Four different two-dimensional models of the cross-section of the square tube are used: the full model, a half model with one reflection symmetry, a quarter model with two reflection symmetries, and a quarter model with cyclic symmetry. The full, half, and quarter models are shown in Figure 5.1.18–1. The two-dimensional models imply that the tube extends infinitely in the direction normal to the cross-section.

Three different models of the square section tube are used. In all cases the complete cross-section is modeled, and the infinite extent of the tube is simulated by using periodic symmetry in the direction normal to the cross-section of the tube. The three models differ in the number of repetitions used for the periodic symmetry.

Four different two-dimensional models of the cross-section of the square tube and the blocking object are used: the full model, a half model with one reflection symmetry, a quarter model with two reflection symmetries, and a quarter model with cyclic symmetry. The full, half, and quarter models are shown in Figure 5.1.18–3. The two-dimensional models imply that the tube and the blocking object extend infinitely in the direction normal to the cross-section.

Six different models of the square section tube and the blocking object are used. These models involve different combinations of the cross-sectional model and the number of periodic symmetry repetitions used to simulate the infinite extent of the tube and the blocking object. Three cross-section models are used: the full model, a quarter model with two reflection symmetries, and a quarter model with cyclic symmetry. Figure 5.1.18–4 shows the cross-section models used.

A unit-length tube with a square cross-section is analyzed. Four different models of the square section are used: the full model, a half model with one reflection symmetry, a quarter model with two reflection symmetries, and a quarter model with cyclic symmetry. Figure 5.1.18–5 shows the cross-section models used.

A unit-length square cross-section tube and a blocking object are analyzed. Three cross-section models are used: the full model, a quarter model with two reflection symmetries, and a quarter model with cyclic symmetry. Figure 5.1.18–6 shows the cross-section models used.

A tubular ring with a square cross-section is analyzed. Two different models of the square section are used: the full model and a half model with one reflection symmetry. Figure 5.1.18–7 shows the cross-section models used.

A square cross-section tubular ring with a blocking object inside it is analyzed. Two different models of the square section are used: the full model and a half model with one reflection symmetry. Figure 5.1.18–8 shows the cross-section models used.

An infinite array of cubic objects is simulated. The two-dimensional models imply that the array extends to infinity in the third direction. Three different models are used: an array of nine by eleven objects, an array of nine objects with periodic symmetry in the direction perpendicular to the array, and a single object with periodic symmetry in two directions. The number of repetitions in the models using periodic symmetry makes these models equivalent to the nine by eleven array model. The models are shown in Figure 5.1.18–9 where the black square represents the model with two periodic symmetries and the gray squares represent the model with one periodic symmetry.

An infinite array of cubic objects is simulated. The three-dimensional models consist of a single cubic element with periodic symmetry in three directions. Two models are used where the number of periodic symmetry repetitions is varied. The single element on which the models are based is shown in Figure 5.1.18–10.

Radiation between an infinitely long, finned tube inside another infinitely long simple tube is simulated. The axisymmetric mesh used is shown in Figure 5.1.18–11. The infinite extent of the tubes is modeled with periodic symmetry in the direction of the length of the tubes. Three models with a varying number of repetitions for the periodic symmetry are used.

Radiation between an infinitely long finned tube inside another infinitely long simple tube is simulated. The two three-dimensional meshes used are shown in Figure 5.1.18–12: one is a full 360° mesh, and the other is a slice of this mesh that is used in conjunction with cyclic symmetry. The number of cycles used in the cyclic symmetry is varied. The infinite extent of the tubes is modeled with periodic symmetry in the direction of the length of the tubes.