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Öğe A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs(Cell Press, 2024) Ali, Nasir; Siddiqui, Hafiz Muhammad Afzal; Riaz, Muhammad Bilal; Qureshi, Muhammad Imran; Akgul, AliThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZDgraphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if their product results in zero (x . y = 0). The set of zero divisors in ring R is referred to as L(R). To analyze various algebraic properties of R, a graph known as the zero-divisor graph is constructed using L(R). This manuscript establishes specific general bounds for the dominant metric dimension (Ddim) concerning the ZD-graph of R. To achieve this objective, we examine the zero divisor graphs for specific rings, such as the ring of Gaussian integers modulo m, denoted as Zm[i], the ring of integers modulo n, denoted as Zn, and some quotient polynomial rings. Our research unveils new insights into the structural similarities and differences among commutative rings sharing identical metric dimensions and dominant metric dimensions. Additionally, we present a general result outlining bounds for the dominant metric dimension expressed in terms of the maximum degree, girth, clique number, and diameter of the associated ZD-graphs. Through this exploration, we aim to provide a comprehensive framework for analyzing commutative rings and their associated zero divisor graphs, thereby advancing both theoretical knowledge and practical applications in diverse domains.Öğe A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect(Elsevier B.V., 2023) Ahmad, Bilal; Ozair Ahmad, Muhammad; Farman, Muhammad; Akgül, Ali; Riaz, Muhammad BilalThe aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations are nonlinear, the partial differential equations are transformed into ordinary differential equations using a workable similarity transformation. By using the Bvp4c module of the MATLAB program, the simplified mathematical framework can be numerically solved. The computation of Coefficients of skin friction, Nusselt numbers, different patterns of velocity profiles, fluid temperature, and concentration profiles reveals the physical nature of this study. As compared to earlier investigations, it was found that the obtained results demonstrated high degrees of symmetry and precision. A decline observes in velocity for boosted values of MHD, inclination, and rotatory parameter. However thermal transportation increases by increasing brownien motion, thermophoresis, radiation and Sorrot effect. The study has significant application in heat control systems, food factories, thermal exchangers, biomechanics, biomedical engineering, and aero dynamical systems © 2022Öğe Characteristics of heat transportation in MHD flow of chemical reactive micropolar nanofluid with moving slip conditions across stagnation points(Elsevier, 2024) Jawad, Muhammad; Khalifa, Hamiden Abd El-Wahed; Shaaban, Abeer A.; Akgul, Ali; Riaz, Muhammad Bilal; Sadiq, NaeemIn current study, the steady electrically conducting flow of micropolar nanofluid past a porous stretched surface across stagnation points is investigated. For motivation of problem, the impressions of the nonlinear thermal radiation and convectively heated have been analyzed. In additions, the influence of thermophoresis and heat transfer are the part of this study. The governing firm of PDEs are converted to a system of nonlinear and coupled ODEs using the similarity approach. Moreover, the resulting problem is numerically integrated with the aid of shooting approach by utilizing the bvp4c programmer of MATLAB. The numerical outcomes are calculated using various physical parameter values and contrasted with previously published results. Numerical values of the physical quantities like velocity, micropolar rotation, temperature and concentration profile for involving parameters such as Prandtl number Pr, radiation R, slip parameter alpha, thermophoresis Nt, suction/injection velocity fw, Brownian motion Nb, magnetic parameter M and Lewis number Le are also computed and deliberated in this consideration.