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Computer Modeling in Engineering & Sciences 2022年第1期130卷 205-220页

作者： S.M.Atif w.a.khan Muhammad Abbas Umair Rashid Department of Mathematics Capital University of Science and TechnologyIslamabadPakistan Department of Mechanical Engineering College of EngineeringPrinceMohammad Bin Fahd UniversityAl KhobarSaudi Arabia Department of Mathematics University of SargodhaSargodhaPakistan CASKey Laboratory of Mechanical Behavior andDesign of Materials Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiChina

In this numerical study,the effect of quartic autocatalysis type of chemical reaction,buoyancy force and thermal radiation phenomenon and magnetic effect on tangent hyperbolic nanofluid past an upper horizontal surface of a paraboloid has been *** considering the Buongiorno model approach,a diffusion of unequal coefficients in the presence of gyrotactic microorganism is *** of microorganism’s idea is used to stabilize the nanoparticles through *** modeled PDEs of the problems are converted into nonlinear ODEs with the assistant of the similarity *** tackle nonlinear ODEs,MATLAB package bvp4c is *** addition,a hallmark of the Matlab code with the reported results in the literature is achieved by *** variations in motion,concentration,temperature,and motile density due to sundry parameters have been analyzed in-depth via *** analysis shows that the density profile of motile of microorganism is hiked with an increment in the bioconvection Rayleigh number but decreases for higher thermal Grashof number.

关键词： Quartic autocatalysis tangent hyperbolic nanofluid brownian motion paraboloid of revolution MHD flow thermophoresis

A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable

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Computer Modeling in Engineering & Sciences 2023年第4期135卷 187-209页

作者： N.Alam w.a.khan S.Obeidat G.Muhiuddin N.S.Diab H.N.Zaidi A.Altaleb L.Bachioua Department of Basic Sciences Deanship of Preparatory YearUniversity of Ha’ilHa’il2440Saudi Arabia Department of Mathematics and Natural Sciences Prince Mohammad Bin Fahd UniversityAl Khobar31952Saudi Arabia Department of Mathematics Faculty of ScienceUniversity of TabukTabuk71491Saudi Arabia

In this article,we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler *** fundamental properties of these functions are *** using these generating functions and some identities,relations among trigonometric functions and two parametric kinds of Bell-based Bernoulli and Euler polynomials,Stirling numbers are *** formulae for these polynomials are *** a partial derivative operator to these generating functions,some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also *** addition,some remarks and observations on these polynomials are given.

关键词： Bernoulli polynomials euler polynomials bell polynomials stirling numbers

Magnetohydrodynamic Stagnation Point Flow of a Maxwell Nanofluid with Variable Conductivity

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Communications in Theoretical Physics 2019年第12期71卷 1493-1500页

作者： M.Irfan M.khan w.a.khan M.Alghamdi Department of Mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China Department of Mathematics Faculty of ScienceKing Khalid UniversityAbha 61413Kingdom of Saudi Arabia

This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto Maxwell *** Buongiorno’s theory has been established to picture the inducement of Brownian and thermophrotic diffusions ***,the aspect of heat sink/source is *** homotopic analysis method(HAM)has been worked out for the solution of nonlinear *** behavior of inferential variables on the velocity,temperature,concentration and local Nusselt number for Maxwell nanofluid are sketched and *** attained outcomes specify that both the temperature and concentration of Maxwell fluid display analogous behavior,while the depiction of Brownian motion is quite conflicting on both temperature and concentration *** is further noted that the influence of variable thermal conductivity on temperature field is similar to that of Brownian motion ***,for the confirmation of our study comparison tables are reported.

关键词： Maxwell nanofluid stagnation point flow magnetohydrodynamic(MHD) variable conductivity chemical reaction

Dual Solutions of MHD Boundary Layer Flow of a Micropolar Fluid with weak Concentration over a Stretching/Shrinking Sheet

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Communications in Theoretical Physics 2017年第4期67卷 449-457页

作者： Z.H.khan M.Qasim Naeema Ishfaq w.a.khan Department of Mathematics University of MalakandChakdaraDir(Lower)Khyber PakhtunkhwaPakistan Department of Mathematics COMSATS Institute of Information TechnologyPark RoadChak ShahzadIslamabadPakistan School of Mathematical Sciences Peking UniversityBeijing 100871China Department of Mechanical and Industrial Engineering College of Engineering Majmaah UniversityMajmaah 11952Kingdom of Saudi Arabia

we investigate the dual solutions for the MHD flow of micropolar fluid over a stretching/shrinking sheet with heat transfer. Suitable relations transform the partial differential equations into the ordinary differential *** forms solutions are also obtained in terms of confluent hypergeometric function. This is the first attempt to determine the exact solutions for the non-linear equations of MHD micropolar fluid model. It is demonstrated that the microrotation parameter helps in increasing Nusselt number and the dual solutions exist for all fluid flow parameters under consideration. The dual behavior of dimensionless velocity, temperature, microrotation, skin-friction coefficient,local Nusselt number is displayed on graphs and examined.

