**Simulation of Natural Convection in Porous Media by Boundary Element Method Boundary Element Method**

**Simulation of Natural Convection in Porous Media by** 

DOI: 10.5772/intechopen.71230

Janja Kramer Stajnko, Renata Jecl and Jure Ravnik Additional information is available at the end of the chapter

Janja Kramer Stajnko, Renata Jecl and Jure Ravnik

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71230

### **Abstract**

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In this chapter, the boundary element method (BEM) is introduced for solving problems of transport phenomena in porous media domains, which is an important topic in many engineering and scientific branches as well as in fields of practical interest. The main objective of the present work is to find a numerical solution of the governing set of equations written for fluid flow in porous media domains, representing conservation of mass, momentum, and energy. The momentum equation is based on the macroscopic Navier-Stokes equations and is coupled with the energy equation. In order to use BEM for the solution of the obtained set, the governing equations are transformed by the velocity-vorticity formulation, which separates the computational scheme into kinematic and kinetic computational parts. A combination of single- and sub-domain BEM is used to solve the obtained set of partial differential equations. Solution to a problem of natural convection in porous media saturated with pure fluid and nanofluid, respectively, for examples of 2D and 3D geometries, is shown. Results are compared to published work in order to estimate the accuracy of developed numerical algorithm. Based on the results, the applicability of the BEM for solving wide range of various problems is stated.

**Keywords:** boundary element method, porous media, velocity-vorticity formulation, natural convection, nanofluids
