Prediction of thermal and energy transport of MHD Sutterby hybrid nanofluid flow with activation energy using Group Method of Data Handling (GMDH)

The present research work pursues GMDH for predicting thermal and energy transport of 2-D radiative magnetohydrodynamic (MHD) flow of hybrid Sutterby nanofluid across a moving wedge with activation energy. An exclusive class of nanoparticles SWCNT-Fe(3)O(4 )and MWCNT-Fe3O4 are dispersed into the ethylene glycol as regular fluid. The hybrid nanofluid mathematical model has been written as a system of partial differential equations (PDEs), which are then converted into ordinary differential equations (ODEs) through similarity replacements. Numerical solutions are attained Runge-Kutta-Fehlberg's fourth fifth-order (RKF-45) scheme by adopting the shooting technique. The ranges of diverse sundry parameters used in our study are Hartree parameter 0.1 <= m <= 0.5, magnetic parameter 0.3 <= M <= 1, Deborah number 0.1 <= De <= 1, moving wedge parameter 0.3 <= gamma <= 0.9, Reynolds number 0 <= Re <= 2.5, solid volume fraction of Fe3O4 and CNTs0.005 <= phi(1) <= 0.1,0.005 <= phi(2) <= 0.06, Browanian motion 0.1 <= Nb <= 0.4, thermophoresis parameter 0.1 <= Nt <= 0.25, Eckeret number 0.05 <= Ec <= 1, radiation parameter 1 <= R-d <= 2.5, Lewis number 0.5 <= Le <= 1.5, chemical reaction rate 0.1 <= sigma <= 0.7, heat source parameter, 0 <= delta <= 1.5 and activation energy 1 <= E <= 4 which shows up during the speed, thermal, and focus for Fe3O4/C2H6O2 nanofluid and CNTs-Fe3O4/C2H6O2 hybrid nanofluid. Additionally, the friction coefficient (C-fx), rate of heat transport (H-tx), and rate of nanoparticle transport (Nt(x) are calculated using GMDH. The numerical results for the current analysis are illustrated via tables, graphs, and contour plots. The efficiency of the proposed GMDH models is assessed using statistical measures such as MSE, MAE, RMSE, R, Error mean and Error StD. The predicted values are very close to the numerical results, and the coefficient of determination R-2 of C-fx,N-tx, and H-tx are 1, 0.97836 and 0.9960, respectively, which shows the best settlement

Theoretical Analysis of Superphenalene Using Different Kinds of VDB Indices

Topological indices (TIs) are numerical quantities that enable theoretical chemists to analyse molecular structures mathematically. These TIs are essential to exploring chemical compounds using theoretical techniques like QSAR/QSPR methods. Superphenalene is a large polycyclic aromatic hydrocarbon molecule which has been quickly gaining importance as a building block for alternate energy providers due to its photovoltaic properties. The exciting features of this compound, coupled with its potential applications, warrant an investigation of its nature and properties from a structural perspective. The objective of this research is to compute the proper analytical expressions of four kinds of vertex degree-based (VDB) indices for superphenalene. The numerical values of these indices and 3D graphical representations also help in understanding the relationship between the VDB indices of the compound and its underlying chemical structure quantitatively

Investigation of Magnetized Casson Nanofluid Flow along Wedge: Gaussian Process Regression