关键词： MHD micropolar fluid stretching/shrinking sheet exact and dual solutions

Numerical Study of Unsteady MHD Flow and Entropy Generation in a Rotating Permeable Channel with Slip and Hall Effects

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Communications in Theoretical Physics 2018年第11期69卷 641-650页

作者： Z.H.khan O.D.Makinde R.Ahmad w.a.khan State Key Laboratory of Hydraulics and Mountain River Engineering College of Water Resource & HydropowerSichuan University Key Laboratory of Advanced Reactor Engineering and Safety Ministry of Education Tsinghua University Faculty of Military Science Stellenbosch University School of Mathematics and Physics University of Queensland Faculty of Engineering Sciences GIK Institute of Engineering Sciences and Technology Department of Mechanical Engineering College of Engineering Prince Mohammad Bin Fahd University

This article investigates an unbiased analysis for the unsteady two-dimensional laminar flow of an incompressible, electrically and thermally conducting fluid across the space separated by two infinite rotating permeable *** influence of entropy generation, Hall and slip effects are considered within the flow analysis. The problem is modeled based on valid physical arguments and the unsteady system of dimensionless PDEs (partial differential equations) are solved with the help of Finite Difference Scheme. In the presence of pertinent parameters, the precise movement of the flow in terms of velocity, temperature, entropy generation rate, and Bejan numbers are presented graphically, which are parabolic in nature. Streamline profiles are also presented, which exemplify the accurate movement of the flow. The current study is one of the infrequent contributions to the existing literature as previous studies have not attempted to solve the system of high order non-linear PDEs for the unsteady flow with entropy generation and Hall effects in a permeable rotating channel. It is expected that the current analysis would provide a platform for solving the system of nonlinear PDEs of the other unexplored models that are associated to the two-dimensional unsteady flow in a rotating channel.

关键词： unsteady flow rotating permeable channel MHD slip hall effects entropy analysis finite difference method

Melting and second order slip effect on convective flow of nanofluid past a radiating stretching/shrinking sheet

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Propulsion and Power Research 2018年第1期7卷 60-71页

作者： M.J.Uddin w.a.khan A.I.Md.Ismail American International University-Bangladesh BananiDhaka 1213Bangladesh PN Engineering College PNS JauharNational University of Sciences and TechnologyHabib Ibrahim Rehmatullah RoadKarsazKarachiPakistan School of Mathematical Sciences Universiti Sains MalaysiaPenang 11800Malaysia

A mathematical model is presented for forced convective slip flow of a nanofluid past a radiating stretching/shrinking *** boundary condition is taken into *** nanofluid model involves the Brownian motion and thermophoresis *** group transformation is used to the transport equations as well as the boundary conditions to develop the similarity equations,before being solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical *** show the effects of the controlling parameters on the dimensionless velocity,temperature,nanoparticle volume fraction,skin friction factor,local Nusselt,and local Sherwood numbers,numerical results are presented both in graphical and tabular *** is found that the friction factor decreases with slip and melting parameters for both stretching/shrinking *** is also found that the Nusselt number decreases with the first order slip while it increases with melting and radiation parameters in both ***,the Sherwood number decreases with the melting parameter both for radiating and non-radiating stretching/shrinking *** excellent agreement is found between the present numerical results and published results.

关键词： Nanofluid Melting effect Lie group Thermal radiation Slip boundary condition

Hydrodynamics and Sensitivity Analysis of a williamson Fluid in Porous-walled wavy Channel

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Computers, Materials & Continua 2021年第9期68卷 3877-3893页

作者： A.Shahzad w.a.khan R.Gul B.Dayyan M.Zubair Department of Mathematics COMSATS University IslamabadAbbottabad Campus22060Pakistan Department of Mechanical Engineering College of Engineering Prince Mohammad Bin Fahd UniversityAl Khobar31952Kingdom of Saudi Arabia

In this work,a steady,incompressible williamson fluid model is investigated in a porous wavy *** situation arises in the reabsorption of useful substances from the glomerular filtrate in the *** 80%reabsorption,urine is left,which behaves like a thinning *** laws of conservation of mass and momentum are used to model the physical *** analytical solution of the problem in terms of stream function is obtained by a regular perturbation expansion *** asymptotic integration method for small wave amplitudes and the RK-Fehlberg method for pressure distribution has been used inside the *** is demonstrated that the forward flow becomes fast in the narrow region(at x=0.75),which dominates the upward flow inside the *** study the impact of model parameters on outputs,we applied normalized local sensitivity analysis and noticed that the most influential parameter for the longitudinal velocity profile is the dimensionless wave *** reabsorption parameter is sensitive for transverse velocity in the narrow region,and the weissenberg number has a strong effect on the pressure inside the ***,the least sensitive parameters for the velocity components and pressure have been identified.