Öğe Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm(Elsevier, 2023) Qayyum, Mubashir; Khan, Amna; Saeed, Syed Tauseef; Akgul, Ali; Riaz, Muhammad BilalParabolic equations play an important role in chemical engineering, vibration theory, particle diffusion and heat conduction. Solutions of such equations are required to analyze and pre-dict changes in physical systems. Solutions of such equations require efficient and effective tech-niques to get reasonable accuracy in lesser time. For this purpose, current article proposes residual power series algorithm for higher order parabolic equations with variable coefficients in multiple dimensions. The proposed algorithm provides closed-form solutions without linearization, discretization or perturbation. For efficiency testing of the proposed methodology, initially it is implemented to homogeneous multidimensional parabolic models, and exact solutions are com-puted. In next stage of testing, proposed algorithm is enforced to three-dimensional non-homoge-neous fourth order parabolic equation, and closed form solutions are recovered. The obtained results indicate the validity and effectiveness of proposed methodology, hence proposed algorithm can be extended to more complex scenarios in engineering and sciences. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Öğe Comparative analysis of numerical with optical soliton solutions of stochastic Gross-Pitaevskii equation in dispersive media(Elsevier, 2023) Baber, Muhammad Zafarullah; Ahmed, Nauman; Yasin, Muhammad Waqas; Iqbal, Muhammad Sajid; Akgul, Ali; Riaz, Muhammad Bilal; Rafiq, MuhammadThis article deals with the stochastic Gross-Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation (SSE) and modified exponential rational functional (MERF) techniques. The exact solutions are constructed in the form of exponential, hyperbolic, and trigonometric forms. Finally, the comparison of the exact solutions with numerical solutions is drawn in the 3D and line plots for the different values of parameters.Öğe Complex dynamics of multi strain TB model under nonlocal and nonsingular fractal fractional operator(Elsevier, 2021) Adnan; Ahmad, Shabir; Ullah, Aman; Riaz, Muhammad Bilal; Ali, Amir; Akgul, Ali; Partohaghighi, MohammadResearchers have recently begun to use fractal fractional operators in the Atangana-Baleanu sense to analyze complicated dynamics of various models in applied sciences, as the Atangana-Baleanu operator generalizes the integer and fractional order operators. To analyze the complex dynamics of the multi-strain TB model, we use the AB-fractal fractional operator. We use the Banach fixed point theorem to ensure that at most one solution exists to the model. Further, the Ulam-Hyers type stability of the model is investigated with the help of functional analysis. The Adams-Bashforth approach is used to get numerical results for the proposed model. The analysis of the chaotic behavior of the proposed TB model was missing in the literature. Therefore, for different values of fractional and fractal order, we study the nonlinear dynamics and chaotic behavior of the obtained results of the proposed model.Öğe Computational analysis of microgravity and viscous dissipation impact on periodical heat transfer of MHD fluid along porous radiative surface with thermal slip effects(Elsevier, 2024) Alqahtani, Bader; El-Zahar, Essam R.; Riaz, Muhammad Bilal; Seddek, Laila F.; Ilyas, Asifa; Ullah, Zia; Akgul, AliThe current thermal slip and Magnetohydrodynamic analysis plays prominent importance in heat insulation materials, polishing of artificial heart valves, heat exchangers, magnetic resonance imaging and nanoburning processes. The main objective of the existing article is to deliberate the impact of thermal slip, thermal radiation and viscous dissipation on magnetized cone embedded in a porous medium under reduced gravitational pressure. Convective heating characteristics are used to increase the rate of heating throughout the porous cone. For viscous flow along a heated and magnetized cone, the conclusions are drawn. The simulated nonlinear partial differential equations are transformed into a dimensionless state by means of suitable non -dimensional variables. The technique of finite differences is implemented to solve the given model with Gaussian elimination approach. The FORTRAN language is used to make uniform algorithm for asymptotic results according to the boundary conditions. The influence of controlling parameters, such as thermal radiation parameter R d , Prandtl number P r , porosity parameter Omega , viscous dissipation parameter E c , delta thermal slip parameter, R g reduced gravity parameter and mixed convection parameter lambda is applied. Graphical representations were created to show the consequences of various parameters on velocity, temperature and magnetic field profiles along with fluctuating skin friction, fluctuating heat and oscillatory current density. It is found that velocity and temperature profile enhances as radiation parameter enhances. It is noted that the amplitude and oscillations in heat transfer and electromagnetic waves enhances as magnetic Prandtl factor increases.