# Tut Small Study on Conjugate Heat Transfer

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## 1 heatTransfer

### 1.1 Problem setup

The problem studied is a hot air flow injected into a container coupled with the heat transfer from the flow to and into the container walls. Numerically, this is solved in a Large Eddy Simulation framework, with a one equation transport model for the subgrid turbulent kinetic energy.

## 2 Complete Solution

The first approach was to take into account both domains, and to solve two different sets of equations:

#### 2.1 Compressible fluid flow

$\frac{\partial\rho}{\partial t}+\nabla\cdot\rho U=0$

$\frac{\partial\rho U}{\partial t}+\nabla\cdot\phi U-\nabla\cdot\mu\nabla U=-\nabla p$

$\frac{\partial\rho h}{\partial t}+\nabla\cdot\phi h=0$

#### 2.2 Heat conduction in the solid domain

$\frac{\partial T}{\partial t}+k\cdot\Delta T=0$

The written solver is called \u201cconjHeat\u201d, and is based on two other existing OpenFOAM solvers, namely \u201crhoTurbFoam\u201d and \u201claplacianFoam\u201d. The sources are accesible through the following link: Media:conjHeat.tgz. The test case consists in a solid can (see Figure 1b), in which a hot fluid (700 K) is injected with 0.1m/s through a small area (green face in Figure 1). The exterior wall surface of the can is kept at a constant temperature of 300 K.

Figure 1: Solid and fluid domains