Defining a Thermal Interaction for a Gasket Element

You can define thermal interaction between the top and bottom surfaces of a coupled temperature-displacement gasket element.

A thermal interaction between the top and bottom surfaces of a three-dimensional coupled temperature-displacement gasket element:

can be included in a thermal-stress analysis (Fully Coupled Thermal-Stress Analysis);
can involve conductive heat transfer between the top and bottom surfaces; and
can be specified for gasket behavior defined by a material model or a gasket behavior model.

This page discusses:

Specifying Thermal Conductance of a Gasket Element
Modeling Conductance between the Top and Bottom Surfaces of a Gasket Element

Specifying Thermal Conductance of a Gasket Element

The thermal conductance between the top and bottom surfaces of a three-dimensional coupled temperature-displacement gasket element can be specified for gasket behavior defined by a material model or a gasket behavior model.

Input File Usage

Use the following options to define the thermal conductance with a material model:

GASKET SECTION, ELSET=name, MATERIAL=name
MATERIAL, NAME=name
GAP CONDUCTANCE

Use the following options to define the thermal conductance with a gasket behavior model:

GASKET SECTION, ELSET=name, BEHAVIOR=name
GASKET BEHAVIOR, NAME=name
GAP CONDUCTANCE

Modeling Conductance between the Top and Bottom Surfaces of a Gasket Element

The conductive heat transfer between the top and bottom surfaces of a gasket element is assumed to be defined by

q = k (θ_{A} - θ_{B}),

where q is the heat flux per unit area crossing the gasket from point A on the top surface to point B on the bottom surface, $θ_{A}$ and $θ_{B}$ are the temperatures of the points on the surfaces, and k is the gap conductance. Point A is a node on the top surface; and point B is the corresponding node on the bottom surface.

You can define k directly or, in Abaqus/Standard, in user subroutine GAPCON.

Defining Gap Conductance Directly

When defining k directly, define it as

k = k (c, p, \bar{θ}, \bar{| \dot{m} |}, {\bar{f}}_{γ}),

where

c: is the closure between A and B,
p: is the pressure transmitted across the gasket between A and B,
$\bar{θ} = \frac{1}{2} (θ_{A} + θ_{B})$: is the average of the surface temperatures at A and B,
$\bar{| \dot{m} |}$: is the average of the magnitudes of the mass flow rates per unit area. This variable is not considered here and should be set as zero.
${\bar{f}}_{γ} = \frac{1}{2} (f_{γ}^{A} + f_{γ}^{B})$: is the average of any predefined field variables at A and B.

Defining Gap Conductance as a Function of Closure

You can create a table of data defining the dependence of k on the variables listed above. The default in Abaqus is to make k a function of the closure c. When k is a function of closure, c, the tabular data must start at zero closure and define k as c increases. At least two pairs of $k - c$ points must be given to define k as a function of the closure. The value of k drops to zero immediately after the last data point, so there is no heat conductance when the closure is greater than the value corresponding to the last data point.

Input File Usage

GAP CONDUCTANCE 
 $k$ , c,  $\bar{θ}$

Defining Gap Conductance as a Function of Contact Pressure

You can define k as a function of the pressure, p. When k is a function of pressure in gasket elements, the tabular data must start at zero pressure and define k as p increases. The value of k remains constant for pressures outside of the interval defined by the data points.

Input File Usage

GAP CONDUCTANCE, PRESSURE 
 $k$ , p,  $\bar{θ}$

Gap Conductance as a Function of Both Closure and Contact Pressure

If both closure-dependent and pressure-dependent conductances are specified, the pressure-dependent curves are used to evaluate the conductance.

Defining Gap Conductance to Be a Function of Predefined Field Variables

In addition to the dependencies mentioned previously, the gap conductance can be dependent on any number of predefined field variables, ${\bar{f}}_{γ}$ . To make the gap conductance depend on field variables, at least two data points are required for each field variable value.

Input File Usage

GAP CONDUCTANCE, DEPENDENCIES=n 
k, c,  $\bar{θ}$ ,  $\bar{| \dot{m} |}$ ,  ${\bar{f}}_{γ}$

Defining the Gap Conductance Using User Subroutine GAPCON

In Abaqus/Standard k can be defined in user subroutine GAPCON. In this case there is greater flexibility in specifying the dependencies of k. It is no longer necessary to define k as a function of the average of the two surface's temperatures, mass flow rates, or field variables:

k = k (c, p, θ_{A}, θ_{B}, {| \dot{m} |}_{A}, {| \dot{m} |}_{B}, f_{γ}^{A}, f_{γ}^{B}) .

The mass flow rates in user subroutine GAPCON are not used to model conductance in gasket elements, and the variables should be set to zero.

Input File Usage

GAP CONDUCTANCE, USER