Okay. We're in chapter 8. What's on the board,
right hand side is pretty much were we were
last class meeting. We're looking at tube
flow, okay. Flow inside of a tube. We are
looking at two possible cases. One is a constant
wall heat flux. qs double prime is a constant.
The other one is a constant tube surface temperature
ts equal constant. The, let's box that guy
in. We talked about those two cases and where
they might appear in the real world last time.
To get the equation, now there, each one of
these guys has two equations. One gives you
the temperature at any position along a tube.
The other one gives you the amount of heat
transfer that's occurred. Temperature at any
point along a tube, the amount of heat transfer
that's occurred. We got this equation by looking
at a little differential element of fluid
in the tube, bx in length. It led to a differential
equation that we solve and got this equation.
This is x, this is linear. Okay. That's a
linear equation. Okay. This guy here, we took,
again, a small differential element of fluid,
bx in length. Solving the differential equation,
we got this thing, exponential variation of
temperature with x. Then, we got the heat
transfer q and something we defined as delta
t log mean. That's called the logarithmic
mean temperature difference. Logarithmic mean
temperature difference, and here's how we
defined it. We drew a picture on the board
last time so you know what delta t out and
delta t in are. Okay. So, that's where we
ended up last time. Now, these, this equation's
fine except the only problem is nobody's going
to give us h-bar. We're expected to find h-bar
from chapter 8 material. So, how do you find
h-bar? Okay, so, we'll start over here to
get h-bar. So, to find h-bar for tubes.
Okay. We can, the derivation is, let's do
the first one first. qs double prime equal
constant.
This is all for laminar flow.
Laminar flow, number based on diameter less
than 2300. Okay. Now, h for this.
That guy comes from calculations done in chapter
8. Takes about a page, a little more than
a page to do it. I'm not going to go through
it, but what it is looking at, it is equating
the conduction at the tube surface, because
the velocity is 0 there. The conduction at
the tube surface which has a dt, dt/dr at
r equal r offside. And then, the equation
for Newton's Law cooling q equal hats minus
t mean. So, there's a derivation, takes a
page. When you go through that, you end up
with this very simple equation, and then if
you want to get a Nusselt number based on
diameter which is hd over k, you can do that.
If you do that, you get 4.34. It's just a
constant value. Doesn't depend on Reynolds
number. It just is a constant value. Now,
this has to be done for fully developed conditions.
Fully developed velocity, fully developed
temperature. Okay, so the conditions are fully
developed velocity, fully developed temperature
and laminar flow. Properties at t mean, mean
temperature.
ts equal constant. Again, you have to go.
The book doesn't even go through it. But,
you have to go through some pretty lengthy
calculations for that. The book just presents
the answer. The answer similar to the constant
wall heat flux is the Nusselt number based
on d is 3.66. It's a constant.
Properties at t mean.
Fully developed velocity and temperature for
both. Laminar flow for both. Everything in
this panel is for laminar flow, fully developed
velocity, fully developed temperature and
properties at t mean. those two equations.
You want to find h? That's how you find h.
Where does that h go? Over here for ts equal
constant, you put that h right here where
the h-bar is. You put the h down here for
the q calculation. You get the h from that
if it's fully developed velocity, fully developed
temperature, and laminar flow.
Yeah, this guy here is for that guy. This
guy here is for that guy. Is that what you're
thinking? Okay. All right. Now, let's just
look at the tube flow again. Here's the tube
flow. What's entering here is t mean n and,
as we said before, as the flow enters the
tube, boundary layers develop around the parameter
of the tube. The temperature boundary layer,
then, eventually meet at the center line.
that distance is called x fully developed.
That's the entrance region.
Okay. Now, once they meet at the center, the
normalized temperature profiles become constant,
and this is called our fully developed region.
This is the temperature profiles. I'll draw
one here just so you see it again. Here's
the surface temperature ts. Let's say the
surface temperature's hot. Here's ts, and
then the temperatures, this temperature tmi
is colder. So, it looks something like this.
Okay. Now, as long as we're in the fully developed
region to the right of my hand, you can use
those expressions right there. Either one
of them. As long as you're to the right of
my hand, you can use those. Assuming the velocity
is also fully developed. Both have to be fully
developed. Okay, but, of course, in many tubes,
that's not true. You're not in the fully developed
region. I think I mentioned last time things
like maybe oils especially. They develop fully
developed velocity very quickly. They develop
temperature over a long time. We had the,
we also had the one problem. It was a Reynolds
number like it was 1000 laminar flow, or 2000,
2000. Laminar flow, a one inch tube. How long
did it take to become fully developed? Well,
we found out, it took 100 inches to become
fully developed with a one inch tube that
big around. So, a lot of flows in the real
world aren't fully developed velocity and
temperature. Well, how do we handle those?
