We used the material properties for titanium (Table 1) and the provided numerical data (Table 2) which correspond to the constants labeled in Figures 1 and 2.

## Results

Figure 3 shows the temperature distribution of the mesh when only the boundary condition Tg = 100◦C is prescribed to the tubes.

Figure 4 shows the temperature distribution in the steady state condition after convection coefficients and initial boundary temperatures are applied.

Figure 5 shows the Transient heat solution with sample step sizes. These steps were generated using dt = dt^1.6. Because the thermal solution approaches steady state as t → ∞, an exponential scale allows us to continue to observe the heating behavior as temperatures increase.

Figure 6 shows the undeformed and deformed mesh along with the stress parabola applied along border AB.

Figure 7 shows the von Mises yield criterion stress distribution in the mesh. A maximum of about 4.15 ∗ 106[Pa] at the bottom center is displayed in dark red. A minimum of about .01∗106[Pa] is displayed in blue at the top, along the right and left edge, and at the bottom right and left corners.