Defining Thermal Convection for a Cohesive Element

The thermal convection contributes toward the energy balance. The energy equation is given by:

where

${\rho }_f$

is the fluid density,

$c_f$

is the specific heat of the fluid,

$k$

is the conductivity of the fluid,

$h$

is the heat convection coefficient,

$\theta$

is the temperature of the gap flow,

${\theta }_t$

is the temperature on the top surface, and

${\theta }_b$

is the temperature on the bottom surface.

All of the other variables (such as $q$, $d$, $p_i$, $p_t$, $p_b$, $c_t$, and $c_b$) are defined in Defining the Constitutive Response of Fluid Transitioning from Darcy Flow to Poiseuille Flow.

You can define the gap fluid density.

You can define the specific heat of the pore fluid in a porous medium.

You can define the conductivity of the pore fluid in a porous medium.

The heat convection coefficient is defined as

where $\mathrm{N}\mathrm{u}$ is the Nusselt number. You can specify the Nusselt number as a function of temperature and field variables.