Hot water at 60 C enters a thin copper tube with an inside dia of 6mm and a leng

Question

Hot water at 60 C enters a thin copper tube with an inside dia of 6mm and a length of 20m. The copper tube is exposed to air at 20C with a convective heat transfer coefficient of 10 W/m^2K. The Reynolds number of the flow in the tube is 1000 (laminar)

What is the mass flow rate of water?

What is the average convective heat transfer coeff on the inside of the tube?

What is the temp of the water at the outlet?

If the flow rate of the water was increased (say by 50 percent), what would happen to the convective heat transfer coeff?

Can the surface temp be assumed constant? I can't find where to use the transfer coeff of copper. Also assuming the entire 20m as fully developed flow with Nu=3.66 doesnt give the right answer because the high transfer coeff for the entire length (x=~ 1.25 m) brings up the average h.

Explanation / Answer

a)Dynamic viscosity of water at 60 degree=0.4658*10^-3

so reynolds number=1000*v*6*10^-3/0.4658*10^-3

v=0.077 m/s ans

b) now prandtl number =Cp*%u03BC/k

=4.18*0.4658/0.56

=3.47

NOW Nusselt number Nu=1.86*(Re*Pr)^1/3*(D/L)^1/3*(%u03BCb/%u03BCw)^0.14

Nu=1.86*(1000*3.7)^1/3*(6*10^-3/20)^1/3*(0.6531/1.002)^0.14

Nu=1.81

Now Nu=hL/k

average convective heat transfer coeff on the inside of the tube h=Nu*k/L

=1.81*20/0.56

=64.64 W/(m2K) ans

c)applying conservation of energy we have

10*(60-20)=64.64*(60-T)

T=53.81 C

d)If the flow rate of the water was increased (say by 50 percent) then reynolds number will increase and hence prandtl number. therefore convective heat transfer coeff will increase

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