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Our study delves into the dynamics of a convective Magneto-Hydrodynamic Bioconvective Nanofluid model (MHD-BCNFM) flowing over a convectively heated stretched sheet. To accomplish this, we utilize the distinctive capabilities of the Supervised Stochastic Approach for Computational Analysis (SSACA). By integrating similarity transformations, we convert the partial differential equations (PDEs) governing the system into coupled ordinary differential equations (ODEs). We generate the dataset for our approach using the Adam numerical technique specifically tailored for the (MHD-BCNFM). Achieving this involves systematic modulation of parameters such as λ , bioconvection Péclet number P e , Bioconvection constant σ , Brownian motion parameter N b , and thermophoresis parameter N t. "Moreover, we utilize a reference dataset to compute numerical values of various physical quantities in the (MHD-BCNFM) employing SSACA-based Artificial Intelligence methods. The effectiveness of our devised SSACA approach is demonstrated by a negligible mean squared error, ranging from approximately 10−8 to 10−10. Histograms exhibit a maximum error range of 10−5, closely aligning with optimal correlation/regression measures. Outstanding performance metrics in terms of Mean Squared Error (MSE) are attained at levels such as l 9.93E−12, 1.07E−11, 6.28E−10, 1.43E−11, 2.09E−09, 3.65E−11, 2.97E−11, and 2.80E−13 against 320, 430, 209, 85, 356, 295, 66, and 136 epochs. A comparative study between the proposed and reference datasets underscores the authenticity and precision of SSACA, supported by error analyses ranging from E-05 to E-09 across all scenarios. [ABSTRACT FROM AUTHOR]

The present article summarized the effects of double magnetic dipole for chemically reactive viscoelastic fluid in the presence of two different ferromagnetic particles, namely, nickel zinc ferrite N i Z n F e 2 O 4 and magnetite ferrite ( F e 3 O 4 ). Due to double magnetic dipole, an external magnetic field is applied normal to the flow. Blood is used as base fluid due to its viscoelastic fluid properties. The Cattaneo-Christov heat flux model is used for heat transport phenomena. The physical model is formulated in the form of partial differential equations which are then converted into ordinary differential equations using the suitable transformations. The system is solved numerically using shooting method along with Runge-Kutta-Fehlberg method. The characteristics of different parameters like the strength of homogeneous-heterogeneous reactions ( k 1 and k 2 ), ferrohydrodynamic interaction ( β 1 ), Schmidt number ( S c ), Deborah number ( α 1 a ), and thermal relaxation time ( α 1 c ) on velocity, temperature, and concentration profiles are analyzed through graphs and in tabular form. It has been observed that as magnetic dipole creates a force which attracts the ferrite particles, hence, it slows down the velocity profile. Concentration field depresses due to the presence of strength of heterogeneous reaction parameter k 2 .It is also noted that by expanding values of thermal relaxation time ( α 1 c ), the temperature profile shows a reverse behavior. [ABSTRACT FROM AUTHOR]

Matrix nanocomposites are high performance materials possessing unusual features along with unique design possibilities. Due to extraordinary thermophysical characteristic contained by these matrix nanocomposites materials they are useful in several areas ranging from packaging to biomedical applications. Being an environment friendly, utilization of nanocomposites offer new technological opportunities for several sectors of aerospace, automotive, electronics and biotechnology. In this regards, current pagination is devoted to analyze thermal features of viscous fluid flow between orthogonally rotating disks with inclusion of metallic matrix nanocomposite (MMNC) and ceramic matrix nanocomposites (CMNC) materials. Morphological aspects of these nanomaterials on flow and heat transfer characteristics has been investigated on hybrid viscous fluid flow. Mathematical structuring of problem along with empirical relations for nanocomposites materials are formulated in the form of partial differential equations and later on converted into ordinary differential expressions by using suitable variables. Solution of constructed coupled differential system is found by collaboration of Runge–Kutta and shooting methods. Variation in skin friction coefficient at lower and upper walls of disks along with measurement about heat transfer rate are calculated against governing physical parameters. Impact of flow concerning variables on axial, radial components of velocity and temperature distribution are also evaluated. Contour plots are also drawn to explore heat and thermal profiles. Comparison and critical analysis of MMNc and CMNc have been presented at lower and upper porous disks. Our computed analysis indicates that hybrid nanofluids show significant influence as compared to simple nanofluids with the permutation of the different shape factors. [ABSTRACT FROM AUTHOR]

