1. Heat transfer method

1. Heat conduction

When there is no relative displacement between various parts of an object, the heat energy transfer generated by the thermal movement of microscopic particles such as molecules, atoms, and free electrons is called thermal conduction. The basic law of heat conduction is Fourier's law:

$\Phi =-\lambda A\frac{\Delta T}{\delta }$

Among them, $\Phi$ is the heat flow; $\lambda$ is the thermal conductivity; A is the area; T is the temperature; $\delta$ is the wall thickness. Except for water, aqueous solutions and glycerol, the thermal conductivity of most other liquids decreases with increasing temperature.

2. Thermal convection

The relative displacement between various parts of the fluid caused by the macroscopic motion of the fluid, and the heat transfer process caused by the mixing of hot and cold fluids is called thermal convection. Thermal convection can only occur in fluids, and because the molecules in the fluid are undergoing irregular thermal motion at the same time, thermal convection must be accompanied by heat conduction.

What is of interest in engineering is the heat transfer process between the fluid and the surface of the object when the fluid flows through the surface of an object, which is called convective heat transfer. In fact, in most cases, the so-called thermal convection also refers to this situation. According to the causes of flow, convective heat transfer can be divided into two categories: natural convection and forced convection. The basic formula for convective heat transfer is Newton’s cooling formula:

$\Phi =hA\Delta T$

Among them, h is the convection heat transfer coefficient (surface heat transfer coefficient).

3. Thermal radiation

The phenomenon of objects emitting radiant energy due to heat is called thermal radiation. Theoretically, as long as the temperature of an object is higher than absolute zero, the object will continue to convert thermal energy into radiant energy and emit thermal radiation outward. The basic formula of thermal radiation is the Stefan-Boltzmann law, also known as the fourth power law:

$\Phi =\varepsilon A\sigma T^{4}$

Among them, $\varepsilon$ is the radiation coefficient of the object, its value is always less than 1; $\sigma$ is the Stefan-Boltzmann constant.

2. Three types of boundary conditions for thermal conduction problems

1. The temperature value on the boundary is specified, which is called the first type of boundary condition, also known as Dirichlet condition. Such conditions generally specify that the temperature of the boundary is constant.

2. The heat flow density value on the boundary is specified, which is called the second type of boundary condition, also known as Neumann condition. Such conditions generally stipulate that the heat flux density at the boundary is constant.

3. The surface heat transfer coefficient h between the object on the boundary and the surrounding fluid and the temperature of the surrounding fluid are specified, which is called the third type of boundary condition, also known as Robin condition.

In addition, when dealing with actual engineering problems, you will also encounter radiation boundary conditions, that is, only radiation heat exchange occurs between the object surface and the external environment, such as the heat dissipation of the heating element on the spacecraft to space.

3. Setting of thermal boundary in Fluent

During Fluent simulation, the default wall surface is adiabatic, that is, the heat flow through the wall surface is 0. If you want to analyze heat transfer, first open the energy equation, and then select it in the "Wall"-"Thermal" tab. The first three types of Heat Flux, Temperature, and Convection correspond to the second type, first type, and The third type of boundary conditions. Radiation is the radiation boundary condition, and Mixed is the mixed boundary condition. In addition to the normal boundary conditions, Fluent can also set the heating power of the wall. If the wall is an ordinary solid wall, it will be 0 here.

It should be noted that when there is a conjugate heat transfer problem in the calculation, Fluent will automatically generate a shadow surface for the conjugate heat transfer interface when importing the mesh. Under normal circumstances, such wall surfaces do not require additional settings.

4. Calculation methods for different heat transfer methods

1. Calculation of heat conduction

In engineering calculations, the problem of heat transfer is usually presented in terms of thermal resistance settings. The thermal resistance is defined as:

$R=\frac{\delta }{\lambda A}$

The meaning of each parameter has been explained above. Fluent generally has three methods to deal with thermal resistance:

(1) Set up a thin wall with thickness, mesh it, and set the material to calculate the thermal resistance value through the solver. This method can take into account the heat transfer process in all directions, but tends to significantly increase the number of meshes.

