Temperature-dependent film condition

This problem contains basic test cases for one or more Abaqus elements and features.

The following topics are discussed:

Elements tested
Features tested
Problem description
Results and discussion
Input files
Figures

ProductsAbaqus/StandardAbaqus/Explicit

Elements tested

CPE3T

CPE4RT

CPS3T

CPS4RT

DC2D4

S4RT

Features tested

Temperature-dependent film conditions.

Problem description

An infinite plate of width 0.1 unit and thickness 1 unit is considered. A zero flux boundary condition is imposed on all of the surfaces except the top surface. A film condition and sink temperature are imposed on the top surface, and the transient solution to the heat transfer problem is sought.

In Abaqus/Standard the problem is modeled with 10 DC2D4 elements of dimension 0.01 × 0.01. In Abaqus/Explicit two-dimensional (plane strain and plane stress) elements are used to model the plate: 10 elements are used through the width of the plate when using CPE4RT and CPS4RT elements, while 20 elements are used when using CPE3T and CPS3T elements. The problem is also modeled using S4RT elements in Abaqus/Explicit. Only one coupled thermal shell element is used, and the shell's thickness represents the length of the model. The film condition is applied on one face of the shell, and a large number of temperature points are considered through the thickness (19 points, which is the maximum allowable temperature points.)

Material:

Thermal conductivity, $k =$ 1.4; sink temperature, $θ_{0} =$ 100(1 + t/3600); specific heat, $c_{p} =$ 260; film coefficient, $h =$ 10 + 0.02 $θ$ ; density, $ρ =$ 7800; initial temperature, $θ_{i} =$ 0.

In Abaqus/Explicit dummy mechanical properties are prescribed to complete the material definition.

Results and discussion

The transient solution at $t =$ 3600 units is plotted for all four cases; the finite difference solution is plotted as a solid line, and the three finite element results as markers at the centroid of the elements.

The results obtained with Abaqus/Explicit are in close agreement with those obtained with Abaqus/Standard.

Input files

Abaqus/Standard input files

ec24dfd1.f

Fortran program to compute the finite difference solution to the differential equation

k \frac{\partial^{2} θ}{\partial x_{2}^{2}} = ρ c_{p} \frac{\partial θ}{\partial t}

with appropriate boundary conditions for the film and sink conditions. The solution is computed at 101 points through the width of the plate at time steps of 0.01 units.

ec24dfd2.inp