Browsing by Author "Siddique, Imran"

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Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3 + 1) -dimensional WBBM equation
(2023) Siddique, Imran; Mehdi, Khush Bukht; Jarad, Fahd; Elbrolosy, Mamdouh E.; Elmandouh, Adel A.
The nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied sciences. In this study, we observe the dynamical behavior of nonlinear traveling waves for the M-fractional (3 + 1)-dimensional Wazwaz-Benjamin-Bona-Mohany (WBBM) equation. Novel exact traveling wave solutions in the form of trigonometric, hyperbolic and rational functions are derived using (1/G′), modified (G′/G2) and new extended direct algebraic methods with the help of symbolic soft computation. We guarantee that all the obtained results are new and verified the main equation. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions, and this provides useful information about the dynamical behavior. Further, bifurcation behavior of nonlinear traveling waves of the proposed equation is studied with the help of bifurcation theory of planar dynamical systems. It is also observed that the proposed equation support the nonlinear solitary
Citation - WoS: 13
Citation - Scopus: 10
Bioconvection Attribution for Effective Thermal Transportation of Upper Convicted Maxwell Nanofluid Flow Due To an Extending Cylindrical Surface
(Elsevier, 2022) Siddique, Imran; Abdal, Sohaib; Jarad, Fahd; Ali, Rifaqat; Salamat, Nadeem; Hussain, Sajjad; Mariam, Amna
The growth of compact density heat gadgets demands effective thermal transportation. The option of nanofluid plays a dynamic role in this requirement. This research shows the impact of gyrotactic microorganisms on non-Newtonian fluid (Maxwell fluid) passing on the expanding cylindrical surface. The main objective of the present observation is to determine the heat and mass transportation of Maxwell nanofluid. The convective boundary condition and zero mass flux conditions are incorporated. In mathematical derivation, the approximation of the boundary layer is applied. The primal motivation pertains to exaggerating the thermal transport of heat exchangers in industrial processes. To attain the effects of Brownian motion as well as thermophoresis the Buongiorno nanofluid is utilized. By assimilating suitable transformation, the concluding simultaneous for a non-linear set of equations is tackled numerically by hiring Runge-Kutta procedure. The coding is developed and run in the Matlab environment. The leading partial differential system is converted into an ordinary differential system. The role of emerging parameters is elaborated. Also tangible quantities i.e. Skin friction factor, Nusselt number, Sherwood number, and motile density coefficient are enumerated. An accession in the magnetic field causes depreciation in the velocity profile. Where increment in Schmidt number Sc causes a decrement in Sherwood number. The suitable ranges of parameters where increasing or decreasing behavior becomes smooth are taken as 0.0 <= M <= 6.0, 0.0 <= gamma <= 0.8, 0.7 <= Pr <= 1.0, 0.1 <= Nt <= 0.7, 0.01 <= Nb <= 0.1, 3.0 <= Sc <= 6.0, 2.0 <= Lb <= 7.0, 0.1 <= Pe <= 0.7 and 1.0 <= delta <= 7.0. The applications of the current study can be seen in chemical and metallurgical industries, the process of thermo-fluid, power generation, executed via condensers, cooling, and heating in large buildings, transportation, etc.
Citation - WoS: 11
Citation - Scopus: 15
Engine Oil Based Mos2 Casson Nanofluid Flow With Ramped Boundary Conditions and Thermal Radiation Through a Channel
(Elsevier, 2022) Sadiq, Kashif; Jaradat, Mohammed M. M.; Ali, Rifaqat; Jarad, Fahd; Siddique, Imran
The modern era is a time to have cost-effective and energy-efficient technology. This demand has made nanotechnology the most effective field. The focus of this article is to increase the efficiency of engine oil (EO). The flow of EO-based Casson nanofluid containing Molybdenum disulfide (MoS2) nanoparticles is investigated with ramped wall conditions and thermal radiation. Analytical results are calculated via the Laplace transform. The impact of physical parameters on isothermal and ramped conditions is illustrated graphically and discussed in detail. The researchers found that flow, mass, and energy can be controlled by using ramped conditions. The variation in concentration, temperature, and velocity is exponential for isothermal conditions and steady for ramped wall conditions. Finally, the results of Nusselt numbers, skin frictions, and Sherwood numbers on both walls of the channel for both isothermal and ramped conditions are graphically depicted and discussed. For higher values of time the results of ramped and isothermal wall conditions are identical. It is found that the nanoparticles of MoS2 enhance the lubrication and heat transport rates of EO.