All right. We'll take one right now. Let's
take a fully developed velocity, not fully
developed temperature.
Okay if you do that, the equation for the
Nusselt number.
If you go through the derivation, this is
what you end up with.
That's the equation we end up with for how
do you find h-bar if the velocity profiles
are fully developed but the temperature profiles
are not. Notice it still, you start out, oh,
by the way, this is for ts equal constant.
So, you start out, like, over here, 3.66.
So, here it is 3.66. Then, you add something
to take care of the not fully developed temperature.
This is what you add, this term right here.
gr stands for the Graetz number.
A dimensionless number. Again, there is a
ton of dimensionless parameters in fluids
and heat transfer. Right here, we've got four
of them on the board right here. The Nusselt
number, the Graetz number, the Reynolds number,
the Prandtl number. Oh, yeah, our equations
of heat transfer are typically formulated
in terms of dimensionless parameters because
they're so useful. And, again, that's why
in ME 312, you spend part of the time going
over dimensionless numbers because they're
so important to engineers. Okay. Properties
at t mean bar.
t mean bar is the average of the inlet and
the outlet.
So, that's how, now where do you use that
h-bar? Go over here. ts is constant. You would
solve for that h-bar first, then you'd put
the h-bar in the equation for the temperature
at any x location and the heat transfer over
the tube. Okay. Third case, not fully developed
velocity. Not fully developed temperature.
That's officially called the combined entry
length equations. Neither one's developed.
They're both in, partially in the developing
region. By the way, I'll put the equation
numbers down here. Okay. This one, fully developed,
53 and 55.
This one 857.
This one equation 858.
I'm not going to put on the board. It's way
too long. It's way too complicated. It's,
when you look at, you'll see. It's not a fun
equation. So, it's there. Okay. Properties
of t mean bar. Our author's done a really
good job. That's one of the reason why we
use this textbook. He really helps you. He
tries to help you. At the end of chapter 8,
there is a summary table, table 84. It has
just about every important equation in chapter
8. It has that boxed equation 4.34. It has
the boxed equation 3.66. It has this one right
here, 3.66 plus the correction factor. It
has this one right here, 858. They're all,
they're all in there, okay? 858. The good
news is he gives you the equation, the equation
number in the textbook, then he gives you
the conditions. Now, this table is on your
data package for the final exam. You've got
this. Okay? So, if I look at this equation
here, okay, there it is. Okay, it says this
equation 857. Yeah, so I got. It says it's
for laminar flow. Yeah, I got laminar flow.
It said, its thermal entry, thermal entry.
This means thermal entry. Thermal or temperature
is not fully developed. For the entry region,
is not fully developed there. It's called
thermal entry. This is called combined length.
Thermal entry. Uniform surface temperature.
Yeah, I said that. It's for ts equal constant,
big box on top. Okay. And, it says the Graetz
number is d over x Reynolds Prandtl. Okay,
gave you the Graetz number. So, this is a
nice little summary table. You don't need
to page the whole book to find it. It's all
right here on one page, all, almost all the
important equations. Okay. All right. 5:36.
Chapter 7. There it is. All the important
equations in chapter 7 on one page. It's on
your data package. Okay. I can find flat plate
equations. I can find circular cylinder equations.
I can find a sphere equation. For what? For
the delta? [inaudible] thickness for the average
convection coefficient? Yeah, with all the
conditions given, it's laminar. It's the local
h, properties of tf. Yeah, they're all right
here, so two tables. One chapter 7, one chapter
8. Author's done a great job of just summarizing
things because he knows those chapters are
very lengthy, and there's a ton of equations
in there. And, to go through them all is a
horrendous job, so he summarized the most
important equations in those two tables. Okay.
So, that's what you've got for a resource.
That's your library. Plus, check those against
what I've put on the board and boxed. The
ones I've boxed on the board, obviously, also
important. They might not be in that table.
