Question

A stainless-steel rod of outer diameter 1 cm originally at a temperature of 320⁰ C is suddenly immersed in a liquid 120⁰ C for which the convective heat transfer coefficient is 100 W/m2K. Determine the time required for the rod to reach a temperature of 200⁰ C?

Answer 1

Answer:

GIVEN: d=0.01m,  Ti = 320°C ,  Ta= 120°C ,  h= 100W/m2K, p= 7800Kg/m3,  

C= 490 J/Kg-K,  k=14W/m-k

Explanation:

Here C is specific heat, p is density and k is thermal conductivity

Lc = V/A

Lc = $(\pi d^{2} h)/\pi 4dh = d/4$

Lc = 0.01/4

Now we know that,

$(T-T_{a})/(T_{i} - T_{a}) = exp(-hAt/pVC)$

$(T-T_{a})/(T_{i} - T_{a}) = exp(-ht/pCL_{c} )$

$\frac{200-120}{320-120}$ = exp[(-100 x t x 4)/7800 x 490 x 0.01)]

Multiply by log on both the sides

$log(2/5) = (-4t/382.2)$

$-0.397 = (-4t/382.2)$

t= (0.397 X 382.2)/4

t= 37.93 sec

Therefore, the time required for the rod to reach the temp 200 degree celsius is 37.93sec.