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The coexistence in nature of thermally stratified fluids and directionally inclined porous structures abound in geophysical fluid flow. Despite their important applications especially in underground flow, their combined effects on natural convection have not been intensively investigated. This article aims to investigate a fully developed time dependent natural convection of viscous incompressible stably stratified fluid in the presence of anisotropic porous material. The semi analytical solutions of the governing equations for the temperature and velocity fields are obtained using the Laplace Transform Technique, Riemann Sum Approximation and D’Alembert Methods. The choice of the D’Alembert Method is to provide a systematic decoupling procedure for the coupled governing equations while still retaining their original orders. This research establishes that the fluid maximum or minimum velocity can be attained by properly manipulating the anisotropic parameters.

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