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Homework Help: Heat Transfer Pipe Problem dilemma

  1. Aug 8, 2016 #1
    1. The problem statement, all variables and given/known data
    Problem data:


    2. Relevant equations
    Rconduction=ln(rout/rin)/2*pi*Length*thermal conduct
    Rconvection=1/2*pi*Length*routside*convective heat transfer outside

    =>Qconduct=2*pi*Length*thermal conduct*(Tin-Tout)/ln(rout/rin)
    =>Qconv=2*pi*Length*routside*convective heat transfer outside*(Tout-Tair)

    3. The attempt at a solution



    For a)
    I do not understand why we need to find Toutside by equating Qcond=Qconv?
    And why we need to calculate Q from the pipe just as Qconvection instead of Q total?
    Why we cannot do Q=delta T/Resistance Total
    Rtotal=Rconduction+Rconvection,because we do not need temperatures in those 2 R formulas
    and delta T=(Tin-Tair) specifficaly 300 and 5 degrees celsius

    As for b) They do Rtotal and then Qtotal=delta T/Rtotal
    and then they do Qtotal=Qconv and they get T2.
    Why we cannot proceed the same for a)?
    Last edited: Aug 8, 2016
  2. jcsd
  3. Aug 8, 2016 #2
    Actually you can use that method (adding up individual resistances) and you will get the same result. I guess the question requires you to find the temperature of the outer surface of the pipe hence employ this method.
  4. Aug 8, 2016 #3
    Does this mean that Qtotal=Qconvection? We neglect Qconduction ?
    They were asking for Q emerging from pipe
    If I do like them as Q from pipe =Qconvection=75760 W
    if I do like Q=delta T/Rtotal , where Rtotal=Rconduction+Rconvection it gives me Q=75758 W
    Last edited: Aug 8, 2016
  5. Aug 8, 2016 #4
    You are missing an important point here. Note that the heat that is conducted through the pipe is then convected from the surface of the pipe to the atmosphere. Heat transfer passes through different stages: first conduction and then convection.
    As long as there is no internal heat generation in the heat transfer medium and steady state in maintained (the pipe in this case) Qtotal=Qconduction=Qconvection
  6. Aug 8, 2016 #5
    Yes I agree and I understood it is conduction+convection , it is obvious but I do not understand why at a) they did Q as it was just convection?and at b) they did Qtotal and equated Qtotal=Qconvection to get Temp2?
  7. Aug 8, 2016 #6
    If by T2 you mean outer surface temperature of the pipe then you can either use Qtotal=Qconvection or Qtotal=Qconduction. You will get the same value of T2.
  8. Aug 8, 2016 #7
    Thank you for your quick answer, for a) they did Q from pipe as Qconvection and they got 75760 W .If I do Qtotal=delta T/Rtotal
    where delta T=(300-5) and Rtotal =Rcond+Rconv . I should get same answer right?
    Why were they searching for Toutside and T2 at surface of pipe?If they were not asking for them?
  9. Aug 8, 2016 #8
    Absolutely. If 300 is the temperature of the inner surface of the pipe and 5 is the temperature of the outer convecting fluid you should get the same answer.
  10. Aug 8, 2016 #9
    Does all the heat flow (Q total) pass through the tube wall?
    Does all the heat flow then pass through the convective boundary layer?
    So, is Qcond = Qconv = Q total (or not)?
  11. Aug 8, 2016 #10
    Heat is transferred firstly by conduction within the pipe , then by convection from pipe surface to the air.
    To answer the questions I would say , yes Qtotal passes through tube wall, yes Qtotal passes through boundary layer.
    There is no insulation at the moment, furthermore no generation,no accumulation so I would say Qtotal=Qconduction=Qconvection
  12. Aug 8, 2016 #11
    Good. So in part (a), for conduction through the pipe, we have:
    $$Q=2\pi kL\frac{(300-T_0)}{\ln{(r_{out}/r_{in})}}$$
    and for conduction through the convective boundary layer, we have:
    $$Q=2\pi r_{out}hL(T_0-5)$$where ##T_0## is the temperature at the outer surface of the pipe. If we solve for the temperature differences, we obtain:
    $$(300-T_0)=\frac{\ln{(r_{out}/r_{in})}}{2\pi kL}Q$$
    $$(T_0-5)=\frac{1}{2\pi r_{out}hL}Q$$
    So, you have two equations in the two unknowns, ##T_0## and Q. If you add these two equations together, you can eliminate ##T_0## to obtain:
    $$(300-5)=\left[\frac{\ln{(r_{out}/r_{in})}}{2\pi kL}+\frac{1}{2\pi r_{out}hL}\right]Q$$
    You can then solve this equation for Q and substitute back into either of the other equations to get ##T_0##.

    Now, when you add the insulation layer in part (b), you end up with three equations in three unknowns, Q and the two unknown temperatures at the two interfaces. You set up and solve these three equations in basically the same way as part (a). Questions?
  13. Aug 8, 2016 #12
    Everything clear, thanks.
  14. Aug 20, 2016 #13
    I understood everything, but I still have a question.
    We know Q=m*cp*ΔT=m*cp*(Tout-Tin)
    Why we are doing ΔT=Tin-Tout?
  15. Aug 20, 2016 #14
    This question does not relate to the present problem. It relates to a flow problem.
  16. Aug 20, 2016 #15
    Thank you for your quick answer.

    In general we know Q=m*cp*ΔT=m*cp*(Tout-Tin)
    but in this problem, in their answer they are doing ΔT=(Tin-Tout)
    I am confused why they did like this in their answer on this exercise.
  17. Aug 20, 2016 #16
    Do you see any Cp in the exercise?
  18. Aug 21, 2016 #17
    No , I don't.
    I cannot understand why they did in this problem ΔT=Tin-Tout=300-5.Why they did like that?
    Usually we know ΔT=Tout-Tin=Tfinal-Tinitial not Tinitial-Tfinal
  19. Aug 21, 2016 #18
    Don't forget that minus sign in the heat conduction equation. q = - k dT/dx
  20. Aug 21, 2016 #19
    Thank you, understood now.
  21. Aug 21, 2016 #20
    But also in convection they did To-Tair,not Tair-To.
    I always thought we take ΔT=Tout-Tin not Tin -Tout, this is what confused me.
  22. Aug 21, 2016 #21
    Good point. I guess convection is just one of those instances when you have to use your judgment and know that the heat flows from hot to cold. However, in the case of conduction, no judgment is required.
  23. Aug 21, 2016 #22
    Thank you!
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