# Non Equilibrium Porous Medium Heat Transfer CFD Simulation

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A porous medium is a material consisting of a solid network that is interconnected by spaces or pores between them.

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## Description

## Porous Media

Empty spaces between the pores allow fluid to flow into the grid. One of the most important applications of porous media is to provide more heat transfer to increase heat transfer in equipment and tools that require cooling. Porous media are used in the oil and gas industry, water engineering, soil engineering, building materials, etc.

## Problem Description

In this problem, air flows downstream into the cylindrical chamber. The airflow must be assumed to be developed; hence, the cylindrical height is assumed to be relatively high. At the bottom of the cylinder is a small cylindrical fin which is made of aluminum as a solid part. In the space between the outer and inner cylinders, the porous medium is made of aluminum foam. At the bottom of the entire floor of the model, a heat source of copper is applied.

This problem is characterized by the application of interface surfaces in three areas: the common boundary between the porous medium and the aluminum fin, the common boundary between the air and the aluminum fin, and the common boundary between the porous medium and the open air.

In the first two states, since aluminum solids are used on one side of the border, only heat transfer is carried out across the boundaries and no mass transfer is achieved; while in the latter case, in addition to heat transfer, the mass transfer also takes place. The purpose of this problem is to increase the surfaces of heat transfer by using aluminum fin and porous aluminum environment to increase the heat transfer between the heat source and the surrounding environment and consequently the heat source cooling.

## The Assumptions for Non-Equilibrium Porous Simulation

There are several assumptions used for the present simulation. The simulation is Steady-State and the solver is Pressure-Based, also gravity is ignored.

## Geometry & Mesh

The geometry of the present model is designed using Design Modeler software. The present model is two-dimensional and is symmetrically drawn due to its symmetrical structure. The model consists of three main parts: the open-air intake space, the aluminum porous media space, and the solid aluminum fin space. The meshing of the present model is carried out by ANSYS Meshing software. The mesh type is structured and the element number is 7860.

## Non-Equilibrium Porous CFD Simulation

Here are some summaries of the problem definition and problem-solving steps in the table:

Models |
||

Laminar | Viscous model | |

On | Energy | |

Boundry conditions |
||

Velocity-inlet | Inlet | |

4.421952 m.s^{-1} |
velocity magnitude | |

300 K | temperature | |

Pressure-outlet | Outlet | |

0 Pa | gauge oressure | |

Wall | Walls type | |

temperature 330 K | heat wall porous | |

heat flux 0 W.m^{-2}.K^{-1} |
Other walls | |

Mesh interface | ||

q, u, w | 3 interfaces | |

Solution Methods |
||

Simple | |
Pressure-velocity coupling |

Second order upwind | pressure | Spatial discretization |

Second order upwind | momentum | |

Second order upwind | energy | |

Initialization |
||

Standard | Initialization method | |

-4.421952 m.s^{-1} |
y-velocity | |

300 | temperature |

### Interface

According to the present problem, the boundaries between airflow, solid fin, and porous media are defined. To allow heat transfer or mass transfer between these boundaries, the mesh interface command should be used, as the boundary between the porous medium and the solid fin, as well as the boundary between the solid fin and the airflow, is only for the heat transfer, but the boundary between the porous medium and the airflow is for both mass and heat transfer.

The interface between the porous area and the airflow is denoted by the symbol “e”, the interface between the porous area and the aluminum fin with the symbol “q” and the interface between the aluminum fin and the airflow with the symbol “w”.

### Porous Zone

The viscous resistance in the porous medium is the inverse of the permeability of the fluid in the porous medium, which is 58888270 1.m-2 in the problem. Inertial resistance is also considered to be 1000.794 1.m-1. The porosity coefficient in the porous media is equal to the ratio of vacuum to total space, which is 0.87 in the present problem. The porous medium in the problem is non-equilibrium; therefore, a non-equilibrium option must be activated.

In general, it is sometimes not appropriate to assume a thermal equilibrium between a solid and a fluid environment, for reasons such as the physical properties of the fluid and solid phases, or the existence of different geometrical scales at the boundaries, causing local temperature differences between the phases. When using non-equilibrium heat equations, a term related to the heat source is obtained which requires the definition of hsf and Asf according to the relation:

h_sf A_sf (T_s-T_f).

### Equations

Therefore, the interfacial area density value is 2864.27 1.m-1 and the heat transfer coefficient value is 54.78671 W.m-2.K-1.The amount of viscous resistance and the amount of fluid permeability in this model is obtained by the following equation:

r_viscous = 1 / a; α = 0.00037 (1-ԑ) ^ (- 0.224) 〖d_f〗 ^ (- 1.11) 〖d_p〗 ^ 0.89

The value of the inertia resistance in this model is obtained from the following relation:

r_inertial = (2C_i) / √α; C_i = 0.00212 (1-s) ^ (- 0.132) (d_f / d_p) ^ (- 1.63)

The interfacial area density value in this model is obtained by the following equation:

A_sf = (〖3πd〗 _f (1-e ^ (- ((1-ԑ)) / 0.04)) / (〖0.59d〗 _p) ^ 2

The value of heat transfer coefficient in this model is obtained from the following relation:

h_sf = k_f / d_f (0.36+ (0.51 〖Ra_d〗 ^ (1⁄4)) / (1+ (0.599 / Pr) ^ (9⁄16)) ^ (4⁄9)) Ra_d = 〖β gβΔd 〗 _F〗 ^ 3 / (α_f ν_f)

In the above equations dp equals the mean diameter, df equals the diameter of the cell, ԑ equals the porosity coefficient, 𝛂 equals the permeability, and β equals the liquid volume fraction.

All files, including Geometry, Mesh, Case & Data, are available in Simulation File. By the way, Training File presents how to solve the problem and extract all desired results.

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