This paper explores the physical and computational aspects of normally applied magnetic field on non-Newtonian Prandtl-Eyring fluid flow over a stretching sheet. The Prandtl-Eyring fluid is a non-Newtonian viscoinelastic fluid model capable of describing zero shear rate viscosity effects. Stretching of a sheet induces the flow (Couette flow). The mathematical formulation of the problem gives a highly non-linear system of partial differential equations. By means of a scaling group of transformations, the partial differential equations are transfigured into ordinary differential equation. The implicit finite difference scheme Keller-Box is implemented to solve the resulting equation. The expression for dimensionless velocity is calculated numerically and inclusive pictures of its physical characteristics are analyzed very concisely and briefly. The influence of different pertinent parameters is displayed via graphs, which are plotted against variation in parameters. Computation of the skin friction coefficient is accomplished, and effects of influential parameters are analyzed via graphs and tables. The accuracy of the present solution is certified by displaying contrast between present and existing literature. It is important to remark that the results have shown excellent agreement up to significant number of digits. [ABSTRACT FROM AUTHOR]

The aim of the present analysis is to examine the effects of slip boundary conditions and mixed convection flow of Williamson fluid over a stretching cylinder. The boundary layer partial differential equations are transformed into ordinary differential equations by using group theory transformations. The required ordinary differential equations are solved numerically by using implicit finite difference method known as Keller box method. The influence of dimensionless physical parameters on velocity and temperature profile as well as skin friction coefficient and local Nusselt number are presented graphically. Comparison has been made to the previous literature in order to check the accuracy of the method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to figure out the flow and heat problem of two dimensional steady axisymmetric laminar mixed-convection boundary-layer flow of Sisko fluid model along a stretching cylinder in a thermally stratified medium. The similarity transformations are used to reduce coupled partial differential equations to ordinary differential equations. To solve these equations, a numerical approach called shooting method has been used for the computation of different physical parameters of velocity and temperature field, respectively. The dependence of skin friction and Nusselt number has been analyzed in details in tables. [ABSTRACT FROM AUTHOR]

Present study carried out the speculative investigation of Hall current effects on MHD viscous fluid flow over stretching sheet with variable thickness. For heat transfer analysis, Christov–Cattaneo heat flux model is used instead of classical Fourier law. The mathematical formulation of current flow configuration yields the set of partial differential equations with higher order of nonlinearity. The modeled partial differential equations are switched into ordinary differential equations with the aid of an appropriate set of local similarity transforms. The resulting similarity equations are tackled numerically with the assistance of fifth order Runge–Kutta integration scheme. The expressions for axial velocity, transverse velocity and temperature are numerically computed and analyzed against variations in the controlling parameters with the help of graphs. To insight flow behavior in the neighbourer region of sheet surface, local skin friction coefficients and local Nusselt number are calculated. The effects of involving flow parameters on these interesting quantities are elaborated through tabular representations. A suitable correlation of current results with previously reported data (in limiting case) is presented for the validation of computed results. • Fluid velocities show depreciating trend due to the resistance provided by magnetic field whereas temperature profile upsurges. • Both wall friction factors grows verses Hartmann number while temperature gradient reduces against it. • Hall parameter provides opposition to transverse velocity while it slightly accelerates the axial velocity. • An increase in wall thickness parameter upsurges both components of velocities and temperature as well. • The nonlinearly stretching surface bestowed the favorable situation to fluid movement in axial direction while reverse pattern is depicted in case of transverse velocity. • Prandtl number declines the fluid temperature whereas wall heat flux coefficient intensifies. [ABSTRACT FROM AUTHOR]

A mathematical model is presented to discuss magnetohydrodynamic Sisko fluid flow over a stretching cylinder with cumulative effects of viscous dissipation and Joule heating in the presence of nanoparticles. The mathematical modelling of the physical problem produced nonlinear set of partial differential equations which are transfigured into simultaneous system of ordinary differential equations with appropriate boundary conditions via suitable scaling group of transforms. Shooting technique is used to solve nonlinear set of flow govern equations. Comparison of numerical solution is made with previously reported data to validate the accuracy. The influence of governing parameters on the velocity, temperature and concentration is discussed under different parametric conditions. The numerically computed results are deliberated via graphs by selecting suitable values of the relevant physical parameters. Additionally to insight physical phenomenon in the vicinity of surface skin friction coefficient, local Nusselt number and local Sherwood number are computed and explicated through tables as well as graphs. [ABSTRACT FROM AUTHOR]