If a metal tube is designed so that it is made up of several constant
temperture sections each of which is at a lower temperture from the
previous one what would be the equation that describes the temperture
distribution within the flow inside the tube?

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Clarification of Question by johnoughterard-ga on 31 Jan 2005 01:34 PST

Hello and thanks for your comments.

Yes i am asking what the temperture distribution would be in a *fluid*
that is flowing through a hollow tube that is made up of a series of
end-to-end,constant temperature segments, each of which is at a
different temperature and each segment is at a lower temperture than
the previous one.

The "fluid" would be humid air and the flow in the tube would be
laminar. The temperature of the fluid at the point when it enters the
pipe is a fixed constant value.

I hope this clarifies it. Also if you do the equation i would like to
know how you worked it out and or the liturture you sourced it from

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Clarification of Question by johnoughterard-ga on 18 Feb 2005 02:47 PST

Hello and thanks for the comments,


I do  need the solution to the transient problem and alsothe full
temperature profile (both radial and longitudinal) of the fluid?

Your question is not clear.  Are you asking what the temperature
distribution would be in a *fluid* that is flowing through a hollow
tube that is made up of a series of end-to-end, constant temperature
segments, each of which is at a different temperature?

If so, one would also need to know:

1.  the characteristics of the fluid flow within the pipe, i.e, is the
flow laminar or turbulent?

2.  whether the temperature of the fluid at the point when it enters
the pipe is a fixed, constant value or if it varies over time.

You rock on there little dude.  Since your system is cylindrically
symmetric you can use the hand calculator for the flow of a fluid over
a plate provided at www.efunda.com.  And it includes the math for you
to actually understand the answer you've been given.

Since you've decided not to look up the appropriate book at the
library I guess you either (a) are playing around or (b) just want an
answer for homework.  Either way a little math should not frighten
you.

Model your pipe as a series of plate sections, assuming no temperature
change between each plate
(pipe).  Also assume that the heat capacity of your fluid is too low
to affect the each isothermal plate.

And there you have it.

The calculator link is --

http://www.efunda.com/formulae/heat_transfer/convection_forced/calc_lamflow_isothermalplate.cfm

The link for you to actually learn about the procedure is --

http://www.efunda.com/formulae/heat_transfer/convection_forced/isothermalplate_lamflow.cfm


Now you are empowered to perform a set of calculations on your own --
and you don't have to troll for silly answer guys on this web site
that rarely know the correct answer.

Thats not really what I am looking for. WHat i want is an equation
that can work out me the temperture of the flow at any point in the
flow inside the tube

Two more clarifications -- 

Do you need the solution to the transient problem, or will a
steady-state solution suffice?

The temperature in the fluid will vary radially, as well as
longitudinally.  Do you need the full temperature profile (both radial
and longitudinal) of the fluid, or will a radially average temperature
as a function of longitudinal coordinate do?