Tn the present research article, we address the magnetically controlled thermal and solutal Marangoni convection in the flow of self-rewetting power-law liquid over a disk, in the existence of a space dependent heat source. The self re-wetting property of fluid is modelled by considering a quadratic dependence of surface tension on temperature and species concentration. The aforementioned problem is modelled by simplified NavierStokes equations. Tdentifying the appropriate transform variables is essential for developing ordinary differential equations from original partial differential equations that describe the flow conditions. The resulting ordinary differential equations are solved by using the hvp4c routine of MATLAB and numerical solutions are presented via graphs and tables, illustrating the impact of several factors on fluid velocity, temperature, and concentration. Computation of the quantities of physical interest such as Nusselt and Sherwood numbers are also done from those numerical solutions. One of the key findings of present research work is that the Marangoni convection works differently for pseudo-plastic fluid and dilatant fluid. On increasing thermal Marangoni convection the temperature of dilatant fluid reaches a peak value much closer to the disk than temperature of pseudo plastic fluid. (c) 2024 Sharif University of Technology. All rights reserved.

The current study investigates the three-dimensional radiative and convective Casson hybrid nanofluid flow and heat transfer with the Cattaneo–Christov heat flux model over an inclined spinning and extending disk subjected to an applied magnetic field. Additionally, the study considers the impacts of Joule’s heating and viscous dissipation. Mathematical modelling of the nanofluid flow problem containing Ag and multiwalled carbon nanotubes (MWCNT) nanoparticles with water as the base fluid in a Darcy medium is done using a cylindrical coordinate system. The simplified system of equations is subjected to the spectral quasilinearisation method (SQLM) approach for the graphical and tabular representations. Examining key parameters, such as magnetic field, Bejan number, angle of inclination, disk movement parameter and disk rotation reveals interesting results on velocity and temperature profiles. The research concludes that the Bejan number increases with higher values of temperature ratio, radiation and magnetic parameters, while it decreases with increasing Casson parameter and Brinkman number. Radial wall friction decreases with improved magnetic field, temperature ratio, stretching and porosity parameters, but tangential wall friction increases. The present results are compared with the one already existing in literature to validate the numerical scheme and the results are found to agree well with the previously published work. The application of hybrid nanofluid flow over rotating and stretching disks is widespread in various fields, including rotating machinery, electronic devices, patient treatment instruments, crystal growth method, etc.

The present analysis deals with the three-dimensional radiative, convective hybrid nanofluid flow over a rotating and stretching inclined disk under the action of the applied magnetic field, Joule's heating, and viscous dissipation effects. The mathematical model considers nanoparticles graphene oxide (GO) and molybdenum disulfide (MoS2) suspended in water as the base fluid within a Darcy medium. The cylindrical coordinate system is used to express continuity, momentum, and energy partial differential equations, out of which momentum and energy partial differential equations are transformed into ordinary differential equations using a suitable transformation method under the boundary-layer approximation. The transformed equations are further solved using the spectral quasi-linearization method. Graphical and numerical data are presented to investigate the behavior of velocity and temperature under various parameters and shape factors. The nature of fluid flow at the boundary wall is determined by tables of skin friction and the Nusselt number. Statistical analysis of the parameters for axial and tangential skin friction and the Nusselt number is performed using the quadratic regression model.

The current research examines the problem of swirling flow for the Reiner-Rivlin liquid where the surface of rotating disk admits the Navier's velocity slip condition within the environment of magnetic field. The temperature jump condition as a result of imperfect liquid-solid energy accommodation is also taken into account. The Karman similarity transforms are implemented to transform the flow narrating differential equation into coupled ODEs which are solved via a suitable numerical method. On velocity and temperature profiles, the impacts of the heat production parameter, magnetic parameter, non-Newtonian parameter, and slip coefficients are explored. The effect of parameters on the velocities (axial and radial) and temperature distributions are sketched in the graphical form. Moreover, expressions of wall skin friction and heat transfer rate at the surface of the disk are calculated and are given in the tabular form. When the magnetic and slip parameters increase, the fluid velocities (radial and azimuthal) decrease. Skin friction and driving torque get lowered with the rise in the value of Reiner-Rivlin fluid parameter while these physical quantities increase for the higher magnetic parameter.

