An electrical resistor dissipating $0\mathrm{.}1$ W has been mounted is mounted in an

electrical cabinet away from all other components. The resistor is cylindrical with

$3\mathrm{.}6$mmOD,$L=10mm.$ If the air in the cabinet is $35$ C and at rest, and the resistor

has $h=13\frac{W}{m^2}-K$ for natural convection, and emissivity of the resistor is $=0\mathrm{.}9,$

compute:

$($a$)$ Show that the radiation heat transfer coefficient, can be approximated as

$h_{\text{r}\text{a}\text{d}}=4F_{1-2}{T}_m^3$

Valid for

$\frac{(T{)}^2}{2}<mn>2</mn><msubsup><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msubsup>$

where

$T_m=\frac{T_1+T_2}{2}$

$T=T_1-T_2$

$($b$)$ for the parameters listed above compute $h_{\text{r}\text{a}\text{d}}(\frac{W}{m^2}-K)$

$($c$)$ compute the resistor's temperature

$($d$)$ show that that use of the hrad approximation holds for this case

ANS.

$($a$)$ derivation

$($b$)6\mathrm{.}44\frac{W}{m^2}-K$

$($c$)72\mathrm{.}3C$

$($d$)$ check if $\frac{(\frac{T}{T_m}{)}^2}{4}1$

i$.$e thus approximation is valid