Öğe Effect of Magnetic Field with Parabolic Motion on Fractional Second Grade Fluid(Mdpi, 2021) Iftikhar, Nazish; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Akgul, AliThis paper is an analysis of the flow of magnetohydrodynamics (MHD) second grade fluid (SGF) under the influence of chemical reaction, heat generation/absorption, ramped temperature and concentration and thermodiffusion. The fluid was made to flow through a porous medium. It has been proven in many already-published articles that heat and mass transfer do not always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such a dynamical process very accurately; thus, a different concept of differentiation is needed to capture such a process. Very recently, new classes of differential operators were introduced and have been recognized to be efficient in capturing processes following the power law, the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in Caputo sense (ABC) fractional derivatives. The Laplace transform, inversion algorithm and convolution theorem were used to derive the exact and semi-analytical solutions for all cases. The obtained analytical solutions were plotted for different values of existing parameters. It is concluded that the fluid velocity shows increasing behavior for ? , G(r) and G(m), while velocity decreases for P-r and M. For K-r, both velocity and concentration curves show decreasing behavior. Fluid flow accelerates under the influence of S-r and R. Temperature and concentration profiles increase for S-r and R. Moreover, the ABC fractional operator presents a larger memory effect than C and CF fractional operators.Öğe Einstein Aggregation Operators under Bipolar Neutrosophic Environment with Applications in Multi-Criteria Decision-Making(Mdpi, 2022) Jamil, Muhammad; Afzal, Farkhanda; Akgul, Ali; Abdullah, Saleem; Maqbool, Ayesha; Razzaque, Abdul; Riaz, Muhammad BilalIn this article, we introduce bipolar neutrosophic (BN) aggregation operators (AOs) as a revolutionary notion in aggregation operators (AOs) by applying Einstein operations to bipolar neutrosophic aggregation operators (AOs), with its application related to a real-life problem. The neutrosophic set is able to drawout the incomplete, inconsistent and indeterminate information pretty efficiently. Initially, we present essential definitions along with operations correlated to the neutrosophic set (NS) and its generalization, the bipolar neutrosophic set (BNS). The Einstein aggregation operators are our primary targets, such asthe BN Einstein weighted average (BNEWA), BN Einstein ordered weighted average (BNEOWA), BN Einstein hybrid average (BNEHA), BN Einstein weighted geometric (BNEWG), BN Einstein ordered weighted geometric (BNEOWG) and BN Einstein hybrid geometric (BNEHG), as well as their required properties. The most important benefit of using the suggested approaches is that they provide decision-makers with complete sight of the issue. These techniques, when compared to other methods, provide complete, progressive and precise findings. Lastly, by means of diverse types of newly introduced aggregation operators and a numerical illustration by an example, we suggest an innovative method to be used for multi-criteria community decision-making (DM). This illustrates the utility and applicability of this new strategy when facing real-world problems.Öğe Exact Analysis of Second Grade Fluid with Generalized Boundary Conditions(Tech Science Press, 2021) Saeed, Syed Tauseef; Riaz, Muhammad Bilal; Baleanu, Dumitru; Akg, Ali; Husnine, Syed MuhammadConvective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by mass transfer process; for instance condensation, evaporation and chemical process. Due to the applications of the heat and mass transfer combined effects in different field, the main aim of this paper is to do comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of time dependent generalized boundary conditions. The non-dimensional forms of the governing equations of the model are developed. These are solved by the classical integral (Laplace) transform technique/method with the convolution theorem and closed form solutions are developed for temperature, concentration and velocity. Obtained generalized results are very important due to their vast applications in the field of engineering and applied sciences. The attained results are in good agreement with the published results. Additionally, the impact of thermal radiation with the magnetic field is also analyzed. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.