The present investigation deliberates the impact of the magnetic dipole for the flow of non‐Newtonian Williamson nanoliquid by considering the thermal radiation and chemical reaction defined by the Arrhenius model. The flow model is established by incorporating the well‐known Buongiorno's nanofluid model, and as a result, Brownian motion and thermophoretic diffusion are assimilated in mathematical modeling. The heat transportation process is accomplished by thermal radiation, heat generation owing to internal energy generation/absorption of the fluid, and viscous dissipation. The coupled nonlinear mathematically formulated partial differential equations (PDEs) are metamorphosed into the ordinary differential equations (ODEs) through the transformation. The bvp4c method is utilized to obtain the solution of formulated ODEs together with the additional conditions at the boundary. The impact of pertinent flow characteristics on temperature, velocity, and concentration profiles is outlined graphically. Also, the strength of energy, surface drag force, and mass transport are calculated and formed in the tabular form. The outcomes show that a rise in activation energy causes fluid concentration to increase. Velocity gets reduced with the increment in either ferrohydrodynamic interaction factor or Weissenberg number.

The authors present a new algorithm for solving the shortest path problem (SPP) in a mixed fuzzy environment. With this algorithm, the authors can solve the problems with different sets of fuzzy numbers e.g., normal, trapezoidal, triangular, and LR-flat fuzzy membership functions. Moreover, the authors can solve the fuzzy shortest path problem (FSPP) with two different membership functions such as normal and a fuzzy membership function under real-life situations. The transformation of the fuzzy linear programming (FLP) model into a crisp linear programming model by using a score function is also investigated. Furthermore, the shortcomings of some existing methods are discussed and compared with the algorithm. The objective of the proposed method is to find the fuzzy shortest path (FSP) for the given network; however, this is also capable of predicting the fuzzy shortest path length (FSPL) and crisp shortest path length (CSPL). Finally, some numerical experiments are given to show the effectiveness and robustness of the new model. Numerical results show that this method is superior to the existing methods.

An examination of simultaneous effects of Hall current and heat radiation on three-dimensional micropolar CNT-based nanofluid flow between two rotating sheets is carried out. The upper sheet is considered to be porous, and the fluid flow is induced due to stretching of the lower sheet. The flow model is presented by a system of nonlinear partial differential equations (PDEs). The leading PDEs are transformed into dimensionless coupled ordinary differential equations by the usual procedure of transformation. The transformed differential equations are solved by the optimal homotopy analysis method in order to analyze the velocity as well as temperature of nanofluid and microrotation of nanotubes. Analysis for physical quantities of interest, viz. skin friction coefficient and Nusselt number, are also carried out for the two kinds of nanotubes, single-wall carbon nanotubes and multiwall carbon nanotubes. It is observed that microrotation of nanotubes increased with the increase in coupling parameter, whereas it slows down with an increase in spin gradient viscosity parameter. An intense magnetic field results in a reduction of skin friction coefficient, whereas an increase in the suction of fluid through upper plate forces a surge in the value of skin friction coefficient.

This article examines hydromagnetic flow of Carreau nanomaterial over a stretched surface. Buongiorno nanofluid model is used in mathematical modelling. Here thermophoresis and Brownian diffusion are slip mechanisms under consideration. Energy equation is modelled via heat source/sink, Joule heating, nonlinear radiation and dissipation effects. The compact form of flow equations are changed to components forms through implementation of boundary layer concept. Suitable transformations give rise to ODEs. The obtained system is solved through homotopy method. The velocity, mass concentration, entropy generation, temperature, skin friction, Bejan number and Nusselt number are examined through graphical sketch. The obtained outcomes present that entropy generation boosts for higher magnetic parameter, Brinkman number and concentration ratio parameter while it diminishes via Brownian diffusion parameter.

Neutrosophic (NS) set hypothesis gives another way to deal with the vulnerabilities of the shortest path problems (SPP). Several researchers have worked on fuzzy shortest path problem (FSPP) in a fuzzy graph with vulnerability data and completely different applications in real world eventualities. However, the uncertainty related to the inconsistent information and indeterminate information isn't properly expressed by fuzzy set. The neutrosophic set deals these forms of uncertainty. This paper presents a model for shortest path problem with various arrangements of integer-valued trapezoidal neutrosophic (INVTpNS) and integer-valued triangular neurrosophic (INVTrNS). We characterized this issue as Neutrosophic Shortest way problem (NSSPP). The established linear programming (LP) model solves the classical SPP that consists of crisp parameters. To the simplest of our data, there's no multi objective applied mathematics approach in literature for finding the Neutrosophic shortest path problem (NSSPP). During this paper, we tend to introduce a multi objective applied mathematics approach to unravel the NSPP. The subsequent integer valued neutrosophic shortest path (IVNSSP) issue is changed over into a multi objective linear programming (MOLP) issue. At that point, a lexicographic methodology is utilized to acquire the productive arrangement of the subsequent MOLP issue. The optimization process affirms that the optimum integer valued neutrosophic shortest path weight conserves the arrangement of an integer valued neutrosophic number. Finally, some numerical investigations are given to demonstrate the adequacy and strength of the new model.

