ChE 350 Problem 7\ Supplementary Reading: Section 3.6 in Bergman\ Radioactive wastes

(k_(w)

)

=

(

25Wm^(-1)K^(-1))

are to be stored in spherical stainless steel

(k_(s)

)

=

(

18Wm^(-1)K^(-1))

containers. The wastes generate thermal energy non-uniformly according to\

Q_(v)^()=(5)/(2)Q_(o)[1-((r)/(r_(i)))^(2)]

\ where

Q_(0)=69kWm^(-3)

is the mean rate of generation,

r

is the radial distance from the center of the container, and

r_(i)

is the inner radius of the container. The outer surface of the container is cooled by

25\\\\deg C

water with a convective heat transfer coefficient of

h=1.0kWm^(-2)K^(-1)

,\ a. Safety considerations require that the maximum steady-state temperature of the system remain below

475\\\\deg C

. Will a spherical container with inner and outer diameters of

1.0m

and

1.2m

, respectively, satisfy this requirement?

Supplementary Reading: Section 3.6 in Bergman Radioactive wastes (kw=25Wm1K1) are to be stored in spherical stainless steel (ks=18Wm1K1) containers. The wastes generate thermal energy non-uniformly according to Qv=25Qo[1(rir)2] where Q0=69kWm3 is the mean rate of generation, r is the radial distance from the center of the container, and ri is the inner radius of the container. The outer surface of the container is cooled by 25C water with a convective heat transfer coefficient of h=1.0kWm2K1. a. Safety considerations require that the maximum steady-state temperature of the system remain below 475C. Will a spherical container with inner and outer diameters of 1.0m and 1.2m, respectively, satisfy this requirement