An unsteady two-dimensional magnetized Casson nanofluid flow model is constructed over a wedge under the effect of thermal radiation and chemical reaction. The multiple slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. This study investigates the application of soft computing techniques to address the challenges posed by the complexity of problem modeling and numerical methods. Traditional approaches incorporating various model factors may struggle to provide accurate solutions. To resolve this issue, Gaussian process regression (GPR) is employed to predict the solution of the proposed flow model. With the help of the numerical shooting method together with Runge–Kutta–Fehlberg fourth-fifth-order (RKF-45) reference data, the GPR model is trained. The numerical simulation illustrated that the Casson fluid parameter β and the unsteadiness parameter S strengthen the friction factor, and the heat transfer rate is enhanced as the radiation parameter Rd becomes larger. In addition, the Biot numbers Bi1 & Bi2 lead to strengthen nanoparticle temperature; an opposite behavior is noticed with the skin friction coefficient S˜fxRex0.5, heat transfer rate H˜tx Rex0.5, and nanoparticle transfer rate C˜txRex0.5. The GPR model with the exponential Kernel function provided better performance than other functions on both training and checking datasets to predict S˜fxRex0.5,H˜tx Rex0.5, and C˜txRex0.5. Statistical metrics including RMSE, MAE, MAPE, MSE, R2, and R are employed to check the accuracy and convergences of the predicted and numerical solutions obtained through GPR and RKF-45. It is observed that all three GPR models had an R2 value of higher than 0.9. The proposed study demonstrates the advantages of employing soft computing methods (GPR) to effectively analyse the behavior of complex flow models

Wiener Index of Intuitionistic Fuzzy Graphs with an Application to Transport Network Flow

The Wiener index WI is one of the connectivity parameters used to know the biochemical and physicochemical properties of compounds depending upon their molecular structures. Intuitionistic fuzzy graphs IFGs are a convenient tool to represent the objects and relations between them with two types of information using truth membership degree and falsity membership degree. This research work presents the concept of WI under the structure IFGs, IF trees, and IF cycles. Some bounds on WI are investigated. The relationship between WI and connectivity index CI is also studied. In the end of this study, an application of the WI in transport network flow is proposed

The Y-Index of Some Complement Graph Structures and Their Applications of Nanotubes and Nanotorus

Topological descriptors play a significant role in chemical nanostructures. These topological measures have explicit chemical uses in chemistry, medicine, biology, and computer sciences. This study calculates the Y-index of some graphs and complements graph operations such as join, tensor and Cartesian and strong products, composition, disjunction, and symmetric difference between two simple graphs. Moreover, the Y-polynomial of titania nanotubes and the formulae for the Y-index, Y-polynomial, F-index, F-polynomial, and Y-coindex of the HAC5C7q,p and HAC5C6C7q,p nanotubes and their molecular complement graphs have been investigated

Modified Zagreb Connection Indices for Benes Network and Related Classes

The study of networks such as Butterfly networks, Benes networks, interconnection networks, David-derived networks through graph theoretical parameters is among the modern trends in the area of graph theory. Among these graph theoretical tools, the topological Indices TIs have been frequently used as graph invariants. TIs are also the essential tools for quantitative structure activity relationship (QSAR) as well as quantity structure property relationships (QSPR). TIs depend on different parameters, such as degree and distance of vertices in graphs. The current work is devoted to the derivation of 2-distance based TIs, known as, modified first Zagreb connection index ZC1∗ and first Zagreb connection index ZC1 for r− dimensional Benes network and some classes generated from Benes network. The horizontal cylindrical Benes network HCBr, vertical cylindrical Benes network VCBr, and toroidal Benes network TBr are the three classes generated by identifying the vertices of the first row with the last row, the first column with the last column of the Benes network. The obtained results are also analyzed through graphical tools

Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation

Abstract This work examines the fractional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) by utilizing three well-known analytical methods, the modified $$\left( \frac{G^{'}}{G^2}\right)$$ G ′ G 2 -expansion method, $$\left( \frac{1}{G^{'}}\right)$$ 1 G ′ -expansion method and the Kudryashov method. The gKdV-ZK equation is a nonlinear model describing the influence of magnetic field on weak ion-acoustic waves in plasma made up of cool and hot electrons. The kink, singular, anti-kink, periodic, and bright soliton solutions are observed. The effect of the fractional parameter on wave shapes have been analyzed by displaying various graphs for fractional-order values of $$\beta$$ β . In addition, we utilize the Hamiltonian property to observe the stability of the attained solution and Galilean transformation for sensitivity analysis. The suggested methods can also be utilized to evaluate the nonlinear models that are being developed in a variety of scientific and technological fields, such as plasma physics. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complex models