Answer to Question #254913 in Mechanical Engineering for ben

Question

The armor of a tank can be simulated by a slab of thickness L= 152mm (6in) that is insulated on the right hand side as shown in the Figure A below. The slab is infinite in the y-direction. The left hand side is exposed to enemy fire, that is, an explosion at the surface of the slab. The explosion can be simulated by a surface temperature that varies as shown in Figure B. For the time t>2b the left hand side can be considered as insulated. You are asked to find a) the temperature distribution in the slab, that is T(x,t) for the small time, that is t<2b. b) the temperature in the slab, T(x,t) for large time that is t>>2b c) Determine the length L of the slab such that the temperature does not exceed 150 F after 100 seconds Use a) carbon steel and b) Ni-Cr alloyed steel Tmax= 1500 F; b=1sec; The initial temperature of the slab is 80F a) kst= 43 W/m.K (high k) ρ=7801 kg/m3 cp=473 J/kg.K b) kNi-Cr= 19 W/m.K (low k) ρ=7865 kg/m3 cp=460 J/kg.K L Figure 1 B,Tmax (b,0) 0 T t (2b,0

Answer 1

$T_f = 150°F\\ T_i = 80°F\\ ∆T = 70° F = 21.1°C\\ t = 100s\\ mc∆T = E\\ 43= m×473× 21.1 \\ m= 0.0043kg$

$V= \dfrac m\rho=\dfrac{0.0043}{7801}=5.57×10^{-7}m³\\ = 0.56cm³$