Citation - WoS: 32
Citation - Scopus: 38
Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Set With Their Application To Solve Multi-Attribute Group Decision Making Problem
(Tech Science Press, 2022) Zulqarnain, Rana Muhammad; Siddique, Imran; Iampan, Aiyared; Baleanu, Dumitru
Interval-valued Pythagorean fuzzy soft set (IVPFSS) is a generalization of the interval-valued intuitionistic fuzzy soft set (IVIFSS) and interval-valued Pythagorean fuzzy set (IVPFS). The IVPFSS handled more uncertainty comparative to IVIFSS; it is the most significant technique for explaining fuzzy information in the decision-making process. In this work, some novel operational laws for IVPFSS have been proposed. Based on presented operational laws, two innovative aggregation operators (AOs) have been developed such as interval-valued Pythagorean fuzzy soft weighted average (IVPFSWA) and interval-valued Pythagorean fuzzy soft weighted geometric (IVPFSWG) operators with their fundamental properties. A multi-attribute group decision-making (MAGDM) approach has been established utilizing our developed operators. A numerical example has been presented to ensure the validity of the proposed MAGDM technique. Finally, comparative studies have been given between the proposed approach and some existing studies. The obtained results through comparative studies show that the proposed technique is more credible and reliable than existing approaches.
Citation - WoS: 35
Citation - Scopus: 45
Numerical Simulation of Mhd Couette Flow of a Fuzzy Nanofluid Through an Inclined Channel With Thermal Radiation Effect
(Hindawi Ltd, 2021) Zulqarnain, Rana Muhammad; Nadeem, Muhammad; Jarad, Fahd; Siddique, Imran
The present study especially concerns the investigation of the Couette flow and heat transfer with thermal radiation through an inclined channel. Single-wall carbon nanotube (SWCNT) and multiple-wall carbon nanotube (MWCNT) are nanoparticles embedded in the host fluid. The dimensionless highly nonlinear differential equations (DEs) are solved via numerical scheme bvp4c. The effects of the physical parameters on heat transfer are presented in the form of graphs. The results demonstrate that the heat transfer is enhanced by using solid particle frictions (SWCNT and MWCNT). The large estimation of a magnetic parameter declines the velocity component. The current and existing results with their comparisons are shown in the tabular form for the validation of our code. The current results are in good agreement with their existing results. Generally, fuzziness or uncertainty is inherent in modeling, analysis, and experimentation. Due to the uncertain environmental conditions, fuzziness broadly exists in various engineering heat transfer problems. In this work, the nanoparticles' volume fraction of the SWCNT and MWCNT is taken as uncertain parameters in terms of triangular fuzzy numbers (TFNs). The TFNs are controlled by the alpha-cut which has less computational effort for analyzing the fuzziness or uncertainties. Also, a comparison between the SWCNT and MWCNT through the membership function and the variability of the uncertainty is studied.
Citation - WoS: 23
Citation - Scopus: 23
Significance of Double Diffusion for Unsteady Carreau Micropolar Nanofluid Transportation Across an Extending Sheet With Thermo-Radiation and Uniform Heat Source
(Elsevier, 2021) Siddique, Imran; Jarad, Fahd; Ali, Rifaqat; Abdal, Sohaib; Hussain, Sajjad; Afzal, Saima
The main objective of this manuscript is to glance into the assets of nanoparticles in the stream of generalized micropolar fluid and Carreau fluid against an intensified elongated surface. In order to assess, the heat and mass diffusion occurrences, the Cattaneo-Christov implications are also experienced in the temperature and concentration computations. In contrast to prior studies, rheological attributes on non-Newtonian fluids are depicted by engaging micropolar fluid and Carreau liquid that reflect a clear difference of transport phenomena. By minimizing the number of independent factors, the regulating equations are transmuted into non-dimensional types, that are then tackled numerically using the RK-4 algorithm along with the shooting strategy. For velocity, micro-rotation, temperature and concentration distributions, a visualization evaluation of the entangled flow parameters is executed. It has been revealed that expanding magnetic and micropolar constraints enhance micro-rotation velocity. The unsteadiness parameter enhances all three physical quantities, surface drag force, Nusselt number, and Sherwood number.
