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The current article investigates the numerical study of the micropolar nanofluid flow through a 3D rotating surface. This communication may manipulate for the aim such as the delivery of the drug, cooling of electronic chips, nanoscience and the fields of nanotechnology. The impact of heat source/sink is employed. Brownian motion and thermophoresis aspects are discussed. The rotating sheet with the impacts of Darcy-Forchheimer law is also scrutinized. Furthermore, the influence of activation energy is analyzed in the current article. The numerical analysis is simplified with the help of befitted resemblance transformations. The succor of the shooting algorithm with built-in solver bvp4c MATLAB software is used for the numerical solution of nonlinear transformed equations. The consequences of different physical factors on the physical engineering quantities and the subjective fields were examined and presented. According to outcomes, it can be analyzed that the flow profile declined with the rotational parameter. It is observed that angular velocity diminishes via a larger porosity parameter. Furthermore, the temperature gradient is declined via a larger magnitude of the Prandtl number. The heat transfer is enhanced in the occurrence of Brownian motion. The activations energy parameter causes an increment in the volumetric concentration field. Moreover, the local Nusselt number is reduced via a greater estimation of the porosity parameter.

The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost.

In this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis functions from radial and nonradial aspects. The first scheme is fulfilled by considering time variable as normal space variable to construct an “isotropic” space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the hyperbolic telegraph equations can be solved in a direct way. Numerical experiments performed with the proposed numerical scheme for several two-dimensional second-order hyperbolic telegraph equations are presented with some discussions, which show that the DMM solutions are converging very fast in comparison with the various existing numerical methods.