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Are these statement true? (Regarding heat flow)? 
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#1
Apr1813, 06:47 PM

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I'm revising for an exam, and this is what I think I know so far.
It will really help if someone can confirm these statements for me. Consider an iron pipe with inner diameter 20mm and outer diameter 30mm. The inside surface of the pipe is maintained at 100 degrees celsius, and the outside surface is at 90 degrees celsius. Air is flowing past the outside of the pipe at temperature 20 degrees celsius. Are these statements true:
Thank you! 


#2
Apr1813, 07:02 PM

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The way to figure out if these statements are true is to work out the reasons for stating them in the first place  in terms of physics. If you make a statement simply because some authority says this is so, then you are relying on (a) the authority got it right, (b) you remembered it correctly, and (c) the statement does not apply to a similar but crucially different situation.
eg. for #1 heat flows from a hot place to a cold place the outside of the pipe is colder than the inside  therefore the direction of travel is correct heat does not flow instantly  it flows at a rate ... so there must be something resisting the flow... so the comment about "resistance" sounds good (it is actually the definition of thermal resistance). If the heat flow is a current, and the temperature difference is the voltage, then the expression is Ohms' Law. #2 the thicker the pipe, the more/less (pick one) resistance it should have. are the dimensions correct? ... etc. The idea is to think about what the statements would mean. i.e. 4,5 and 6 are saying that, how fast the air carries off heat depends mainly on how fast the air is going and how much heat each bit of air can hold. Does this sound reasonable? If the air is a bunch of trucks and the heat is dirt, and you want to know how fast the trucks can carry off the dirt, what would that depend on? Now you should be able to answer your own question. 


#3
Apr1813, 08:02 PM

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There is an inconsistency between items 1 and 2 with item 3. If statements 1 and 2 are correct, then dQ/dt represents the local heat flow per unit length of pipe. If item 3 is correct, then dQ/dt is the total heat flow over the entire length of the pipe.
Item 5 is a little puzzling. The Reynolds number depends on the viscosity and density of the air, which are functions of the temperature. If the temperature of the outside of the pipe is thought to be variable, then the Re will be a function of the temperature in addition to the velocity. If the temperature is thought to be fixed, then the Re will depend mainly on the velocity. For item 6, the Prantdl number is equal to the heat capacity times the viscosity, over the thermal conductivity. Here again, the viscosity is a function of the temperature, as is the heat capacity. If the temperature is though of as being fixed, this then fixes the Prantdl number, which will then not depend on anything. 


#4
Apr1813, 08:28 PM

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Are these statement true? (Regarding heat flow)?
I like the truck analogy, thats made me feel a little more confident with statements 5 and 6. 


#5
Apr1813, 08:34 PM

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I don't know how you are supposed to interpret 5 or 6.
If you assume all the data given in the question is "fixed" (that includes the air temperature), then Re does mainly depend on the air velocity. On the other hand if anything can vary it also depends strongly on the pipe diameter. For 6, Pr for air is almost constant for quite a wide range of conditions, so you could argue it doesn't "depend" on anything relevant to the conditions in the question. But even a change in Pr from 0.700 to 0.701 depends on some things more than on others... 


#6
Apr1913, 12:35 PM

P: 202

Sorry I should have been more specific with the example situation I gave. The air flowing past this pipe is being continuously replaced by fresh air (with uniform temperature, viscosity, density etc..) ,and the only variable is the velocity of the air.
In this case The Reynolds number will only change with a change in the velocity. Statement 6 was a bit useless to be honest, and I can see why it has caused confusion. The reason I said this was because I remember being taught about heat capacity rate, which equals the specific heat capacity multiplied by the mass flow rate. I got a little bit confused, and remembered that specific heat capacity was important, as so was mass flow rate, so I thought Re was like the mass flow rate and Pr was like the specific heat capacity. Looking over these equations again I can see it's much more than this though. I didn't really understand what it meant by dimensionless number. I had a revision lecture today and the tutor explained why we use dimensionless numbers, which has helped me understand this a lot more. 


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