The scalar models

The stationary diffusion equation

$$ -\lambda\triangle T = \Phi+\lambda_{sf}(T_f-T) $$

where

$T$ the main unknown is the solid temperature field
$\lambda$ is the solid thermal conductivity possibly set by the user (default value is 1)
$\Phi$ is the heat source term possibly set by the user (default value is 0)
$\lambda_{sf}$ is the fluid-solid heat transfer coefficient set by the user (default value is 0)
$T_f$ is the fluid temperature field provided by the user

See the Stationary diffusion equation page

The diffusion equation

$$ \partial_t T =d\triangle T +\frac{ \Phi+\lambda_{sf}(T_f-T)}{\rho c_p} $$

where

$T$ the main unknown is the rod temperature field
$\rho$ is the rod density assumed constant (default value 10000)
$c_p$ is the rod specific heat, provided by the user and assumed constant (default value 300)
$d=\frac{\lambda}{\rho c_p}$ is the rod diffusivity (default value 5/(10000*300))
$\lambda_{sf}$ is the fluid-rod heat transfer coefficient provided by the user (default value 0)
$\Phi$ is the heat source term if explicitely known (default value 0)
$T_f$ is the fluid temperature field provided by the user

See the Diffusion equation page

The transport equation

$$ \partial_t h + \vec{u}\cdot\vec{\nabla} h = \Phi+\lambda_{sf}(T_s-T) $$

where

$h$ the main unknown is the fluid enthalpy field
$\vec{u}$ is the constant transport velocity
$\Phi$ is the heat source term if explicitely known
$T_s$ is the rod temperature field provided by the user
$T=T_0+\frac{H-H_0}{c_p}$ is the fluid temperature field
$\lambda_{sf}$ is the fluid-rod heat transfer coefficient provided by the user
$c_p$ is the fluid specific heat, provided by the user and assumed constant

See the Transport equation page