Heat Transfer

Heat transfer is the exchange of thermal energy between media at different temperatures. Heat transfers from locations of high temperature to locations of low temperature in order to reach an equilibrium state. The three main mechanisms of heat transfer are: conduction, convection, and radiation.

In Simcenter STAR-CCM+, heat transfer can be calculated within a fluid (single or multi-component), between different fluid streams, between a fluid and a solid, and within a solid. The coupled heat transfer within a fluid and an adjoining solid is called conjugate heat transfer. For a conjugate heat transfer analysis, the energy equation is solved throughout the fluid and the solid solution domain with an efficient implicit thermal coupling at the fluid/solid interface. All other conservation equations are solved within the fluid only.

Energy Equation in Fluids

Simcenter STAR-CCM+ implements the energy equation in the following integral form:

Figure 1. EQUATION_DISPLAY

\frac{\partial}{\partial t} \int_{V} ρ E d V + \oint_{A} ρ H v \cdot d a = - \underset{Conduction}{\underset{︸}{\oint_{A}^{} \dot{q} ″ \cdot d a}} + \underset{Viscous Work}{\underset{︸}{\oint_{A}^{} T \cdot v d a}} + \int_{V} f_{b} \cdot v d V + \oint_{A}^{} \sum_{i}^{} h_{i} J_{i} d a + \int_{V} S_{u} d V

(1657)

where:

$E$ is the total energy.
$H$ is the total enthalpy.
$\dot{q} ″$ is the heat flux vector.
$T$ is the viscous stress tensor.
$v$ is the velocity vector.
$f_{b}$ is the body force vector representing the combined body forces of rotation, gravity, and the fan mode.
$h_{i}$ is the enthalpy of component $i$ .
$J_{i}$ is the diffusive flux of component $i$ .
$S_{u}$ is a user-specified source term.

Total energy is related to the total enthalpy H by:

Figure 2. EQUATION_DISPLAY

E = H - p / ρ

(1658)

where:

Figure 3. EQUATION_DISPLAY

H = h + {| v |}^{2} / 2

(1659)

and $h$ is the static enthalpy.

Energy Equation in Solids

The governing equation for energy transport within a solid is given as follows:

Figure 4. EQUATION_DISPLAY

\frac{d}{d t} \int_{V} ρ C_{p} T d V + \oint_{A} ρ C_{p} T v_{s} \cdot d a = - \oint_{A} \dot{q} ″ \cdot d a + \int_{V} S_{u} d V

(1660)

where:

$ρ$ is the solid density.
$C_{p}$ is the specific heat.
$T$ is the temperature.
$\dot{q} ″$ is the heat flux vector.
$v_{s}$ is the solid convective velocity (only applicable when the region is a pure body of rotation).
$S_{u}$ is a user-defined volumetric heat source within the solid.

Simcenter STAR-CCM+ solves for Eqn. (1660) using either the finite volume method (Segregated Solid Energy and Coupled Solid Energy models) or the finite element method (Finite Element Solid Energy model). The finite element implementation does not include the second term on the left-hand side of Eqn. (1660).