Okay. The other case won't occur. We're not
going to consider it. It won't occur. It's
the one which is not fully developed velocity
but fully developed temperatures. So, don't
worry about that one. You won't see that on
homework or an exam. Okay. So, now, let's
box that guy in. I'm not going to write it
down, but I'm going to box it in. Properties
at t mean bar. Yeah, same thing. Okay. Let
me add one more over here. For what we're
doing in this class, we're going to also use
q equal m dot c sub p t mean out minus t mean
in. From thermal. It doesn't matter. I could
use that for this problem. I can use that
for this problem. I can use that for either
one. It holds for either one. Okay. Everything
to the left of my hand is for laminar flow
only. Laminar flow only. Everything to the
right of my arm is for laminar flow or turbulent
flow, either one. Everything to the right
of my hand, that's tus, that's that one over
there. And, this is ts constant. That's this
one, this one, and this one. You don't have
these two guys for qs double prime of constant,
so don't worry about that. You don't have
these two guys for that. This is, again, I'll
put it up there again. This is ts equal constant.
The good news is you probably won't need that
for qs double prime of constant because look
at the qs double prime equal constant equations.
Do you see an h in them? No, I don't. So,
I probably don't need them. Look at the equations
down here. Oh, yeah. I need h-bar here, and
I need h-bar there. I need them. Where are
they? Here, here, and here. Okay. All right.
Laminar flow left of my arm. These guys, doesn't
matter laminar or turbulent. Guess what he's
going to be? Obviously turbulent. Yeah. Turbulent
heat transfer.
Okay. the equation that we need for that,
and again, these guys are not derived from
governing partial differential equations.
Their derivation goes back to chapter six,
but just in a real quick two sentences, it
comes from the analogy between heat transfer
and fluid mechanics. So, in the fluid mechanics,
you get equations on a [inaudible] tube with
a surface sheer stress towel at the wall.
You can, then, relate that to the heat transfer.
Okay. That's the Reynolds analogy. It's in
chapter six. You can relate the results of
fluid mechanics to heat transfer. You use
that to develop these equations, and the only
one we're going to use, there's about three
of them in the chapter, but the only one we're
going to use is this equation. Nusselt d bar.
Okay. And, that came from taking experimental
data for fluid mechanics and then using Reynold's
analogy to convert that to heat transfer.
Chapter 6 stuff combined with chapter 8 stuff.
The bar, again, what does the bar mean? The
bar means the average over the length of the
tube l, the average over the length of the
tube l. Okay. Now, this guy here, properties
at t mean bar. Okay. Just like this. This
is ts equal constant, qs double prime equal
constant.
Doesn't matter. It's valid for both. You don't
need to ask the question is the tube surface
temperature constant or is the tube surface
heat flux constant. You don't need to ask
the question. One equation handles both because
turbulent flow is so unusual. It's such a
mixing phenomenon that it really doesn't matter
what's kept constant. As opposed to laminar
flow which is not serious mixing. So, in laminar
flow, you have to ask the question. Here's
the question. Answer yes or no. Are the velocity
profiles fully developed? Answer yes or no.
Are the temperature profiles fully developed?
Answer yes or no. Same thing here. Same thing
here. Here's the answers. Yes, yes. Here's
the answer. Yes, no. Here's the answer. No,
no. That guides you to the correct equation
once you answer that question. First of all,
get the Reynolds number. First question you
answer, is it laminar turbulent? If it's laminar,
everything to the left of my arm. If it's
turbulent, between here and here. Then, over
here. If it's laminar, what question do you
ask yourself? Is it constant wall heat flux?
Is it constant wall temperature? Answer what
it is. If it's constant surface temperature,
then you answer the question fully developed.
Yes or no. And, finally, you focus down on
the equation you want to use to solve the
problem. That's the way it works. Okay. These
guys over here, I know laminar and turbulent
both. Both, both laminar and turbulent. Turbulent
only. Laminar that way. Okay. So, that's in
a nutshell. Those are the equations in the
chapter you want to be concerned about. And,
there's more questions. All the stuff here's
for smooth tubes. Most of the tubes in the
world are smooth. Now, comes rough tubes.
How do you handle it? Look in the book. It's
in there. Go on a search, online search. It's
there. We're not going to do it. All of our
tubes are assumed to be smooth, okay? Yeah.
[inaudible] for heating and for cooling [inaudible]?
Now, which, oh, yeah. Exactly.
Right. Which means the other way to put it,
which means that t surface is greater than
t mean n. This one. t surface is less than
t mean n. Okay. Now, we're going to work some
problems, but we're going to, I'm going to
work problems on chapter 8 Monday. I'm going
to work problems similar, or your homework
problems, I'll set them up for you because
you're not turning those in for grading. So,
I'll set them up and make sure you get off
on the right track on chapter 8 homework.
