that transport equations can be converted to ODEs with the help of suitable similarity transformations. The analysis and computed results shows that various dimensional and non-dimensional parameters influence the velocity, temperature and concentration profiles. The pattern and behavior of boundary layer is depicted graphically. The results for skin friction coefficient and heat transfer coefficient are outlined in tabular form. The result of passive control of nanoparticles at the surface is that Brownian motion parameter does not influence the temperature profiles of nanofluid flow and heat transfer rate at the surface. Heat transfer coefficient is positively correlated to thermal relaxation parameter and Biot number, whereas thermophoresis parameter causes it to decrease. The flow of nanofluid is aided by buoyancy ratio parameter and thermophoresis parameter but contrary behavior is seen for magnetic parameter. The effect of volume fraction and suction parameter is to increase the value of skin friction coefficient.

Explicit and Approximate Solutions for the Conformable-Caputo Time-Fractional Diffusive Predator–Prey Model

Abstract: The aim of this work is twofold. First, we seek functional explicit solutions to the conformable-time fractional predator–prey model by adapting the extended Kudryashov method. Second, we find fractional power series solution to the same model when the fractional derivative is of Caputo type. Graphical analysis will be presented to serve two features; to recognize the physical shapes and the propagations of the predator–prey densities, and to observe the impact of the fractional derivatives acting in the model.

Approximate Analytical Solutions of Generalized Zakharov–Kuznetsov and Generalized Modified Zakharov–Kuznetsov Equations

Abstract: This paper investigates the generalized Zakharov–Kuznetsov (GZK) equation and generalized modified Zakharov–Kuznetsov equation in the presence of external periodic forcing term together with damping. An approximate analytical solution is obtained by employing the direct assumption technique. The framework staged here reveals number of beautiful wave features such as positive amplitude soliton, rare effective soliton, periodic rational soliton, kink type soliton, etc. Moreover, two new parameters along with a control function is introduced to extend the study of traveling wave solution and to create new types of solitary wave solution that are depicted from a numerical standpoint. It is noticed that the generalized wave solution for GZK in presence of external periodic forcing with a damping, positive potential soliton may transform into a rare effective soliton due to an increase in the nonlinearity of the system.

Melting Heat Transfer of MHD Micropolar Fluid Flow Past An Exponentially Stretching Sheet with SLip and Thermal Radiation

Abstract: The effects of velocity slip and radiation on MHD flow and melting heat transfer of a micropolar fluid due to an exponentially stretched sheet are presented. By means of similarity transformations the leading partial differential equations are changed to a set of ordinary differential equations which are nonlinear. Numerical solutions of the nonlinear system of equations are then obtained by changing the boundary value problem first to an initial value problem. It is observed that the pertaining parameters have significant effects on the flow and heat transfer characteristics, which are presented and talked about in detail through their illustrations. Due to boost in the melting parameter, the fluid velocity, angular velocity and temperature are found to decrease. Fluid velocity and angular velocity both decrease with a rise in slip at the boundary but quite opposite is the effect on the temperature.

Economic Ordering Policies for Growing Items (Poultry) with Trade-Credit Financing

Abstract: Numerous economic order quantity (EOQ) models have by and large been ascertained for assembling items. Several distinctive EOQ models have been anticipated in order to incorporate the significant features related to a particular class of items. This paper intends a model aimed at a particular class of inventory i.e. growing items. Some genuine instances of growing items are poultry and livestock. We commence by intending a wide-ranging scientific model, that might be utilized for several categories of growing items, trailed by a specific numerical model considering a certain category of chickens. The model aims to ascertain the optimum order quantity of the items to be ordered in the beginning of a cycle, the optimum length of the growing cycle and the optimum total profit of the retailer in the presence of allowable deferment in payments. Numerical examples are provided to represent the model. A sensitive study is exhibited to examine the impact of the primary factors of the model as far as it’s decision variables and objective function are considered.

