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

its surface temperature = 54.84 ° C

Step-by-step 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 :

`(T-T_( \infty) )/(T_i - T_(\infty))= e^{-(hA)/(\rho V c_p)}*t`

where.

`(V)/(A)= (r)/(3)`

Replacing our values ;we have:

`(T-25 )/(124.978 - 25)= e^{-(-103.067*3)/(2700*897*0.081029)}*767.276`

`(T-25 )/(124.978 - 25)= e^{{-0.001576}*767.276`

`(T-25 )/(124.978 - 25)= e^(-1.209)`

`(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