Öğe Exact solutions involving special functions for unsteady convective flow of magnetohydrodynamic second grade fluid with ramped conditions(Springer, 2021) Riaz, Muhammad Bilal; Abro, Kashif Ali; Abualnaja, Khadijah M.; Akgul, Ali; Rehman, Aziz Ur; Abbas, Muhammad; Hamed, Y. S.A number of mathematical methods have been developed to determine the complex rheological behavior of fluid's models. Such mathematical models are investigated using statistical, empirical, analytical, and iterative (numerical) methods. Due to this fact, this manuscript proposes an analytical analysis and comparison between Sumudu and Laplace transforms for the prediction of unsteady convective flow of magnetized second grade fluid. The mathematical model, say, unsteady convective flow of magnetized second grade fluid, is based on nonfractional approach consisting of ramped conditions. In order to investigate the heat transfer and velocity field profile, we invoked Sumudu and Laplace transforms for finding the hidden aspects of unsteady convective flow of magnetized second grade fluid. For the sake of the comparative analysis, the graphical illustration is depicted that reflects effective results for the first time in the open literature. In short, the obtained profiles of temperature and velocity fields with Laplace and Sumudu transforms are in good agreement on the basis of numerical simulations.Öğe Fractal-fractional Klein-Gordon equation: A numerical study(Elsevier, 2022) Partohaghighi, Mohammad; Mirtalebi, Zahrasadat; Akgul, Ali; Riaz, Muhammad BilalIn this work, we solve a new kind of the fractional Klein-Gordon problem numerically. In fact, we study the mentioned problem under fractal-fractional operator with the Riemann-Liouville frame with Mittag-Leffler kernel. We use an efficient operational matrix (OM) technique employing the shifted Chebyshev cardinal functions (CCFs) to get the approximate solutions of the considered equation. Moreover, an OM for the considered derivative is gained using the basic functions. To get the approximate solutions of the presented equation we change the principal model into an algebraic system. To see the numerical results of the problem, we provide the related graphs of the exact and approximate solutions along with the absolute errors of each example. The accuracy and reliability of the numerical solutions can be found form the figures. Also, for each example Tables displaying the values of solutions and errors are reported.Öğe Fractal-fractional operator for COVID-19 (Omicron) variant outbreak with analysis and modeling(Elsevier, 2022) Farman, Muhammad; Amin, Maryam; Akguel, Ali; Ahmad, Aqeel; Riaz, Muhammad Bilal; Ahmad, SherazThe fractal-fraction derivative is an advanced category of fractional derivative. It has several approaches to real-world issues. This work focus on the investigation of 2nd wave of Corona virus in India. We develop a time-fractional order COVID-19 model with effects of disease which consist system of fractional differential equations. Fractional order COVID-19 model is investigated with fractal-fractional technique. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. Fractional order system is analyzed qualitatively as well as verify sensitivity analysis. The existence and uniqueness of the fractional-order model are derived using fixed point theory. Also proved the bounded solution for new wave omicron. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the actual behavior of the OMICRON virus. Such kind of analysis will help to understand the behavior of the virus and for control strategies to overcome the disseise in community.Öğe Further study of eccentricity based indices for benzenoid hourglass network(Cell Press, 2023) Iqbal, Hifza; Aftab, Muhammad Haroon; Akgul, Ali; Mufti, Zeeshan Saleem; Yaqoob, Iram; Bayram, Mustafa; Riaz, Muhammad BilalTopological Indices are the mathematical estimate related to atomic graph that corresponds biological structure with several real properties and chemical activities. These indices are invariant of graph under graph isomorphism. If top(h1) and top(h2) denotes topological index h1 and h2 respectively then h1 approximately equal h2 which implies that top(h1) = top(h2). In biochemistry, chemical science, nano-medicine, biotechnology and many other science's distance based and eccentricity-connectivity(EC) based topological invariants of a network are beneficial in the study of structure-property relationships and structure-activity relationships. These indices help the chemist and pharmacist to overcome the shortage of laboratory and equipment. In this paper we calculate the formulas of eccentricity-connectivity descriptor(ECD) and their related polynomials, total eccentricity-connectivity(TEC) polynomial, augmented eccentricityconnectivity(AEC) descriptor and further the modified eccentricity-connectivity(MEC) descriptor with their related polynomials for hourglass benzenoid network.