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We investigated accurate results by novelty driven technique with homotopy analysis method (HAM) and Keller–Box Method (KBM) on influence of a chemical reaction in a natural convective motion of permeable media due to a vertical plate with some important parameters. Ancillary to the same, the evolution and process of transfer of heat in the appearance of heat source, thermal radiation, and Joule heating are considered as well. The partial differential equations related to the governing equations have been examined as a set of ordinary differential equations employing non-dimensional quantities, these are analysed by HAM and comparison is made with KBM. Based on the HAM, the convergence and accuracy of the proposed problem is illustrated, which exhibit meaningful structures. Also shown the base functions of solutions are highly convergence. All the obtained outcomes from the above approximate analytic and numerical procedures are displayed through graphs and tables to discuss various resulting parameters. There are an upsurge in the heat throughout the laminar flow for radiation parameter increments.

The novel techniques used on convective motion in a permeable media due to a vertical surface under the effect of heat source