Impact of non-similar modeling on Darcy-Forchheimer-Brinkman model for forced convection of Casson nano-fluid in non-Darcy porous media

Abstract In the study of boundary layer regions, it is in practice to dimensionless the governing equations and grouping variables together into dimensionless numbers in order to curtail the total number of variables. In non-similar flows, in contrast to similar flows the basic quantities change in the flow direction. Flows across porous media are important because of its applications in biological and environmental systems such as tissues, bones soils, etc. In Darcy-Forchheimer-Brinkman framework the basic quantities change in the stream wise direction. Therefore, non-similar boundary layer model is developed for forced convection in the steady flow of Casson nano-fluid over horizontal plate installed in non-Darcy porous media. The governing equations describing Darcy-Forchheimer-Brinkman model are transformed into dimensionless non-similar model by making use of appropriate non-similar transformations. The dimensionless partial differential system is solved through local non-similarity via bvp4c. The impact of emerging non-dimensional parameters, namely, Casson parameter (β ), Schmidt number (Sc), porosity (e), Prandtl number (Pr), 1st order porous resistance parameter (R1), thermophoresis parameter ( Nt), 2nd order porous resistance parameter (R2), Brownian motion parameter (Nb) and dimensionless viscous dissipation on the dimensionless velocity, temperature and concentration distributions are examined in detail. Furthermore, the impacts of these parameters on dimensionless friction coefficient and heat transfer rate are also explored. Finally, comparison of non-similar solutions with local similar solutions has been made with published data.