关键词： Sensitivity analysis williamson fluid regular perturbation method asymptotic approximation RK-Fehlberg method kidney flow

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

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Computers, Materials & Continua 2021年第1期66卷 575-587页

作者： F.Mabood T.A.Yusuf A.M.Rashad w.a.khan Hossam A.Nabwey department of information technology fanshawe college londononn5y 5r6canada department of mathematics university of ilorinilorinkwara240003nigeria department of mathematics faculty of scienceaswan universityaswan81528egypt department of mechanical engineering college of engineeringprince mohammad bin fahd universityal khobar31952saudi arabia department of mathematics college of science and humanities in al-kharjprince sattam bin abdulaziz universityal-kharj11942saudi arabia department of basic engineering science faculty of engineeringmenoufia universityshebin el-kom32511egypt

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe_(3)O_(4) based Brinkmann type nanofluid flow over a vertical rotating *** Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers,including Grashof,Eckert,and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles,Hall current,magnetic field,viscous dissipation,and the chemical reaction on the physical *** dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg(RKF-45)*** variation of dimensionless velocity,temperature,concentration,skin friction,heat,and mass transfer rate,as well as for entropy generation and Bejan number with governing parameters,are presented graphically and are provided in tabular *** results reveal that the Nusselt number increases with an increase in the solid volume fraction of ***,the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.

关键词： Nanofluid flow entropy generation heat and mass transfer viscous dissipation chemical reaction

Sentiment Analysis of Low-Resource Language Literature Using Data Processing and Deep Learning

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Computers, Materials & Continua 2024年第4期79卷 713-733页

作者： Aizaz Ali Maqbool khan Khalil khan Rehan Ullah khan Abdulrahman Aloraini Department of IT and Computer Science Pak-Austria Fachhochschule:Institute of Applied Sciences and TechnologyHaripur22620Pakistan Software Competence Center Hagenberg Softwarepark 32aHagenberg4232Austria Department of Computer Science School of Engineering and Digital SciencesNazarbayev UniversityAstana010000Kazakhstan Department of Information Technology College of ComputerQassim UniversityP.O.Box 1162BuraydahSaudi Arabia

Sentiment analysis, a crucial task in discerning emotional tones within the text, plays a pivotal role in understandingpublic opinion and user sentiment across diverse *** numerous scholars conduct sentiment analysisin widely spoken languages such as English, Chinese, Arabic, Roman Arabic, and more, we come to grapplingwith resource-poor languages like Urdu literature which becomes a challenge. Urdu is a uniquely crafted language,characterized by a script that amalgamates elements from diverse languages, including Arabic, Parsi, Pashtu,Turkish, Punjabi, Saraiki, and more. As Urdu literature, characterized by distinct character sets and linguisticfeatures, presents an additional hurdle due to the lack of accessible datasets, rendering sentiment analysis aformidable undertaking. The limited availability of resources has fueled increased interest among researchers,prompting a deeper exploration into Urdu sentiment analysis. This research is dedicated to Urdu languagesentiment analysis, employing sophisticated deep learning models on an extensive dataset categorized into fivelabels: Positive, Negative, Neutral, Mixed, and Ambiguous. The primary objective is to discern sentiments andemotions within the Urdu language, despite the absence of well-curated datasets. To tackle this challenge, theinitial step involves the creation of a comprehensive Urdu dataset by aggregating data from various sources such asnewspapers, articles, and socialmedia comments. Subsequent to this data collection, a thorough process of cleaningand preprocessing is implemented to ensure the quality of the data. The study leverages two well-known deeplearningmodels, namely Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN), for bothtraining and evaluating sentiment analysis performance. Additionally, the study explores hyperparameter tuning tooptimize the models’ efficacy. Evaluation metrics such as precision, recall, and the F1-score are employed to assessthe effectiv

关键词： Urdu sentiment analysis convolutional neural networks recurrent neural network deep learning natural language processing neural networks

A novel fractional case study of nonlinear dynamics via analytical approach

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Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 276-290页

作者： Hassan khan Adnan khan Rasool Shah Dumitru Baleanu Department of Mathematics Abdul Wali khan UniversityMardan 23200Pakistan Department of Mathematics Faculty of Arts and SciencesCankaya UniversityAnkara 06530Turkey Institute of Space Sciences Magurele-BucharestRomania

The present work describes the fractional view analysis of Newell-whitehead-Segal equations,using an innovative *** work is carried with the help of the Caputo operator of fractional *** analytical solutions of some numerical examples are presented to confirm the reliability of the proposed *** derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order ***,the solution in series form has the desired rate of convergence and provides the closed-form *** is noted that the procedure can be modified in other directions for fractional order problems.

关键词： Homotopy Perturbation method Shehu transform Newell-whitehead-Segel Equation Caputo operator