During a routine check, it was noticed that a $15-$m$-$long section of a $10-$cm$-$diameter steam pipe, was completely exposed to the ambient air. The temperature

measurements indicate that the average temperature of the outer surface of the steam pipe is $75\backslash$deg C when the ambient temperature is $5\backslash$deg C$.$ There are also light winds in the area at $10$ km$/$h$.$ The emissivity of the outer surface of the pipe is $0\mathrm{.}8,$ and the average temperature of the surfaces surrounding the pipe, including the sky$,$ is estimated to be $0\backslash$deg C$.$

Consider the following assumptions:

$$ Steady operating conditions exist, and

$$ Air is an ideal gas with constant properties,

$$ The plant operates every day of the year for $10$ h a day,

$$ The local atmospheric pressure is $1$ atm.

Properties of air at $1$ atm and the film temperature of $($Ts $+$ T infinity$)/2=(75+5)/2=40$ degrees Celsius are:

$$ k$=0\mathrm{.}02662$ W$/$m$\backslash$deg C$,$ v$=1\mathrm{.}70210$ to the power of $-5$ m squared per second

and Pr $=0\mathrm{.}7255$

Requested to determine:

i$.$ Total heat transfer Q total, and

ii$.$ The amount of heat lost from the steam during a $10-$h$-$long workday.

To solve Part $($i$),$ please follow the following steps.

$$ Reynolds number $-$ Re

$$ Nusselt Number $-$ Nu

$$ Thermal Coefficient $-,$

$$ Surface Area $-$ As

$$ Heat transfer by convection $-$ Q convection,

$$ Heat transfer by radiation $-$ Q radiation and

$$ Total heat transfer $-$ Q tota;