Question

A sphere of radius 0.081029 m is made of aluminum. It is submerged in flowing water with a temperature of 25 °C that results in a heat transfer coefficient of 103.067 W/m2•K. Its surface temperature is 124.978 °C at 0 s. What will its surface temperature be at 767.276 s? (Answer in °C.)

Answer 1

Answer:

its surface temperature = 54.84 ° C

Explanation:

The density of aluminium $(\rho)$ = 2700 kg/m ³

Heat capacity $( c_p)$ = 897 J/Kg.K

radius of the sphere (r) = 0.081029 m

$T \infty$ = 25 °C

$T_i$ = 124.978  °C

time (t) = 767.276 s

Using the formula :

$\frac{T-T_{ \infty} }{T_i - T_{\infty}}= e^{-\frac{hA}{\rho V c_p}}*t$

where.

$\frac{V}{A}= \frac{r}{3}$

Replacing our values ;we have:

$\frac{T-25 }{124.978 - 25}= e^{-\frac{-103.067*3}{2700*897*0.081029}}*767.276$

$\frac{T-25 }{124.978 - 25}= e^{{-0.001576}*767.276$

$\frac{T-25 }{124.978 - 25}= e^{-1.209}$

$\frac{T-25 }{99.978}= 0.2985$

${T-25 }= 0.2985*{99.978}$

${T-25 }= 29.843433$

${T= 29.843433+25 }$

${T= 54.843433$

T ≅ 54.84 ° C

Therefore, its surface temperature = 54.84 ° C