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The present study investigates the significance of activation energy during chemical reactions, thermal radiations and temperature gradient of 3-D steady Magnetohydrodynamic Casson nanofluid flow (MHDCNFM) in Darcy−Forchheimer medium over an oscillating disk by using an intelligent numerical-based computing solver through the Levenberg-Marquardt backpropagation neural network scheme (LMBNNS). The adjusted Buongiorno model is utilized to develop the system of partial differential equations (PDEs) for MHDCNFM, and further, by invoking Von Karman similarity transformation, the system of governing PDEs is turned out into ordinary differential equations (ODEs). First, a data set for the magnetohydrodynamic Casson nanofluid flow model (MHDNNFM) is generated for a range of sundry parameters for the radial velocity, tangential velocity, heat distribution and concentration profile by the variations of Casson parameter, magnetic parameter, Brownian motion parameter, thermophoresis parameter, Forchheimer parameter, activation energy parameter, chemical reaction parameter, stretching parameter, porosity parameter and Schmidt number through the Lobatto IIIA technique, and after this, by applying an intelligent computing algorithm through nftool training, testing and validation steps are taken into account to find out the approximate solution for various cases. The designed solver LMBNNS is used to solve the MHDCNFM through mean squared error (MSE), regression, gradient analysis and histogram studies. [ABSTRACT FROM AUTHOR]

This article presents, for the first time, a comparative analysis of two different solution methodologies for the numerical investigation of flow and thermal behavior of Casson fluid through a channel having linearly extending lower wall while the upper wall is kept at rest. MHD Casson fluid boundary layer flow is supposed to be steady, laminar, viscous, and incompressible. We have taken into account the mixed convection effects, whereas the usual no slip condition has been imposed on both walls. The Navier–Stokes equations for the proposed model have been converted into nonlinear and coupled system of ordinary differential equations (ODEs) by employing similarity variables, which are then solved by using the differential transform method (DTM) and the quasi‐linearization method (QLM). We note that the quasi‐linearization approach is better than the DTM, as the latter becomes inappropriate for the increasing values of the parameters involved. Moreover, the variation of the different parameters for velocity and temperature profiles has been analyzed graphically. [ABSTRACT FROM AUTHOR]

In this analysis, we introduced heat convective aspects of stagnation point movement of a magnetohydrodynamic (MHD) stream on a nonlinear oscillating plane with the impacts of velocity and heat slips with variable heat reservoir. By using some appropriate transformations, the governing differential equations are switched into an ordinary differential equation. The semianalytics technique called Homotpy Analysis Method (HAM) has been applied to evaluate the ordinary differential equations. For convergence achievement, a numerical method BVPh2-midpoint method is also applied and an outstanding agreement is found. The impacts of the governing constraints on flow, motion, and temperature distributions are investigated in detail. We observed that the temperature distribution increases with nonlinear heat reservoir parameter. Our results, in some limiting situations, matched well with previously published results, which approve that our obtained results are correct. [ABSTRACT FROM AUTHOR]

In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of S c ≤ S   and   M c ≤ M ( S c > S   and   M c > M ). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised. [ABSTRACT FROM AUTHOR]