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Tutorial FREE SCRIBD,CHEGG AND COURSEHERO UNLOCKS

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Sumitom Shomeanswered this
Given,wall temperature, Tw = 98 C,gas temperature, Tg = 100 C, tube diameter, d = 1.24 cm = 0.0124 m,
Tf = 99C, kf = 0.68W/m.C, hfg = 2.255*106 J/kg,
\rho
f = 960 kg/m3,
\mu
f = 2.82 * 10-4 kg/m.sec, g = 9.81 m/sec2,
n = number of tubes = 25
heat transfer coefficient for laminar film condensation, h = 0.725 * ((g*hfg*
\rho
f2 * kf3) / (n*d*
\mu
f * (Tg - Tw)))1/4 W/m2C
putting variable values, h = 0.725 * ((9.81 * 2.255*106 * 9602 * 0.683) / (25*0.0124*2.82*10-4*(100-98)))0.25 W/m2C
h= 10032.265 W/m2C
heat transfer from gas to wall = Q = h*A*(Tg - Tw) W, where A = heat transfer area = L*
\pi
*d, L = length of tube,
so, Q/L = h*
\pi
*d*(Tg - Tw) W/m for one tube,
putting values of variables, Q/L = 10032.265 * 3.14 * 0.0124 * (100-98) = 781.629 W/m
latent heat of condensation of steam at atmospheric pressure =
\lambda
= 2257 kJ/kg, = 2257000 J/kg
let m (kg) amount of steam is being condensate per second,
so, m*
\lambda
= Q
or, m/L = Q/
\lambda
kg/m.sec = 781.629/2257000 kg/m.sec = 781.629*3600/2257000 kg/m.h = 1.246727 kg/m.h
so water condensed per unit length = 1.246727 kg/h
B) Given k = 0.1W/mC, h = 2.03 W/m2C
For cylinder structure critical radius, rc = k/h = 0.1 / 2.03 m = 0.049 m
pipe radius, r = 50 / 2cm = 25 cm = 0.25m, pipe temperature Tp = 200C, ambient temperature Ta = 20C,
insulation inner radius = pipe radius, r = 0.25m, insulation outer radius ro = r + rc = 0.25+0.049 m = 0.299 m
let pipe lenght = L.(m)
i) heat transfer through insulation, Q = k*2*
\pi
*L * (Tp - Ta) / ln(ro/r) W
or Q/L = 0.1*2*3.14*(200-20)/ln(0.299/0.25) W/m= 620.316 W/m.= heat loss per unit legth of pipe with insulation
ii) heat transfer through wall = Q = h*2*
\pi
*r*L*(Tp - Ta) W
or, Q/L = 2.03*2*3.14*0.25*(200-20) W = 573.97 W/m = heat loss per unit lenght of pipe without insulation,
We know critical radius is the radius when heat flux through the insulation is maximum, the effective insulation radius should be taken greater than insulation radius. here also for critical radius insulation heat flux is greater than the bare pipe heat flux.
 
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