Öğe Heat and Flow Control in Cavity with Cold Circular Cylinder Placed in Non-Newtonian Fluid by Performing Finite Element Simulations(Mdpi, 2022) Bilal, Sardar; Khan, Noor Zeb; Shah, Imtiaz Ali; Awrejcewicz, Jan; Akgul, Ali; Riaz, Muhammad BilalA study on strategies regarding advancement in heat transfer characteristics in two-dimensional closed domains by placing cold cylinders is conducted. This effort is undertaken due to the fact that active and passive control in heat transmission is connected with provision of temperature differences at different locations of enclosures. Based on the experiments, researchers have concluded that placement of cold cylinder in non-uniformly distributed heat in a cavity is the most effective technique to enrich heat transfer rate, along with reducing the the waste of extra heat generation in processes such as polymer and aero dynamical extrusion, glass cooling, refrigeration, heating and cooling systems. Thus, the prime goal of this work is to outline heat and flow characteristics of non-linear fluid occupied in a square enclosure with adjustment of the cold cylinder. Heat transfer attributes are incorporated by accounting buoyancy forces and forming coupling of molecular diffusion of fluid within the flow domain. Formulation of the problem in dimensionless form is attained by encapsulating the aspects of natural convection in view of principal partial differential equations. Parametric study for governing expressions is computed numerically with the finite element method based on COMSOL Multiphysics version 5.6. Quadric interpolating functions are used to obtain information about velocity and temperature on nodes in elements. Hybrid meshing is manifested for discretization of the domain into rectangular and triangular elements. For the optimized variation in flow structures, prospective parameters are varied from 0.5 <= n <= 1.5, 5 <= Pr <= 35 and 10(2) <= Ra <= 10(6). The achieved results are projected graphically through streamlines, isotherms, and local and average Nusselt numbers. Tabular data for kinetic energy and wall heat flux are also calculated. It is inferred through the analysis that, with uplift in the Rayleigh number ( Ra) elevation in the magnitude of kinetic energy and convective heat transfer arises, whereas the reverse pattern is depicted versus the power-law index ( n)Öğe Heat and Mass Transfer Impact on Differential Type Nanofluid with Carbon Nanotubes: A Study of Fractional Order System(Mdpi, 2021) Javed, Fatima; Riaz, Muhammad Bilal; Iftikhar, Nazish; Awrejcewicz, Jan; Akguel, AliThis paper is an analysis of flow of MHD CNTs of second grade nano-fluid under the influence of first order chemical reaction, suction, thermal generation and magnetic field. The fluid is flowing through a porous medium. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in Caputo sense (ABC) fractional derivatives. This shows the novelty of this work. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in Caputo sense (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transform and inversion algorithm. The flow in momentum profile due to variability in the values of parameters are graphically illustrated among C, CF and ABC models. It is concluded that fluid velocity showed decreasing behavior for chi, P, PLANCK CONSTANT OVER TWO PI2, Mo, Pr, & ALEPH; and Sc while it showed increasing behavior for Gr, Gm, kappa and Ao. Moreover, ABC fractional operator presents larger memory effect than C and CF fractional operators.Öğe Heat and mass transport impact on MHD second-grade fluid: A comparative analysis of fractional operators(Wiley, 2021) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Akgul, Ali; Saeed, Syed Tauseef; Baleanu, DumitruThe effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of magnetohydrodynamic (MHD) unsteady second-grade fluid in the presence of ramped conditions. The new governing equations of MHD second-grade fluid have been fractionalized by means of singular and nonsingular differentiable operators. To have an accurate physical significance of imposed conditions on the geometry of second-grade fluid, the constant concentration with ramped temperature and ramped velocity is considered. The fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.