Characteristic Study of Coriolis Force on Free Convection in a Finite Geometry with Isotropic and Anisotropic Porous Media Sudhir Patel, P. A.Dinesh, S. P. Suma, and N. L. Ramesh Abstract Work carried out in this paper deals with classic Rayleigh–B ` enard prob- lem for an unsteady, laminar, viscous incompressible fluid of a horizontal layer heated from below which is extended to the three-dimensional convection in a rectangu- lar box with anisotropic and isotropic porous media rotating with constant angular velocity that is investigated. For the given physical system, seven governing PDEs are transformed to system of non-dimensional ODEs using similarity transformation. The investigation demands to apply Fourier series method to study the characteristic of velocity and temperature for the effect of Taylor number, Rayleigh number and Prandtl number for both isotropic and anisotropic cases. The results of the stream function and isotherms on various parameters have been discussed and found to be good agreement for the physical system. Keywords Isotropic and anisotropic porous media · Free convection · Coriolis force Nomenclature a width of the rectangular channel β Thermal expansion co-efficient c Specific hear at constant pressure S. Patel Department of Mathematics, New Horizon College of Engineering, Bengaluru 560103, India e-mail: sudhirp@newhorizonindia.edu P. A. Dinesh (B ) · N. L. Ramesh Department of Mathematics, M. S. Ramaiah Institute of Technology, Bengaluru 560054, India e-mail: dineshdpa@msrit.edu N. L. Ramesh e-mail: nlramesh1607@yahoo.com S. P. Suma Department of Mathematics, Cambridge Institute of Technology, Bengaluru 560036, India e-mail: drsumasp@gmail.com © Springer Nature Singapore Pte Ltd. 2021 B. Rushi Kumar et al. (eds.), Advances in Fluid Dynamics, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-4308-1_76 985