Sustainable Supply Chain Model for Multi-stage Manufacturing with Partial Backlogging Under the Fuzzy Environment with the Effect of Learning in Screening Process

Abstract: The primary concern of every business manager of supply chain system is to obtain economical sustainability. To achieve this goal they adopt different polices such as multi-stage manufacturing process, promotional strategies, learning effect, screening process etc. In the present study, a supply chain model consisting one retailer and one manufacturer is examined regarding the financial viability. An imperfect multi-stage manufacturing process is considered here with a probabilistic deteriorating item. The screening process under the effect of learning is performed in each stage of production and further the imperfect products are reworked in the same stage. Promotional efforts are initiated by the retailer to boost up demand. Shortages are allowed at the retailer end with partially backlogging. All the cost parameters are imprecise parameters due to the presence of uncertainty in the market. The presence of impreciseness in cost parameters is handled by applying the fuzzy set theory. To defuzzify the objective function of the system, the centroid method is used. Aim of this work is to minimize the average inventory cost so that order quantity and backorder quantity are optimal. Objective function in the developed model is nonlinear optimization problem which is solved with the help of calculus based classical optimization technique. Further, convexity of the objective function is explored with the help of graphs and Hessian matrix. Results indicate that average inventory cost decreases by 5% as the supply chain system shifted to three-stage manufacturing process to five-stage manufacturing process. Further, analysis shows that incorporating impreciseness in costs capture the real picture of business. Sustainability of the proposed model is explored with the help of numerical example and sensitive analysis. Form sensitivity analysis, positive impact of screening rate and promotional efforts are observed on the average cost of the system. Analysis also reflects that inventory cost of the system is high due to high backlogging rate.

Numerical-Solution-for-Nonlinear-Klein–Gordon Equation via Operational-Matrix by Clique Polynomial of Complete Graphs

Abstract: This study introduced a generalized operational matrix using Clique polynomials of a complete graph and proposed the latest approach to solve the non-linear Klein–Gordon (KG) equation. KG equations describe many real physical phenomena in fluid dynamics, electrical engineering, biogenetics, tribology. By using the properties of the operational-matrix, we transform-the non-linear KG equation into a system-of algebraic-equations. Unknown coefficients to be determined by Newton’s method. The present-technique is applied-to four problems, and the obtained-results are-compared with-another-method in the literature. Also, we discussed some theorems on convergence analysis and continuous property.

Numerical Simulation of Radiative MHD Sutterby Nanofluid Flow Through Porous Medium in the Presence of Hall Currents and Electroosmosis

Abstract: Analysis of thermal and fluid phenomena based on the fluid dynamics theory leads to understanding of fundamental mechanisms in modern technologies. Thermal/fluid transport is critical to many applications, such as photothermal cancer therapy, solar thermal evaporation and polymer composites. The current study focusses to investigate the effect of magnetohydrodynamics, Hall currents and electroosmosis on the propulsion of Sutterby nanofluids in a porous microchannel. The Brownian motion and thermophoresis effects have also been considered. The governing equations for the momentum, temperature and nanoparticle volume fraction have been modified under the suitable non-dimensional quantities. The resulting dimensionless system of equations have been solved using bvp4c package in computational software MATLAB. The pictorial representations have been presented for various flow quantities with respect to sundry fluid parameters. It is noted from the investigation that, there is a decrease in fluid velocity with an increase in Hartmann number, temperature decreases with the increment in radiation parameter and nanoparticle volume fraction reduces with the increment of Prandtl number and thermophoresis parameter. The results obtained for the Sutterby nanofluid propulsion model reveal many engrossing behaviors and has many applications such as disease diagnostics and cancerous tissues destruction, and that provide a further dimension to investigate the nanofluid flow problems with thermophysical properties in two/three dimensions.

Analytical Study of $$(3+1)$$ ( 3 + 1 ) -Dimensional Fractional-Reaction Diffusion Trimolecular Models

Abstract: This paper employs two efficient iterative schemes for solving the $$(3+1)$$ -dimensional fractional diffusion-reaction trimolecular models also known as Brusselator models which arises in the mathematical modeling of chemical reaction-diffusion processes. This model is a famous model of chemical reactions with oscillations. The two iterative methods used in this study are the q-homotopy analysis method and the fractional reduced differential transform method. These methods produce exact solutions in some special cases. Error estimates are done when the exact solution is known. The effect of the fractional order on the solutions profile of the system considered is investigated. The numerical results obtained show that these iterative methods are competitive, reliable, and powerful for solving strongly nonlinear higher-order differential equation of fractional type.