To validate computer codes for mathematical simu

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The current investigation carries out the free convection of an electrically conducting viscoelastic nanofluid through an expanding surface. The salient features of Brownian and thermophoresis due to cross-diffusion and thermal radiation enhance the heat transport phenomenon. Furthermore, the chemical reaction plays an important role in enriching the study. The current investigation shows its important role, such as the proper shape and size of the product in the final stage of production and also optimizing the transport phenomena of various industries that depend upon the supplied heat source, etc. With the appropriate selection of transformation rules, the proposed model is designed and transformed into the ordinary. Furthermore, a hybrid methodology such as the “Perturbation Method” and numerical technique, i.e., the “MATLAB solver (bvp4c technique),” is proposed to handle the governing equations. The graph and tabular form illustrate the characteristics of physical parameters blending within the flow phenomena.