An ancient myth describes how a wooden ship was destroyed by soldiers who reflected sunlight from their polished bronze shields onto its hull, setting the ship ablaze. To test the validity of the myth, a group of college students are given mirrors and they reflect sunlight onto a 100 mm x 100 mm area of a t = 10-mm-thick plywood mockup characterized by k 0.8 W/m · K. The bottom of the mockup is in water at T_w = 20°C, while the air temperature is T_∞ = 25°C. The surroundings are at T_sur = 23°C. The wood has an emissivity of ε = 0.90; both the front and back surfaces of the plywood are characterized by h = 5 W/m² · K. The absorbed irradiation from the N students’ mirrors is G_S,N = 70,000 W/m² on the front surface of the mockup.

(a) A debate ensues concerning where the beam should be focused, location A or location B. Using a finite difference method with Δx = y = 100 mm and treating the wood as a two-dimensional extended surface (Figure 3.17a), enlighten the students as to hether location A or location B will be more effective in igniting the wood by determining the maximum local steady-state temperature. 

(b) Some students wonder whether the same technique can be used to melt a stainless steel hull. Repeat part (a) considering a stainless steel mockup of the same dimensions with k = 15 W/m
· K and ε = 0.2. The value of the absorbed irradiation is the same as in part (a).

 

Transcribed Image Text:

Irradiation location A Irradiation location B sur = 23°C 12= 800 mm 1 J L₁ = 500 mm T = 25°C h = 5 W/m².K H = 300 mm T = 20°C