Citation - WoS: 13
Citation - Scopus: 29
Selection of an Effective Hand Sanitizer To Reduce Covid-19 Effects and Extension of Topsis Technique Based on Correlation Coefficient Under Neutrosophic Hypersoft Set
(Wiley-hindawi, 2021) Ali, Rifaqat; Siddique, Imran; Jarad, Fahd; Abdeljawad, Thabet; Samad, Abdul; Zulqarnain, Rana Muhammad; Sermutlu, Emre
Correlation coefficients are used to tackle many issues that include indistinct as well as blurred information excluding is not able to deal with the general fuzziness along with obscurity of the problems that have various information. The correlation coefficient (CC) between two variables plays an important role in statistics. Likewise, the accuracy of relevance assessment depends on the information in a set of discourses. The data collected for numerous statistical studies is full of exceptions. The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The core objective of follow-up research is to develop the concept and characteristics of CC and the weighted correlation coefficient (WCC) of NHSS. We also introduced some aggregation operators in the considered environment, which can help us establish a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) based on CC and WCC under NHSS. A decision-making strategy is established to solve multicriteria group decision-making (MCGDM) problems utilizing developed methodology. Moreover, the proposed method is utilized for the selection of an effective hand sanitizer during the COVID-19 pandemic to ensure the validity of the proposed approach. The practicality, effectivity, and flexibility of the current approach are proved through comparative analysis with the assistance of some existing studies.
Citation - WoS: 44
Citation - Scopus: 59
Numerical Solution of 3D Rotating Nanofluid Flow Subject To Darcy-Forchheimer Law, Bio-Convection and Activation Energy
(Elsevier B.V., 2022) Tayyab, Muhammad; Siddique, Imran; Jarad, Fahd; Ashraf, Muhammad Kamran; Ali, Bagh
This work discourses the dynamics of three dimensional rotating nanofluid flows subject to magnetohydrodynamic, Darcy-Forchheimer law, bioconvection self-motive microorganism, and activation energy. The numerical procedure is indicated when close agreement of the current finding is attained in comparison with the existing ones as limiting case. The leading equations based on preservation of mass, momentum, and energy are formulated with partial derivatives which are then transmuted into dimensionless differential form with the enactment of apposite similarity transformations. So, to tackle the non-linearity of these equations, numerical procedure based on shooting technique and Runge-Kutta method is bound to be coded on MATLAB platform. The emerging parameters are varied to observe the change of microorganism distribution, velocity, concentration of nano species, and temperature distribution. Results are displayed graphically and discussed. It is noticed that liquid velocity is decelerated against the constraints of inertia and porosity. The temperature field is strengthened with thermophoresis and Brownian motion. The concentrations of nanoparticle and microorganism are depreciated against Lewis number and bio-Lewis number respectively. The concentration of microorganism is improved for greater peclet number Pe but it lessens with growth in bioconvection Lewis numberLb. The function 8(i) and rp(i) showed increasing response to thermophoresis parameter Nt. The parameter of Brownian motion has noticeable growing impact on concentration of nano particles but decreasing Nb for 8(i) temperature.
Citation - WoS: 26
Citation - Scopus: 32
Study of Triangular Fuzzy Hybrid Nanofluids on the Natural Convection Flow and Heat Transfer Between Two Vertical Plates
(Hindawi Ltd, 2021) Elmoasry, Ahmed; Siddique, Imran; Jarad, Fahd; Zulqarnain, Rana Muhammad; Alebraheem, Jawdat; Elazab, Naseer S.; Nadeem, Muhammad
The prime objective of the current study is to examine the effects of third-grade hybrid nanofluid with natural convection utilizing the ferro-particle Fe(3)O(4)and titanium dioxide TiO2 and sodium alginate (SA) as a host fluid, flowing through vertical parallel plates, under the fuzzy atmosphere. The dimensionless highly nonlinear coupled ordinary differential equations are computed adopting the bvp4c numerical approach. This is an extremely effective technique with a low computational cost. For validation, it is found that as the volume fraction of Fe3O4+TiO2 hybrid nanoparticles rises, so does the heat transfer rate. The current and existing results with their comparisons are shown in the form of the tables. The present findings are in good agreement with their previous numerical and analytical results in a crisp atmosphere. The nanoparticles volume fraction of Fe(3)O(4 & nbsp;)and TiO2 is taken as uncertain parameters in terms of triangular fuzzy numbers (TFNs) [0, 0.05, 0.1]. The TFNs are controlled by a-cut and the variability of the uncertainty is studied through triangular membership function (MF).