This article presents the study of two-dimensional hydromagnetic stagnation point flow of Casson nanofluid over a stretching sheet in a non-Darcy porous medium with binary chemical reaction stimulated by Arrhenius activation energy. The energy equation is obtained by considering the production of heat due to Joule and viscous dissipations, heat generation/absorption and thermal radiation of the liquid. The flow model is developed and presented in the form of a system of nonlinear partial differential equations together with appropriate boundary conditions. The particle flux at the sheet is taken to be zero. The leading PDEs are transformed into dimensionless coupled ordinary differential equations (ODEs) by the usual procedure of transformation. The obtained ODEs are solved using optimal homotopy analysis method, and the effects of underlying parameters on the fluid velocity, temperature, concentration, entropy generation and Bejan number are demonstrated with the help of graphs. Also, the numerical values of skin friction coefficient, Nusselt number and Sherwood number are presented in tabular form. Linear as well as quadratic regression analysis for quantities of physical interest has also been carried out. Entropy generation is perceived to rise on increasing diffusive variable and Brinkman number, whereas Brownian diffusion has an adverse effect on it. Skin friction coefficient is reduced on increasing Casson fluid parameter and activation energy.

In the present article, an investigation on the impact of Soret effect on unsteady magnetohydrodynamic natural convection flow of a viscous, electrically conducting and incompressible nanofluid over a vertical plate through a medium filled with porous materials with the consideration of a second order chemical reaction, has been investigated. Three kinds of water-based nanofluids, comprising of aluminum oxide (Al2O3), titanium oxide (TiO2) and silver (Ag) as nanoparticles, are chosen for this analysis. Governing equations accompanied by the boundary and initial conditions are changed into non-dimensional form and then they are solved by Crank-Nicolson type finite difference scheme. The impact of relevant flow parameters on nanofluid velocity, nanofluid temperature and species concentration are depicted graphically with comprehensive discussions whereas numerical findings for coefficient of skin friction, wall temperature gradient i.e. Nusselt number and wall concentration gradient are depicted in tabular form. It has been observed that Soret effect has the ability to enhance the species concentration. The investigation we have performed here, has various scientific and industrial applications.

An investigation on the unsteady MHD natural convection heat and mass transfer flow of an electrically conducting, viscous, incompressible, chemically reactive and heat-absorbing nanofluid of Brinkman type past an exponentially accelerated moving vertical plate with ramped wall temperature and ramped surface concentration is carried out. Governing equations are non-dimensionalized and Laplace Transform Technique is used to find the exact solutions for fluid velocity, fluid temperature and species concentration. The quantities of physical interest, i.e. skin friction, rates of heat and mass transfers at the plate are also calculated. Numerical results for the velocity, temperature and species concentration of the fluid are demonstrated with the help of graphs whereas those of skin friction, rate of heat and mass transfers at the plate are displayed in tables for various flow parameters.

In traditional shortest path problem it is always determined that the parameters (Time, Cost and Distance etc.) are fixed between different nodes. But in real life situations where uncertain parameters exist, parameters are considered as fuzzy numbers. In this paper, we explained the application scope of the given fuzzy ranking function. Using this method we can determine both the fuzzy shortest path and fuzzy shortest Distance from origin to Destination.

In this paper we have applied Gabor filter for fiducial point localization.After obtaining the fiducial points the number of fiducial points are reduced using a distance formula.The distance of each of this fiducial point is then calculated by the distance formula and stored in the database of the system.The same methodology is also applied on the input face which is to be matched with the faces available in the database.Then a fuzzy preference relation matrix is obtained .the largest eigen value of this matrix is then determined by algebraic method or numerical method depending on the order of the matrix.To apply the numerical method which is more easier for large order matrices we have used the C programming of this method .Once the largest eigen value is determined the corresponding priority vector can easily be obtained from which we can easily match the input face with the database.

Magnetic surveys around Barren and Narcondam Island have brought out different anomaly pattern during different period of surveys since 1990. This variation in amplitude of anomaly pattern in the magnetic signal, which is responsible for Curie Isotherm Depth (CID), shows distinct picture of thermal eruption from 1990 to recent past. This in turn will raise or lower the CID, which is reflected in the present study. Data collected from the various cruises of R/V Samudra Manthan (SM-61, 78, 113, 136 and 157) of the Geological Survey of India are analysed here.