Computational Analysis of Heat and Mass Transfer in Magnetized Darcy-Forchheimer Hybrid Nanofluid Flow with Porous Medium and Slip Effects

A computational analysis of magnetized hybrid Darcy-Forchheimer nanofluid flow across a flat surface is presented in this work.For the study of heat and mass transfer aspects viscous dissipation,activation energy,Joule heating,thermal radiation,and heat generation effects are considered.The suspension of nanoparticles singlewalled carbon nanotubes(SWCNTs)and multi-walled carbon nanotubes(MWCNTs)are created by hybrid nanofluids.However,single-walled carbon nanotubes(SWCNTs)produce nanofluids,with water acting as conventional fluid,respectively.Nonlinear partial differential equations(PDEs)that describe the ultimate flow are converted to nonlinear ordinary differential equations(ODEs)using appropriate similarity transformation.The ODEs are dealt with numerically by means of MATLAB’s inbuilt routine function bvp4c.Velocity,temperature,and concentration profiles are explained pictorially whereas Sherwood number,local skin friction coefficient,and Nusselt number values are represented through bar charts.Thermal radiation and activation parameters shows direct impact on flow field.Furthermore,hybrid nanofluid admits a higher magnitude of velocity and temperature than nanofluid,but the concentration profile exhibits the opposite trend.The notable findings of the present investigation have significant applications in heat combustion and cooling chambers,space technology,the ceramics industry,paint and conductive coatings,bio-sensors,and many more.

Essential Features Preserving Dynamics of Stochastic Dengue Model

Nonlinear stochasticmodelling plays an important character in the different fields of sciences such as environmental,material,engineering,chemistry,physics,biomedical engineering,and many more.In the current study,we studied the computational dynamics of the stochastic dengue model with the real material of the model.Positivity,boundedness,and dynamical consistency are essential features of stochastic modelling.Our focus is to design the computational method which preserves essential features of the model.The stochastic non-standard finite difference technique is most efficient as compared to other techniques used in literature.Analysis and comparison were explored in favour of convergence.Also,we address the comparison between the stochastic and deterministic models.

A Stochastic Numerical Analysis for Computer Virus Model with Vertical Transmission Over the Internet

We are presenting the numerical analysis for stochastic SLBR model of computer virus over the internet in this manuscript.We are going to present the results of stochastic and deterministic computer virus model.Outcomes of the threshold number C∗hold in stochastic computer virus model.If C∗<1 then in such a condition virus controlled in the computer population while C∗>1 shows virus spread in the computer population.Unfortunately,stochastic numerical techniques fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference scheme(SNSFD)maintains all diverse characteristics such as dynamical consistency,bounded-ness and positivity as well-defined by Mickens.On this basis,we can suggest a collection of plans for eradicating viruses spreading across the internet effectively.

Thermal Analysis of MHD Non-Newtonian Nanofluids over a Porous Media

In the present research,Tiwari and Das model are used for the impact of a magnetic field on non-Newtonian nanofluid flow in the presence of injection and suction.The PDEs are converted into ordinary differential equations(ODEs)using the similarity method.The obtained ordinary differential equations are solved numerically using shooting method along with RK-4.Part of the present study uses nanoparticles(NPs)like TiO_(2) andAl_(2)O_(3) and sodium carboxymethyl cellulose(CMC/water)is considered as a base fluid(BF).This study is conducted to find the influence of nanoparticles,Prandtl number,and magnetic field on velocity and temperature profile,however,the Nusselt number and coefficient of skin friction parameters are also presented in detail with the variation of nanoparticles and parameters.The obtained results of the present study are presented usingMATLAB.In addition to these,some simulations of partial differential equations are also shown using software for graphing surface plots of velocity profile and streamlines along with surface plots and isothermal contours of the temperature profile.

An Effective Numerical Method for the Solution of a Stochastic Coronavirus(2019-nCovid)Pandemic Model

Nonlinear stochastic modeling plays a significant role in disciplines such as psychology,finance,physical sciences,engineering,econometrics,and biological sciences.Dynamical consistency,positivity,and boundedness are fundamental properties of stochastic modeling.A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation.Well-known explicit methods such as Euler Maruyama,stochastic Euler,and stochastic Runge–Kutta are investigated for the stochastic model.Regrettably,the above essential properties are not restored by existing methods.Hence,there is a need to construct essential properties preserving the computational method.The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model.The comparison of the results of deterministic and stochastic models is also presented.Our proposed efficient computational method well preserves the essential properties of the model.Comparison and convergence analyses of the method are presented.

Structure-Preserving Dynamics of Stochastic Epidemic Model with the Saturated Incidence Rate

The structure-preserving features of the nonlinear stochastic models are positivity,dynamical consistency and boundedness.These features have a significant role in different fields of computational biology and many more.Unfortunately,the existing stochastic approaches in literature do not restore aforesaid structure-preserving features,particularly for the stochastic models.Therefore,these gaps should be occupied up in literature,by constructing the structure-preserving features preserving numerical approach.This writing aims to describe the structure-preserving dynamics of the stochastic model.We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling.The usual explicit stochastic numerical approaches are time-dependent.We have developed the implicitly driven explicit approach for the stochastic epidemic model.We have proved that the newly developed approach is preserving the structural,dynamical properties as positivity,boundedness and dynamical consistency.Finally,convergence analysis of a newly developed approach and graphically illustration is also presented.

Ordering Cost Depletion in Inventory Policy with Imperfect Products and Backorder Rebate

This study presents an inventory model for imperfect products with depletion in ordering costs and constant lead time where the price discount in the backorder is permitted.The imperfect products are refused or modified or if they reached to the customer,returned and thus some extra costs are experienced.Lately some of the researchers explicitly present on the significant association between size of lot and quality imperfection.In practical situations,the unsatisfied demands increase the period of lead time and decrease the backorders.To control customers'problems and losses,the supplier provides a price discount in backorders during shortages.Also,an order’s policies may result in including some imperfect products in arrival lots.A discount on price may be offered by the supplier on the out-of-stock products to manage the backorder problems.The study aims to develop a model with imperfect products by permitting the price discount in backorders,and the cost of ordering is considered a decision variable.First,it is assumed that the demand for lead time is followed by a normal distribution and then stops it and assumed that the first two moments of demand for lead time are known.Further,the minimax distribution method is used to solve this model,and a separate algorithm is designed.In this study,two models are discussed with and without a normally distributed rate of demand.The current study verified with the help of some numerical examples over various model parameters.

Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.It is known that many problems in applied sciences and engineering can be formulated as functional equations.Such equations can be transferred to fixed point theorems in an easy manner.Moreover,we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations.Let X be a non-empty set.A fixed point for a self-mapping T on X is a point𝑒𝑒∈𝑋𝑋that satisfying T e=e.One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems.Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Berinde(2004b);Agarwal,O’Regan and Sahu(2007)].The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can.We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al.[Sintunavarat and Pitea(2016);Agarwal,O’Regan and Sahu(2007);Mann(1953);Ishikawa(1974)].We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Abbas and Nazir(2014);Agarwal,O’Regan and Sahu(2007)]schemes.Moreover,we introduce a problem raised from Newton’s law of cooling as an application of our new iteration scheme.Also,we support our application with a numerical example and figures to illustrate the validity of our iterative scheme.