I'm going to go over the homework that we
passed back today, now, though, and mention
some problems I saw on that. Anybody need
the homework that came in late? Okay. [inaudible]
All right. So, let's take a look at that,
then. Let's see [inaudible]. Where did I put
my [inaudible]? Oh, I know. Oh, boy. Okay.
I know where it is. Okay. Now, let's take
a look at the, I'm not going to really look
at the first two. They're too simple, but
I will give you a hint on the first two problems
in chapter 7. This is the homework you turned
in and I just passed back to you today.
Okay. So, problem 7,1 and 7,2. No, 7,2 and
3. Yeah, 7,2 and 3. Just so, to remind you
again what I said. In problem 7,2, I said
don't do anything that is stuff from ME 312.
We're not going to revisit ME 312 on homework
or an exam. So, I'm not going to ask you those
kind of questions on homework and exam. If
you read problem 7,2, it's engine oil. It's
laminar flow. It says, "Find the surface sheer
stress." No, no. We did that in ME 312. It
says, "Find the drag force on the plate."
No, we did that in ME 312. So, those two things,
don't answer them. Don't do them. Problem
7,3. Same rule. Part b, "Evaluate the surface
sheer stress." No, don't do it. That's ME
312 surface sheer stress. Anything to do with
surface sheer stress or drag force, don't
do it. That's ME 312. All right. So, let's
go in, and then the rest of it's pretty straightforward.
Let's take the next problem which is 7, 17.
Okay, 7, 17. Let's put that up on the board
here. This is a flow over a flat plate. Okay.
The plate's at 100. The air's at 50.
All right. So, we got flat plate approaching
fluid stream 50 degrees. t surface of the
plate, 100. We're measuring x from here, and
the plate length is l. Okay. The fluid's air,
air. Okay. Part, it's really not a part a,
but there's two things listed there to do.
I'll list them as a and b. Length of 20 centimeters
in the flow direction of width of 10. l equal
20 centimeters. w equal 10 centimeters. That's
into the blackboard, of course. Okay, Reynolds
number based on plate length is 4 times 10
to the 4th.
Reynolds number is rho u infinity 1 l over
u 1. That's what the Reynolds number is. Call
it Reynolds number 1. Okay. What's the rate
of heat transfer from the plate to the air?
So, q equal h-bar asts minus t infinity. Okay.
I know as is just .1 times .2. I know ts.
It's 100. I know t infinity is 50. Okay, obviously,
chapter 7 was a problem. Find h-bar. First
thing to do answer the question is it laminar,
turbulent, or mixed. Three questions. Laminar,
turbulent, or mixed? All right. 4 times 10
to the 4th. That's less than 5 times 10 to
the 5th. So, it's laminar.
So, h-bar is equal to 0.664 Reynolds l to
the 1/2 Prandtl to the 1/3. Solve for h-bar.
Got it. Plug it in. Done deal. I got a few
now. Next. Increase the free stream velocity
by a factor of 2. Call it u infinity 2. 2
times u infinity 1. And, increase the pressure
to 10 atmospheres. I didn't put in it, but
the pressure here was 1 atmosphere. The problem
said the pressure is, the air is at 50 degrees
C and 1 atmosphere. Okay. 101 KPA, 14.7 PSIA,
whatever you want to do. Oh, by the way, I'll
draw the picture now. It's laminar boundary
layer. Okay. That's part, that's just part
here, part a. Part b. Okay. Find the heat
transfer now. Okay. q, here it is right here.
as, oh, it's .2 times .1. It didn't change.
ts, it didn't change. t infinity, it didn't
change. What changed? Maybe h-bar. Okay, find
new h-bar.
All right. To find new h-bar, I've got to
find, these are all the steps you take. Find
a new Reynolds number. Did the Reynolds number
change? Okay. Let's find out. A Reynolds number,
number 2 is equal to rho 2 u infinity 2 times
l 2 divided by mu 2. There it is. Okay. Let's
see. How about u infinity. Okay. u infinity
right here. 2 times u 1. How about l 2? Did
the plate length change? No, it didn't change
l 1. How about mu? Did mu change? No, it's
mu 2. Mu 1 equal mu 2. l 1 equal l 2. It didn't
change. u infinity 2 equal 2 times u infinity
1. Got it. Where does that pressure come in?
Well, you know where it comes in, right there.
Density. Because he said this is air, and
how do we model air? As an ideal gas, and
what's rho for an ideal gas? p over rho equal
rt, so rho equal p over rt. So, 1, 1, 1. rho
2 p 2 over rt 2. Did temperature change? Look
over here. 50. It did change. t 1 equal t
2. Okay. So, put 
that in here. Equal p 2 over rt 2. That's
this guy right here. Okay. Times 2 u infinity
1 l 1 divided by mu 1. That's a, that's a
t 1, okay. t 1, t 1. And, what is p 2? p 2
right up here. 10 times p 1.
