Imagine a hemispherical dome housing a circular ice rink. The dome's diameter measures 300 meters, while the ice rink spans 200 meters in diameter. The center of the ice rink aligns with the dome's center. The dome's ceiling temperature is maintained at 15 C, whereas the ice rink and surrounding annular region temperatures are kept constant at -5 C. Both the ice rink and the annular region are treated as blackbody surfaces, while the dome ceiling. a gray surface, has an emissivity of 0.5. Label the dome ceiling as surface 1, the circular ice rink as surface 2, and the annular region as surface 3, leading to temperatures of T = 15 C and T = T,= -5 C. Provide detailed explanations for each step of your work to receive credit! (a) (10 pts) Draw a detailed radiation heat transfer network circuit. Label each node clearly with its emissive power or radiosity and indicate the radiation thermal resistances between all the nodes. Note that incomplete circuits will not receive credit. Use the following symbols for denoting emissive powers. (b) (10 pts) Evaluate the following thermal resistances. J, denotes Radiosity from the dome ceiling. Esi. Es. Eso are emissive powers from the dome ceiling, ice rink, and annular region, respectively. Resistance between East and Ji: Resistance between J, and Es Resistance between J and Est (c) (10 pts) Now, estimate the radiosity that leaves from the dome ceiling. (d) (5 pts) Estimate the rate of heat transfer from the dome ceiling to the ice rink.