The technique of Levenberg–Marquardt back propagation with neural networks (TLMB-NN) was used in this research article to investigate the heat transfer of Maxwell base fluid flow of nanomaterials (HTM-BFN) with MHD over vertical moving surfaces. In this study, the effects of thermal energy, concentration, and Brownian motion are also employed. Moreover, the impacts of a heat-absorbing fluid with viscous dissipation and radiation have been explored. To simplify the governing equations from a stiff to a simple system of non-linear ODEs, we exploited the efficacy of suitable similarity transformation mechanism. Through applicability of state-of-the-art Adams numerical technique, a set of data for suggested (TLMB-NN) is generated for several situations (scenarios) by changing parameters, such as the Thermophoresis factor N_t, Hartmann number M, Eckert number E_c, concentration Grashoff parameter G_c, Prandtl number P_r, Lewis number Le, thermal Grashof number G_T, and Brownian motion factor N_b. The estimate solution of different instances has validated using the (TLMB-NN) training, testing, and validation method, and the recommended model was compared for excellence. Following that, regression analysis, mean square error, and histogram explorations are used to validate the suggested (TLMB-NN). The proposed technique is distinguished based on the proximity of the proposed and reference findings, with an accuracy level ranging from 10⁻⁹ to 10⁻¹⁰.

In this research work, an effective Levenberg–Marquardt algorithm‐based artificial neural network (LMA‐BANN) model is presented to find an accurate series solution for micropolar flow in a porous channel with mass injection (MPFPCMI). The LMA is one of the fastest backpropagation methods used for solving least‐squares of nonlinear problems. We create a dataset to train, test, and validate the LMA‐BANN model regarding the solution obtained by optimal homotopy asymptotic (OHA) method. The proposed model is evaluated by conducting experiments on a dataset acquired from the OHA method. The experimental results are obtained by using mean square error (MSE) and absolute error (AE) metric functions. The learning process of the adjustable parameters is conducted with efficacy of the LMA‐BANN model. The performance of the developed LMA‐BANN for the modelled problem is confirmed by achieving the best promise numerical results of performance in the range of E‐05 to E‐08 and also assessed by error histogram plot (EHP) and regression plot (RP) measures.

In this research paper we examined Darcy-Forchheimer three-dimensional micro-polar nanofluid flow of carbon nanotubes (CNTs) based on water. The nanofluid flow is examined between parallel and horizontal plates in a rotating system. The thermal radiation impact is taken to be varying in the absorption/generation for the purpose, to see the concentration as well as the temperature modifications between the nanofluid and the surfaces. The micro-polar nanofluid in permeable media is designated by assuming the Darcy-Forchheimer model where drenching permeable space obeys the Darcy-Forchheimer expression. For Skin friction coefficient it is perceived to be larger for weak concentration and smaller for strong concentration. The impacts of the porosity, rotation and inertia coefficient analysis have been mainly focused in present investigation. Plots have been presented in order to study how the velocities and temperature profile get affected by various flow parameters. The leading equations are converted to a system of nonlinear differential equations and then homotopic method is employed for solution. The other physical features of flow such as Skin friction, heat flux and mass flux have been studied. The impacts of the porosity, rotation and inertia coefficient have been mainly focused in this research.

In the present study, the three-dimensional Darcy–Forchheimer magnetohydrodynamic thin-film nanofluid containing flow over an inclined steady rotating plane is observed. Nanofluid thin-film flows are taken thermally radiated and suction/injection effect is also considered. By similarity variables, the partial differential equations are transformed into a set of first-ordinary differential equations (ODES). By Homotopy Analysis Method, the required ODES is solved. The boundary layer over an inclined steady rotating plane is plotted and observed in detail for the velocity, θ ( η ) , and ϕ ( η ) profiles. The influence of various embedded parameters such as variable thickness, Sc , λ , Nb , Pr, and thermophoretic parameter on velocity, θ ( η ) , and ϕ ( η ) profile. The influence of many parameters is explained by graphs for the velocity, θ ( η ) , and ϕ ( η ) . The crucial terms of Nusselt number and Sherwood number have also been observed numerically and physically for θ ( η ) and ϕ ( η ) . Radiation phenomena is the cause of energy to the liquid system. For more rotation parameters, the thermal boundary-layer thickness is reduced.

This article deals with three-dimensional non-Newtonian Jeffrey fluid in rotating frame in the presence of magnetic field. The flow is studied in the application of Hall current, where the flow is assumed in steady states. The upper plate is considered fixed, and the lower is kept stretched. The fundamental equations are transformed into a set of ordinary differential equations (ODEs). A homotopy technique is practiced for a solution. The variation in the skin friction and its effects on the velocity fields have been examined numerically. The effects of physical parameters are discussed in various plots.