Öğe Heat transport analysis of three-dimensional magnetohydrodynamics nanofluid flow through an extending sheet with thermal radiation and heat source/sink(Elsevier, 2024) Kamran, Tahir; Riaz, Muhammad Bilal; Akgul, Ali; Ali, Mohamed R.Regarding heat transformation efficiency, the hybrid nanofluid performs superior to the nanofluid. The majority of hybrid nanofluid uses are in the industrial sector, producing solar energy, cooling generators, and vehicle heat transformation. Heat transfer and nanofluid velocity are the two most crucial transport properties that must be evaluated before the first and second thermodynamics equations are applied to nanoscale fluids. The objective of this work is to investigate the characteristics of transmission of heat of magnetohydrodynamic (MHD) nanofluid (Ag/H2O)and hybrid nanofluid (Ag + Al2O3/H2O)flow on a linear extensible sheet when magnetic forces are present. Similarity variables are applied to transform a set of nonlinear dimensionless partial-differential equations to collection of ordinary-differential equations. The non-analytical solutions of these transformed equations are found utilizing the MATLAB mathematical program's bvp4c function. The impression of various physical attributes along skin friction coefficients and properties of heat transmission are analyzed. The behavior of key parameters, including surface stretching ratio, rotational and magnetic effects, for temperature and velocity, is shown using graphs and tables. In conclusion, hybrid nanofluids, which comprise silver and aluminum oxide nanoparticles dispersed in water, outperform silver-water nanofluids by around 10-15 % under magnetohydrodynamic (MHD). The higher thermal conductivity of these hybrid nanofluids allows for better heat dissipation, making them an appealing option for applications that need optimal thermal management in the presence of magnetic fields.Öğe Inclusion of Hall and Ion slip consequences on inclined magnetized cross hybrid nanofluid over a heated porous cone: Spectral relaxation scheme(Elsevier B.V., 2024) Darvesh, Adil; Collantes Santisteban, Luis Jaime; Riaz, Muhammad Bilal; Sánchez-Chero, Manuel; Akgül, Ali; Garalleh, Hakim AL; Magsood, HamzahThe cone geometry has a great significant for heat transmission in many industrial processes due to its ability to induce turbulence, enable directional flow, promote uniform temperature distribution, and offer versatility in applications. The current study aims to investigate the heat transport process of an inclined magnetized cross hybrid nanofluid over a heated porous cone under the influence of Hall and Ion slip consequences. Additionally, porous medium the flow is past under the effect of inclined uniform magnetic field and porosity of the medium is used to enhance heat transfer. The framed set of governing equations took the form of dimension free structure through appropriate transformations and then finally solved by an effective spectral relaxation method. Thermal impacts and heat transport mechanism associated with the hybrid flow is seen through different values of emerging parameters. Heat transport is seen higher with higher radiation parameters, as radiation and rising temperature are similar. Augmented values of Fr causes pressure drop in fluids which reduces the fluid motion and brings depreciation in velocity field. Eckert number also boosts the temperature of the fluid stirring via a porous rotating cone. © 2024 The AuthorsÖğe Measuring the energy for the molecular graphs of antiviral agents: Hydroxychloroquine, Chloroquine and Remdesivir(Elsevier, 2024) Aftab, Muhammad Haroon; Akgul, Ali; Riaz, Muhammad Bilal; Hussain, Muhammad; Jebreen, Kamel; Kanj, HassanWe consider the energy for the molecular graphs of antiviral agents like Hydroxychloroquine, Remdesivir and Chloroquine. These drugs play a vital role in the treatment of COVID-19. Let Gamma(1), Gamma(2) and Gamma(3) be the n-dimensional graphs of the molecular structures of antiviral agents Hydroxychloroquine, Chloroquine and Remdesivir, respectively. We define their energies as E '(Gamma(1)) = Sigma vertical bar lambda(i)'vertical bar, E '(Gamma 2) = Sigma vertical bar lambda(j)'vertical bar and E '(Gamma 3) = Sigma vertical bar lambda(k)'vertical bar, respectively. Where the sets {lambda(1)'(Gamma(1)), lambda(2)'(Gamma(1)), lambda(3)'(Gamma(1)), ..., lambda(n)'(Gamma(1))}, {lambda(1)'(Gamma(2)), lambda(2)'(Gamma(2)), lambda(3)'(Gamma(2)), ..., lambda(n)'(Gamma(2))} and { lambda(1)'(Gamma 3), lambda(2)'(Gamma 3), lambda(3)'(Gamma 3), ..., lambda(n)'(Gamma 3)} depict the eigenvalues for the adjacency matrices of Gamma 1, Gamma 2 and Gamma 3, respectively. We have developed some basic ideas and properties in order to measure the energies for the antiviral agents Hydroxychloroquine, Chloroquine and Remdesivir.
