Problem $1$

In a warehouse fire accident, a rack storage system holding flammable objects in boxes is fully engulfed in llames.

The flames, and the hot surfaces of the rack storage system and llammable objects are assumed to act as a black$-$body

radiator $({}_{\text{f}\text{l}\text{a}\text{m}\text{e}\text{s}}=1)$ with an effective temperature an effective temperature $T_{\text{f}\text{i}\text{r}\text{e}}$~~$950C.$ The effective size of

the radiator can be assumed to be $6$ m tall and $10$ m wide.

Ai $t=0.$ an insulating, non$-$combustible curtain protecting an adjacent rack storage system fails. suddenly

exposing a small portion of a cardboard box located $7$ m away from the center of the effective radiating area of the

fire.

With the properties and details for cardboard given below, perform the following analysis:

a$)$ Determine the heat flux to the exposed portion of the cardboard box as a function of the radiator

lemperature, $T_{\text{f}\text{i}\text{r}\text{e}}.$ To receive full credit, show your work with symbolic expressions and a final numerical

answer.In the symbolic answer, all terms must be given information, physical constants, or determined through

equations$/$analysis used in the course. Show your work.

b$)$ Calculate the time to ignition of the cardboard box assuming a steady heat flux from the flames and

ignoring radiant heat losses.

Properties of cardboard and scenario: $h_c=25\frac{W}{m^2*(K)},L=0\mathrm{.}3mm,c_s=2400\frac{J}{kg*K},{}_s=600k\frac{g}{m^3},$

$T_{\text{i}\text{g}\text{n}}=150C.T_o^{\text{'}}=20C,{}_{\text{c}\text{a}\text{r}\text{d}\text{t}\text{o}\text{a}\text{r}\text{d}}={}_{\text{c}\text{a}\text{r}\text{d}\text{b}\text{o}\text{a}\text{r}\text{d}}=0\mathrm{.}8.$ Assume $T_{}=T_o.$

Figure $1$: Schematic for Problems $1$ & $2$