Question

A 12 cm long bar initially at a uniform temperature of 40oC is placed in a medium at 650oC with a convective co efficient of 22 W/m2K. The time taken by the bar to reach the final temperature of 255oC is 360 sec.

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

A 12 cm long bar initially at a uniform temperature of 40oC is placed in a medium at 650oC with a convective co-efficient of 22 W/m2K. The time taken by the bar to reach the final temperature of 255oC is 360 sec.

Explanation:

Given Data-

D= 12cm = 0.12cm

R= 0.06m

To= 40=273=313K

T∞=650+273=293K

T=255+273=528K

h=22W/m2K

K=20W/mK

P=580 Kg/m2.

C= 1050 J/kg K.

To Find-

Time required to reach 255°C (t).

Solution-

Characteristic length for cylinder= Lc=R/2

Lc=0.06/2=0.03m

We know that,

Bi=hlc/K=22×0.03/20.

Bi=0.033<0.1

Biot number is less than 0.1.

Hence, this is lumped heat analysis type problem.

For lumped heat parameter, from HMT data book.

$T-T$∞/$To-T$∞ = e[- hA/CVρ×τ]

We know that,

Lc=V/A

$T-T$∞/$To-T$∞ = e[- hA/CLcρ×τ]

528-923/313-923= e [-22/1050×0.03×580]×τ.

Ln[528-923/313-923]= -22/1050×0.03×580×τ.

τ=360.8sec

Hence, The time taken by the bar to reach the final temperature of 255°C is  360.8 sec.

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