(2) Set a virtual thickness for the wall. Its thickness is not reflected in the geometric model, so it only exists as a 0-thickness wall when meshing. After importing it into Fluent, set a virtual thickness for it in the wall settings. This approach can significantly reduce the number of meshes while considering thermal resistance, but this approach can only take into account the heat transfer process perpendicular to the wall direction. In Fluent, we can consider the impact of thin-wall thermal resistance on heat transfer by specifying wall material and wall thickness.

(3) Set Shell Conduction. This method is similar to (2), but can take into account heat transfer in all directions. Multiple layers of thin walls of different materials can be specified at the same time. In some engineering applications, this approach can greatly reduce the difficulty and quantity of meshing while ensuring accuracy.

2. Calculation of thermal convection

(1) In forced convection calculations, it is generally necessary to select an appropriate turbulence model. It is usually recommended to use the Realizable ke or SST kw model.

(2) In natural convection calculations, the Rayleigh number is generally used to determine whether the flow is turbulent. The formula is:

$Ra=\frac{\beta gL^{3}\Delta T}{\nu \alpha }$

Among them, $\beta$ is the expansion coefficient, g is the acceleration of gravity, L is the characteristic length, $\not$ is the kinematic viscosity, and $\alpha$ is the diffusivity. At that time $Ra> 10^{9}$ , the flow was turbulent and the corresponding turbulence model needed to be opened.

Different from general simulation calculations, natural convection requires the following settings:

Since natural convection is caused by changes in density under the influence of gravity, the gravity item should be turned on and the magnitude and direction of gravity should be set;
The pressure discretization format of natural convection is set to Body Force Weighted or PRESTO!. Using the default second-order format will give incorrect results;
Check Operating Density and set the reference density to make the calculation more stable;
Material density settings: For gases, the density setting can choose Boussinesq assumption or incompressible ideal gas model. For liquids, only the Boussinesq assumption can be selected. For natural convection calculations in closed areas, the Boussinesq assumption also needs to be used. The Boussinesq model assumes that the densities of all terms in the momentum equation are constant except for the body force term. It should be noted that the Boussinesq assumption can only be used when the density change is less than 20%. To open Boussinesq, you need to select Boussinesq in the density setting and set the reference density. At the same time, you need to set the fluid expansion coefficient. Generally, the expansion coefficient of a gas is the reciprocal of its thermodynamic temperature.

3. Calculation of thermal radiation

First, the concept of optical thickness is proposed. Optical thickness is a measure of the ability of a medium to absorb radiation. In Fluent, the formula for optical thickness is:

$Optical\; Thickness=(\alpha +\sigma )L$

Among them, $\alpha$ is the absorption coefficient, which is the amount of radiation intensity change after passing through the medium per unit length due to medium absorption. Since air generally does not absorb radiation, this coefficient can be set to 0 when the fluid medium is air. $\sigma$ is the scattering coefficient, which is the amount by which the radiation intensity changes per unit length of the medium due to scattering by the medium. Similarly, this coefficient can be set to 0 when the fluid medium is air. L is the characteristic length.

Generally speaking, the thermal radiation model is used in high temperature conditions and conditions where only natural convection exists. To consider the influence of thermal radiation in the calculation, you need to open the "Radiation Model" panel and select the corresponding thermal radiation model.

The difference between thermal radiation models
Model	Optical thickness	Calculation amount
Rossland	>5	The amount of calculation is small, but the accuracy is average, and the use is less
P1	>1	The calculation amount is small, and the calculation effect is better in problems with large optical thickness.
DTRM	all	The amount of calculation is small, but it cannot be used for parallel computing and is rarely used.
S2S	0	When the optical thickness is 0, the S2S calculation accuracy is equivalent to that of the DO model, but the calculation amount is less than that of the DO model.
DO	all	It has a wide range of uses, but has the largest amount of calculation and the highest calculation accuracy.

5. Basic steps of Fluent thermal analysis

1. Open the energy equation and determine whether the gravity term needs to be opened;

2. Select the appropriate turbulence model;

3. Set the solid material properties and pay attention to whether the density item needs to be modified;

4. Set appropriate thermal boundary conditions for the wall;

5. Check whether the pressure discrete method needs to be modified;

6. Initialization and calculation.

Fluent Solver - Thermal Analysis