Show your Steps please Water is to be heated from 20oC to as it flows through a

Question

Show your Steps please

Water is to be heated from 20oC to as it flows through a 2.5-cm internal diameter 7 m-long tube (Fig. 1). The tube is equipped with an electric resistance heater that provides uniform heating throughout the surface ofthe tube. The outer surface ofthe heateris well insulated, so that in steady operation all the heat generated in the heater is transferred to in the tube. l the System is to provide hot water at a rate of 10 L/min, (a) determine the power rating of the resistance heater. Also, Ob estimate the inner surface temperature of the tube at the exit constant 20°C 60°C 7 m Fig. 1 for Problem (3)

Explanation / Answer

a)

q_conv = m*Cp*(T_out - T_in)

q_conv = (10/60)*4.179*(60 - 20)

q_conv = 27.86 kW

Surface area = pi*D*L

= 3.14*0.025*7

= 0.5495 m^2

Heater flux = 27.86 / 0.5495

= 50.7 kW/m^2

b)

Cross-section area A = pi/4*d^2 = 3.14/4*0.025^2 = 0.000490625 m^2

Velocity V = Q/A

= (10*10^-3 / 60) / 0.000490625

= 0.34 m/s

Re = V*d/neu

For water, kinematic viscosity neu = 0.637*10^-6 m^2/s

Re = 0.34*0.025 / (0.637*10^-6)

= 13,350

Since Re > 2300, flow is turbulent.

So Nu = hD/k = 0.023* Re^0.8 * Pr^0.4

We have Pr = 4.16 and k = 0.634 W/m-K

So, Nu = 0.023*13350^0.8 * 4.16^0.4

Nu = 81.24

h = 81.24*0.634 / 0.025

h = 2060.2 W/m^2-K

At outlet, q = h(Ts - To)

50.7*10^3 = 2060.2*(Ts - 60)

Ts = 84.6 deg C

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