4 The stationary diffusion equation
5 ---------------------------------
8 -\lambda\triangle T = \Phi+\lambda_{sf}(T_f-T)
11 - $T$ the main unknown is the solid temperature field
12 - $\lambda$ is the solid thermal conductivity possibly set by the user (default value is 1)
13 - $\Phi$ is the heat source term possibly set by the user (default value is 0)
14 - $\lambda_{sf}$ is the fluid-solid heat transfer coefficient set by the user (default value is 0)
15 - $T_f$ is the fluid temperature field provided by the user
17 See the [Stationary diffusion equation page](StationaryDiffusionEq.ipynb)
19 The diffusion equation
20 ----------------------
22 \partial_t T =d\triangle T +\frac{ \Phi+\lambda_{sf}(T_f-T)}{\rho c_p}
25 - $T$ the main unknown is the rod temperature field
26 - $\rho$ is the rod density assumed constant (default value 10000)
27 - $c_p$ is the rod specific heat, provided by the user and assumed constant (default value 300)
28 - $d=\frac{\lambda}{\rho c_p}$ is the rod diffusivity (default value 5/(10000*300))
29 - $\lambda_{sf}$ is the fluid-rod heat transfer coefficient provided by the user (default value 0)
30 - $\Phi$ is the heat source term if explicitely known (default value 0)
31 - $T_f$ is the fluid temperature field provided by the user
33 See the [Diffusion equation page](DiffusionEq.ipynb)
35 The transport equation
36 ----------------------
39 \partial_t H + \vec{u}\cdot\vec{\nabla} H = \Phi+\lambda_{sf}(T_s-T)
44 - $ H $ the main unknown is the fluid enthalpy field
45 - $ \vec{u} $ is the constant transport velocity
46 - $ \Phi $ is the heat source term if explicitely known
47 - $ T_s $ is the rod temperature field provided by the user
48 - $ T=T_0+\frac{H-H_0}{c_p}$ is the fluid temperature field
49 - $ \lambda_{sf}$ is the fluid-rod heat transfer coefficient provided by the user
50 - $ c_p $ is the fluid specific heat, provided by the user and assumed constant
52 See the [Transport equation page](TransportEq.ipynb)