Temperature diffusion in laminates

II.1.11 Temperature diffusion in laminates

The thermal conservation equation in a solid material is written as follows:

ρ C_{p} \frac{\partial T}{\partial t} = - \nabla \cdot q + r,

where $T$ is the temperature, $C_{p}$ is the heat capacity of the material and vector $q$ is the heat flux. Note that $C_{p}$ and $ρ$ are used for transient thermal calculations only. Generally, the heat flux is related to the gradient of temperature by Fourrier’s law:

q = - λ^{T} \cdot \nabla T,

where $λ^{T}$ is the tensor of thermal conductivity coefficients. We consider that thermal conductivity tensor is symmetric. A justification of this symmetry can be found in [LLK $^{+}$ 86] with part of the demonstration in [LL13].

When thermal conductivity calculations are performed with laminates, two homogenized quantities must first be calculated:

The laminate global conductivity tensor,
The laminate global thermal capacity.

These two quantities are obtained by integrating material properties along laminate thickness.

  II.1.11.1 Material thermal parameters
  II.1.11.2 In-plane and out-of-plane components
  II.1.11.3 In-plane rotations of vectorial and tensorial properties
  II.1.11.4 Integration along the laminate thickness
   II.1.11.4.1 In-plane conductivity
   II.1.11.4.2 Out-of-plane conductivity
   II.1.11.4.3 Thermal capacity

[next] [prev] [prev-tail] [front] [up]