Two-dimensional elemental cavity radiation view factor calculations

These examples verify the use of two-dimensional elemental cavity radiation view factor calculations in Abaqus.

This page discusses:

Two infinitely long, directly opposed parallel plates of the same finite width
Two infinitely long parallel plates of different widths; the centerlines of each plate are connected by the perpendicular between the plates
Two infinitely long plates of unequal widths h and w, having one common edge and at an angle of 90° to each other
Two infinitely long plates of equal finite width w, having one common edge and having an included angle of α to each other

ProductsAbaqus/Standard

Relatively simple configurations were selected for these verification problems to ensure that analytical solutions or tabulated results could be found. In some cases certain parameters such as the distance between two surfaces or the number of elements on a surface were varied to illustrate the effects of these parameters on view factor calculations within Abaqus. To duplicate the tabulated results for the cases where parameters were varied, the user can modify the input files provided with the Abaqus release.

Two infinitely long, directly opposed parallel plates of the same finite width

Problem description

Analytical solution

F ​_{1 - 2} = F ​_{2 - 1} = \sqrt{1 + H^{2}} - H,

where $H = h / w$ .

Results and discussion


F $_{1 - 2}$
Abaqus	Analytical
0.2361	0.2361

Input files

xrvd24n1.inp: One DC2D4 element is used to discretize each surface of the cavity.

References

Howell, J. R., A Catalog of Radiation Configuration Factors, McGraw-Hill Book Company, New York, 1982.

Two infinitely long parallel plates of different widths; the centerlines of each plate are connected by the perpendicular between the plates

Problem description

Analytical solution

F ​_{1 - 2} = \frac{1}{2 B} [\sqrt{{(B + C)}^{2} + 4} - \sqrt{{(C - B)}^{2} + 4}],

where $B = b / a$ and $C = c / a$ .

Results and discussion


F $_{1 - 2}$
Abaqus	Analytical
0.4337	0.4337

Input files

xrvd24n2.inp: One DC2D4 element is used to discretize each surface of the cavity.

References

Howell, J. R., A Catalog of Radiation Configuration Factors, McGraw-Hill Book Company, New York, 1982.

Two infinitely long plates of unequal widths h and w, having one common edge and at an angle of 90° to each other

Problem description

Analytical solution

F ​_{1 - 2} = \frac{1}{2} (1 + H - \sqrt{1 + H^{2}}),

where $H = h / w$ .

Results and discussion


F $_{1 - 2}$
Abaqus	Analytical
0.2229	0.2229

Input files

xrvd24n3.inp: One DC2D4 element is used to discretize each surface of the cavity.

References

Siegel, R., and J. R. Howell, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, 3rd, 1992.

Two infinitely long plates of equal finite width w, having one common edge and having an included angle of α to each other

Problem description

Analytical solution

F {}_{1 - 2}= F ​_{2 - 1} = 1 - \sin \frac{α}{2} .

Results and discussion

In xrvd24n4.inp $α$ can be varied to obtain the following results (in xrvd24m4.inp the angle is varied using prescribed rotational motion):


$α$	F $_{1 - 2}$
$α$	Abaqus	Analytical
10°	0.9128	0.9128
20°	0.8264	0.8264
30°	0.7412	0.7412
40°	0.6580	0.6580
50°	0.5774	0.5774
60°	0.5000	0.5000
70°	0.4264	0.4264
80°	0.3572	0.3572
90°	0.2929	0.2929

Input files

xrvd24n4.inp: One DC2D4 element is used to discretize each surface of the cavity; $α = $ 60°.
xrvd24m4.inp: One DC2D4 element is used to discretize each surface of the cavity; the MOTION, ROTATION option is used to vary the angle between the plates.

References

Siegel, R., and J. R. Howell, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, 3rd, 1992.