Citation - WoS: 11
Citation - Scopus: 18
An Approach of Decision-Making Under the Framework of Fermatean Fuzzy Sets
(Hindawi Ltd, 2022) Ahsan, Muhammad; Jarad, Fahd; Altunok, Taner; Sindhu, Muhammad Sarwar; Siddique, Imran
Because of its influence on various elements of human life experiences and conditions, the building industry is a significant business. In the recent past, environmental considerations have been incorporated in the design and planning stages of building supply chains. The process of evaluating and selecting suppliers is one of the most important issues in supply chain management. A multicriteria decision-making (MCDM) problem can be utilized to handle such issues. The goal of this research is to present a new and efficient technique for selecting suppliers with ambiguous data. The suggested methodology's structure is based on technology for order of preference by similarity to ideal solution (TOPSIS), with Fermatean fuzzy sets (F-r FSs) employed to cope with information uncertainty. In this article, authors modified the distance between F-r FSs to propose the similarity measure and implemented it to form the MCDM model to resolve the vague and uncertain data. Moreover, we used this similarity measure to choose the optimal alternative. A practical example for alternative selection is provided, along with a comparison of the acquired findings to existing approach. Finally, to strengthen the outcome obtained through the proposed model, sensitivity analysis and time complexity analysis are performed.
Citation - WoS: 19
Citation - Scopus: 21
Bioconvection of Mhd Second-Grade Fluid Conveying Nanoparticles Over an Exponentially Stretching Sheet: a Biofuel Applications
(Springer Heidelberg, 2023) Nadeem, Muhammad; Ali, Rifaqat; Jarad, Fahd; Siddique, Imran
The current research examines the role of chemical reaction, nonlinear thermal radiation and slippage impact on magnetic second-grade fluid flow with diluted dispersion of nanoparticles using a theoretical bioconvection model over an exponentially stretched sheet. There are also new characteristics such as Brownian motion and thermophoresis. In the problem formulation, the boundary layer approximation is used. Using the suitable transformations, the energy, momentum, micro-organisms and concentration equations are generated into nonlinear ordinary differential equations (ODEs). The solution to the resultant problems was calculated via the Homotopy analysis method (HAM). Environmental parameters' effects on velocity, temperature, microbes and concentration profiles are graphically displayed. When comparing the current results to the previous literature, there was also a satisfactory level of agreement. In comparison with a flow based on constant characteristics, the flow with variable thermal conductivity is shown to be significantly different and realistic. The temperature and motile density of the fluid grew in direct proportion to the thermophoresis motion, buoyancy ratio and Brownian motion parameters. Also, the motile density profile decreases down for Pe and Lb while increasing when bioconvection Rayleigh number and buoyancy ratio. This work is significant to bioinspired nanofluid enhanced fuel cells and nanomaterials production techniques, according to these research studies.
Citation - WoS: 35
Citation - Scopus: 36
Einstein Aggregation Operators for Pythagorean Fuzzy Soft Sets With Their Application in Multiattribute Group Decision-Making
(Wiley, 2022) Iampan, Aiyared; Siddique, Imran; Jarad, Fahd; Hamed, Y. S.; Abualnaja, Khadijah M.; Zulqarnain, Rana Muhammad
The Pythagorean fuzzy soft set (PFSS) is the most proficient and manipulative leeway of the Pythagorean fuzzy set (PFS), which contracts with parameterized values of the alternatives. It is a generalized form of the intuitionistic fuzzy soft set (IFSS), which provides healthier and more accurate evaluations through decision-making (DM). The main determination of this research is to prolong the idea of Einstein's aggregation operators for PFSS. We introduce the Einstein operational laws for Pythagorean fuzzy soft numbers (PFSNs). Based on Einstein operational laws, we construct two novel aggregation operators (AOs) such as Pythagorean fuzzy soft Einstein-weighted averaging (PFSEWA) and Pythagorean fuzzy soft Einstein-weighted geometric (PFSEWG) operators. In addition, important possessions of proposed operators, such as idempotency, boundedness, and homogeneity, are discussed. Furthermore, to validate the practicability of the anticipated operators, a multiple attribute group decision-making (MAGDM) method is developed. We intend innovative AOs considering the Einstein norms for PFSS to elect the most subtle business. Pythagorean fuzzy soft numbers (PFSNs) support us to signify unclear data in real-world perception. Furthermore, a numerical description is planned to certify the efficacy and usability of the projected method in the DM practice. The recent approach's pragmatism, usefulness, and tractability are validated through comparative exploration with the support of some prevalent studies.
