Please show your work 1 Water at 80 degree C with a mass flow rate of 0.1 kg/s e
ID: 2995798 • Letter: P
Question
Please show your work
1
Water at 80 degree C with a mass flow rate of 0.1 kg/s enters a 1.5-cm-lD tube whose surface is maintained al a uniform temperature of 20 degree C. Determine (a) the heat transfer coefficient and (b) tube length required to cool water to 40 degree C. (c) Justify that your answer is valid. A long 8-cm-diameter chrome-steel rod [alpha = 1. 1 times 10-5 m2 / s, k = 40 W/(m degree C)] is initially at a uniform temperature Ti=225 degree C. II is suddenly exposed to a convective environment at T infinity = 25 degree C with a surface heal transfer coefficient W/(m2 degree C). Determine the Biol number Bi (here, lake the characteristic length to be the radius of the rod). Determine the dimensionless time r after 6 min. From transient chart and from the results found in parts (i) and (ii), the dimensionless centerline temperature [0(0,tau) = (T,0-Tinfinity)/(Ti-7infinity)j is found as 0.8 after 6 min. Determine the temperature at the center of the rod after 6 min. Again using the transient chart along with some results determined above, the dimensionless surface temperature [0(1 tau) = (T infinity)/(To - T infinity)] is found to be 0.98 after 6 min. Determine the surface temperature after 6 min.Explanation / Answer
a)
Cross-section Area A = 3.14/4 *0.015^2 = 0.00017666 m^2
Velocity V = 0.1 / (1000*0.00017666) = 0.566 m/s
Re = V*D/neu
For water, neu = 0.461*10^-6 m^2/s
Re = V*D/neu
= 0.566*0.015 / (0.461*10^-6)
= 18,410
Since Re > 2300, flow is turbulent.
Nu = h*D/k = 0.023* Re^0.8 *Pr^0.33
Nu = 0.023* 18410^0.8 *2.88^0.3
Nu = 81.6
h = 81.6*0.656 / 0.015
= 3567.8 W/m^2-K
b)
(Ts - To) / (Ts - Ti) = exp [-PLh / (m*Cp)]
We have perimeter P = pi*D = 3.14*0.015 = 0.0471 m
Cp = 4186 J/kg-K
(20 - 40) / (20 - 80) = exp [-0.0471*L*3567.8 / (0.1*4186)]
L = 2.737 m