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The Galerkin finite element method (FEM) based on the characteristic-based split (CBS) scheme is applied to simulate the nanofluid flow and thermal fields inside an inclined geometry filled by a heat-generating hydrodynamically and thermally anisotropic non-Darcy porous medium using the local thermal non-equilibrium model (LTNEM). Property of the hydrodynamic anisotropy is taken in both the Forchheimer coefficient and permeability and these tools are considered as functions of inclination of the principal axes. Also, the thermal conductivity for the porous phase is assumed to be anisotropic.

The Galerkin FEM based on the CBS scheme is applied to solve the partial differential equations governing the flow and thermal fields.

It is noted that the net rate of the heat transfer between the nanofluid and solid phases are influenced by variations of the anisotropic properties. Also, the system is reached to the thermal equilibrium state at H > 100. Further, the maximum nanofluid temperature is reduced by 12.27% when the nanoparticles volume fraction is varied from 0% to 4%.

This paper aims to study the nanofluid flow and heat transfer characteristics inside an inclined enclosure filled with a heat-generating, hydrodynamically and thermally anisotropic porous medium using the CBS scheme. The LTNEM is considered between the nanofluid and porous phases while the local thermal equilibrium model (LTEM) between the base fluid (water) and the nanoparticles (alumina) is taken into account. The Galerkin FEM is introduced to discretize the governing system of equations. Also, examine influences of the anisotropic properties (permeability, Forchheimer terms and thermal conductivity of the porous medium), inclination angle and nanoparticles volume fraction on the net rate of the heat transfer between the nanofluid and porous phases and on the local thermal non-equilibrium state is one of the concerns of this paper.

This paper aims to study the mixed convective process due to various dynamics, namely, inner rotating cylinders and upper-wavy wall movement for the first time.

The Galerkin finite element method together with the characteristic-based split scheme is applied to solve the governing system.

The main outcomes revealed that the direction of the rotation of the cylinders, radius and locations of the rotating shapes are beneficial controlling elements for the enhancement of heat transfer. Also, for all the considered cases, values of the Bejan number indicate that the fluid friction irreversibility is dominance compared to the heat transfer irreversibility. Further, average values of the heat transfer entropy, fluid friction entropy and total entropy are minimized in the case of fixed cylinders regardless of the cylinder radius.

The authors are interested in the mixed convection case due to regular boundaries and hence this simulation purposes a first attempt to examine the mixed convective flow due to irregular wavy boundaries. This study considered various dynamics, namely, inner rotating cylinders and wavy-lid driven wall which makes it more attractive to the readers. Various cases based on radius of the cylinder and direction of the rotations together with several locations of the rotating shapes are taken into account which makes the current simulation is comprehensive. Various studies presented in this field are made by commercial software and these treatments need special conditions (having limitation) but the current solution methodology is based on a finite element method home-code. Various important impacts, are, also, examined, namely, inclined geometry, inclined magnetic field, thermal radiation and heat generation/absorption. The entropy of the current complex system is analyzed based on the second law of thermodynamics.

The main advantage of the proposed method is that the computations can be performed on a Cartesian grid with complex immersed boundaries (IBs). The purpose of this paper is to device a numerical scheme based on an embedding finite element method for the solution of two-dimensional (2D) Navier-Stokes equations.

Geometries featuring the stationary solid obstacles in the flow are embedded in the Cartesian grid with special discretizations near the embedded boundary to ensure the accuracy of the solution in the cut cells. To comprehend the complexities of the viscous flows with IBs, the paper adopts a compact interpolation scheme near the IBs that allows to satisfy the second-order accuracy and the conservation property of the solver. The interpolation scheme is designed by virtue of the shape function in the finite element scheme.

Three numerical examples are selected to demonstrate the accuracy and flexibility of the proposed methodology. Simulation of flow past a circular cylinder for a range of Re=20-200 shows excellent agreements with other results using different numerical schemes. Flows around a pair of tandem cylinders and several bodies are particularly investigated. The paper simulates the time-based variation of the flow phenomena for uniform flow past a pair of cylinders with various streamwise gaps between two cylinders. The results in terms of drag coefficient and Strouhal number show excellent agreements with the results available in the literature.

Details of the flow characteristics, such as velocity distribution, pressure and vorticity fields are presented. It is concluded the combined embedding boundary method and FE discretizations are robust and accurate for solving 2D fluid flows with complex IBs.