Defining Thermal Convection for a Cohesive Element

You can define convective heat transfer with gap flow as well as thermal convection between the gap fluid and both the top and bottom surfaces of a coupled temperature-pore pressure cohesive element.

Thermal convection modeling using coupled temperature-pore pressure cohesive elements:

can be performed in coupled pore fluid diffusion/stress analyses (Coupled Pore Fluid Diffusion and Stress Analysis);
can also involve convective heat transfer between the gap fluid and both the top and bottom surfaces of a cohesive element; and
can be specified by a material model.

This page discusses:

Modeling Thermal Convection Together with Gap Fluid Flow within a Cohesive Element
Specifying Fluid Density
Specifying Specific Heat of the Fluid
Specifying Conductivity of the Fluid
Specifying Heat Convection between the Fluid and Both the Top and Bottom Surfaces

Modeling Thermal Convection Together with Gap Fluid Flow within a Cohesive Element

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

ρ_{f} c_{f} {(d θ)}_{, t} + ρ_{f} c_{f} \nabla\cdot (d q θ) - \nabla\cdot (d k \nabla θ) - ρ_{f} c_{f} [c_{t} (p_{i} - p_{t}) + c_{b} (p_{i} - p_{b})] - h (θ - θ_{t}) - h (θ - θ_{b}) = 0,

where

$ρ_{f}$: 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,
$θ$: is the temperature of the gap flow,
$θ_{t}$: is the temperature on the top surface, and
$θ_{b}$: 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.

Specifying Fluid Density

You can define the gap fluid density.

Specifying Specific Heat of the Fluid

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

Specifying Conductivity of the Fluid

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

Specifying Heat Convection between the Fluid and Both the Top and Bottom Surfaces

The heat convection coefficient is defined as

h = \frac{N u}{2} \frac{k}{d},

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