451 An ancient myth describes how a wooden ship was destroye

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

are given mirrors and they reflect sunlight

onto a 100 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 Tw= 20 C, while

the air is 25 C. The surroundings are

at Tsurr 23 C. The wood has an emissivity of E = 0.90

both the front and back surfaces of the plywood are char-

by h = 5 W/m2 • K The absorbed irradiation

from the N students\' mirrors is G= 70,000 W/m^2 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 St = Ay 100 mm and

treating the wood as a two-dimensional extended

surface (Figure 3.17\"), enlighten the 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= 15W/in •K and E= 0.2.

The value of the absorbed irradiation is the same xs

in part (a)

Irradiation location irradiation location B 23°C 25 C 800 mm Ha 300 mm 4 500 mm 1. 20°C

Solution

This is derived by Steven Bolts mann law which states P=e*stefen\'s constant*Area (T⁴-T) here A is radiating ara and stefen\'s constant is 5.6703×10^-8 watt / m²k⁴ , emissivity is known . Now as net radiated power is directly promotional to temp difference so location B is preferred .