$100$

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HW$7($WileyPLUS Portion$)$

$2$ of $2$

$\frac{0}{2}$

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A $10-$mm$-$thick workpiece, initially at $25C,$ is to be annealed at a temperature above $725C$ for a period of at least $5$ minutes and then cooled. The workpiece is opaque and diffuse, and the spectral distribution of its emissivity is shown schematically. Heating is effected in a large furnace with walls and circulating air at $750C$ and a convection coefficient of $90\frac{W}{m^2}*K.$ The thermophysical properties of the workpiece are $=2700k\frac{g}{m^3},c=885\frac{J}{k}g*K,$ and $k=165\frac{W}{m}*K.$

Assume that ${}_1=0\mathrm{.}3$ and ${}_2=0\mathrm{.}6.$

$($a$)$

Calculate the emissivitvand the absorptivity

$($a$)$ Calculate the emissivity and the absorptivity of the workpiece when it is placed in the furnace at its initial temperature of $25C.$

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$($b$)$ Determine the net heat flux into the workpiece for this initial condition, in $k\frac{W}{m^2}.$ What is the corresponding rate of change in temperature, $d\frac{T}{d}t,$ for the workpiece, in K$/$s$?$

$q_{\text{n}\text{e}\text{t}\text{,}in}^{\text{'}\text{'}}=,i,k\frac{W}{m^2}$

$d\frac{T}{d}t=,i,\frac{K}{s}$

i

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