Consider Problem 4.51.
(a) The students are each given a flat, first-surface silver mirror with which they collectively irradiate the wooden ship at location B. The reflection from the mirror is specular, and the silver’s reflectivity is 0.98 The solar irradiation of each mirror, perpendicular to the direction of the sun’s rays, is G_S = 1000 W/m². How many students are needed to conduct the experiment if the solar absorptivity of the wood is α_w = 0.80 and the mirror is oriented at an angle of 45° from the direction of G_S? 

(b) If the students are given second-surface mirrors that consist of a sheet of plain glass that has polished silver on its back side, how many students are needed to conduct the experiment? 

Data From Problem 4.51

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 = Δy = 100 mm and treating the wood as a two-dimensional extended surface (Figure 3.17a), enlighten the students as to whether 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:

Gs = 1000 W/m² One of N mirrors 0 = 45° Target I