Citation - WoS: 12
Citation - Scopus: 15
A Survey on Generalized Topological Indices for Silicon Carbide Structure
(Hindawi Ltd, 2022) Mahboob, Abid; Siddique, Imran; Altunok, Taner; Waheed Rasheed, Muhammad; Alam, Sajid Mahboob; Jarad, Fahd
The application of graphs in chemical and molecular structures has exponentially increased during the last few years. Topological indices facilitate the collection of beneficial information and provide an approach to understanding the properties of chemical structure by providing information about algebraic graphs. Let G be a graph with u-vertices and omega u be the degree of uth vertex. In this manuscript, we compute Zagreb index (ZI), first, and second, Hyper F-indices and sum and product connectivity of F-index of silicon carbides, namely, SiC4 - I[r, s] and SiC4 - II[r, s].
Citation - WoS: 10
Citation - Scopus: 10
Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set With Their Application To Solve Mcdm Problem
(Tech Science Press, 2023) Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; Iampan, Aiyared; Zulqarnain, Rana Muhammad
Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval -valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.
Citation - WoS: 8
Citation - Scopus: 10
Aggregation Operators for Interval-Valued Intuitionistic Fuzzy Hypersoft Set With Their Application in Material Selection
(Hindawi Ltd, 2022) Zulqarnain, Rana Muhammad; Siddique, Imran; Jarad, Fahd; Karamti, Hanen; Iampan, Aiyared
The intuitionistic fuzzy hypersoft set (IFHSS) is the most generalized form of the intuitionistic fuzzy soft set used to resolve uncertain and vague data in the decision-making process, considering the parameters' multi-sub-attributes. Aggregation operators execute a dynamic role in assessing the two prospect sequences and eliminating anxieties from this perception. This paper prolongs the IFHSS to interval-valued IFHSS (IVIFHSS), which proficiently contracts with hesitant and unclear data. It is the most potent technique for incorporating insecure data into decision-making (DM). The main objective of this research is to develop the algebraic operational laws for IVIFHSS. Furthermore, using the algebraic operational law, some aggregation operators (AOs) for IVIFHSS have been presented, such as interval-valued intuitionistic fuzzy hypersoft weighted average (IVIFHSWA) and interval-valued intuitionistic fuzzy hypersoft weighted geometric (IVIFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) technique is vigorous for material selection. However, conventional methods of MCGDM regularly provide inconsistent results. Based on the expected AOs, industrial enterprises propose a robust MCGDM material selection method to meet this shortfall. The real-world application of the planned MCGDM method for cryogenic storing vessel material selection (MS) is presented. The implication is that the designed model is more efficient and consistent in handling information based on IVIFHSS.
Citation - WoS: 6
Citation - Scopus: 6
Dufour Effect on Transient Mhd Double Convection Flow of Fractionalized Second-Grade Fluid With Caputo-Fabrizio Derivative
(Wiley-hindawi, 2021) Ayaz, Sehrish; Jarad, Fahd; Siddique, Imran
This article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo-Fabrizio (CF) with nonsingular kernel, respectively. The Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields. Expressions for the skin friction and rates of heat and mass transfer from the plate to fluid with noninteger and integer orders, respectively, are also determined. Furthermore, the influence of flow parameters and fractional parameters alpha and beta on the concentration, temperature, and velocity fields are tabularly and graphically underlined and discussed. Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. This shows how the fractional parameters affect the fluid flow.
Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3 + 1) -dimensional WBBM equation
Siddique, Imran; Mehdi, Khush Bukht; Jarad, Fahd; Elbrolosy, Mamdouh E.; Elmandouh, Adel A.
The nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied sciences. In this study, we observe the dynamical behavior of nonlinear traveling waves for the M-fractional (3 + 1)-dimensional Wazwaz-Benjamin-Bona-Mohany (WBBM) equation. Novel exact traveling wave solutions in the form of trigonometric, hyperbolic and rational functions are derived using (1/G′), modified (G′/G2) and new extended direct algebraic methods with the help of symbolic soft computation. We guarantee that all the obtained results are new and verified the main equation. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions, and this provides useful information about the dynamical behavior. Further, bifurcation behavior of nonlinear traveling waves of the proposed equation is studied with the help of bifurcation theory of planar dynamical systems. It is also observed that the proposed equation support the nonlinear solitary wave, periodic wave, kink and antikink waves and most important supernonlinear periodic wave. © 2023 World Scientific Publishing Company.
Citation - WoS: 33
Citation - Scopus: 39
Numerical Study of Mhd Third-Grade Fluid Flow Through an Inclined Channel With Ohmic Heating Under Fuzzy Environment
(Hindawi Ltd, 2021) Siddique, Imran; Jarad, Fahd; Jamil, Raja Noshad; Nadeem, Muhammad
The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette-Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of alpha-cut approach, which controls the fuzzy uncertainty. It is observed that the fuzzy gravitational and magnetic parameters are less sensitive for a better flow and heat situation. Using triangular fuzzy numbers (TFNs), the left, right, and mid values of the velocity and temperature profile are presented due to various values of the involved parameters in tabular form. For validation, the present results are compared with existing results for some special cases, viz., crisp case, and they are found to be in good agreement.
Citation - Scopus: 1
Minimal Doubly Resolving Sets of Certain Families of Toeplitz Graph
(Tech Science Press, 2023) Jarad, Fahd; Zahid, Zohaib; Siddique, Imran; Ahmad, Muhammad
The doubly resolving sets are a natural tool to identify where diffusion occurs in a complicated network. Many real-world phenomena, such as rumour spreading on social networks, the spread of infectious diseases, and the spread of the virus on the internet, may be modelled using information diffusion in networks. It is obviously impractical to monitor every node due to cost and overhead limits because there are too many nodes in the network, some of which may be unable or unwilling to send information about their state. As a result, the source localization problem is to find the number of nodes in the network that best explains the observed diffusion. This problem can be successfully solved by using its relationship with the well-studied related minimal doubly resolving set problem, which minimizes the number of observers required for accurate detection. This paper aims to investigate the minimal doubly resolving set for certain families of Toeplitz graph T-n(1, t), for t >= 2 and n >= t + 2. We come to the conclusion that for T-n(1, 2), the metric and double metric dimensions are equal and for T-n(1, 4), the double metric dimension is exactly one more than the metric dimension. Also, the double metric dimension for T-n(1, 3) is equal to the metric dimension for n = 5, 6, 7 and one greater than the metric dimension for n >= 8.
Citation - WoS: 8
Citation - Scopus: 8
Analysis of Natural Convection in Nanofluid Flow Through a Channel With Source/Sink Effect
(Hindawi Ltd, 2022) Sadiq, Kashif; Jarad, Fahd; Al Mesfer, Mohammed K.; Danish, Mohd; Yaqoob, Sonia; Siddique, Imran
In this study, the natural convection nanofluids flow through a channel formed by two vertical parallel plates having distance d between them has been examined under the influence of the ramped velocity. Sodium alginate is considered as base fluid, and nanoparticles of titania (TiO2) and alumina (Al2O3) are added to it. Analytical and semianalytical results for temperature and velocity profiles are obtained with Laplace transform and inverse Laplace algorithms (Tzou, Stehfest, Talbot, Honig and Hirdes, and Fourier series), respectively. Furthermore, the impacts of nanoparticles, Prendtl number, heat absorption, and time on velocity and temperature are drawn graphically and discussed. The outcomes show that the high thermal conductivity of particles increases the temperatures, and the high density of particles decreases the velocities of the nanofluids. The current findings are compared to previous findings in the literature. In the tables, the effect of volume fraction on Nusselt numbers and skin frictions is explored.