Divided by mu 1. Okay, that's equal to 20
times my p 1. Let's see my p 1. Oh, I got
to put the, I got to put this in there right.
My rho right here. Right there. I got to put
the rt, rt 1 in here. Okay.
p over rt 1 is rho 1. Okay. 10 times 220 times
rho 1 u infinity 1 l 1 divided by mu 1. That's
the Reynolds number 1. That's equal 20 times
the Reynolds number for 1. Reynolds number
part a was 4 times 10 to the 4th.
800,000.
So, that's my new Reynolds number for the
pressure increasing by a factor of 10 and
the velocity going up by a factor of 2. What
happened? Oh. This one right here? Less than
5 times 10 to the 5th. It's laminar. This
one right here. Greater than 5 times 10 to
the 5th. It's mixed flow.
So, now I go to the mixed flow equation which
is in your notes in the book, and I find h-bar.
And, I put h-bar back in that equation right
there. Get q equal h-bar a surface t surface
minus t infinity. From the mixed flow equation.
But, I'm just showing you the main thing is
how do you get that new Reynolds number. How
do you get the new Reynolds number? Okay.
You write out the Reynolds number there. You
do what he says. Double the velocity, increase
the pressure by 10. When you increase a pressure
by 10, and here's write down ideal gas equation
state. There it is. Did the pressure go up?
Oh, yeah. 10 times. Did the temperature go
up? No, it stayed constant. So, the density,
now, if the pressure goes up by 10, the density
goes up by 10. There is right there, 10. Here's
the catcher. How can you say that? How come
the, how come the absolute, this constancy
didn't change mu 2 equal mu 1? Well, the first
week of ME 311, the first chapter of our fluids
textbook says in there for an ideal gas, the
viscosity, the absolute viscosity is a strong
function of temperature, but it's not a strong
function of pressure. Okay, there it is. Fluids
textbook says that the absolute viscosity,
mu, is not a strong function of pressure.
Conclusion, it's not going to change when
you increase the pressure by 10. It stays
the same. Does the density change? Oh, yeah.
Why? Because you see pressure right there.
Okay. That's the big, long story of how this
problem should be set up to be solved. Okay?
All right. So, if you want to go to the back
of the book and you want to look for air in
the tables, there's air. Okay. Table A4, air.
And, you want to find mu to put in there.
There's mu right there at the film temperature.
There's mu. I pull the value of mu out of
that table. Now, there's a column rho. There's
a rho column there, too, but you'd better
read the top of the page. These are the properties
of gasses at atmospheric pressure. Do not,
conclusion. Do not use this table if the values
of pressure are changing. Don't use the density
from this table. It's changing. But, because
of fluid mechanics chapter 1, ME 311, they
said mu is not a strong function of pressure.
So, these properties are for atmospheric pressure.
They can be used for the pressure 10 times
atmospheric. The mu column, the mu column
right there. Okay, so big, long story, but
that's how you solve that problem. Okay. Any
questions on that guy, then? Okay. Let's go
on to the next one, 7, 20. I think I'll put
20 right here in the middle. All right. 7,
20. This is the refrigerated truck. All right.
Let's draw a picture of how this guy looks.
Let me go to the chapter and kind of read
it again. 7, 20. Oh, yeah. Okay. He told us
there's two thin sheet metal that the top,
the roof is two thin sheet metals and they're
covered by or between those two, sandwiched
in there is insulation. So, here's the model
of the top of the trailer of the truck body.
So, this is the insulation in here, and these
two guys here are the skin on the inside and
the outside of the truck body. So, that's
aluminum alloy panels. Aluminum alloy. And,
the stuff inside of here is supposed to be
kept cold, so its temperature's minus 10 degrees
C. This is a refrigerated truck. Keeps the
stuff inside cold. The top surface of the
truck body trailer is exposed to sun. This
is the middle of the day. So, here comes the
solar radiation, g. That's called the irradiation.
He says that the air outside the truck body
is at a temperature, we know all the lengths.
We know all the aluminum panels. What do we
have for that? Let's see if we're given that.
I think we are. Yeah, there it is. 32 degrees
C, air temperature. t infinity 32 degrees
C. Okay. So, let's assume that the top surface
of the truck body gets hotter than the air.
That's a reasonable assumption. So, from the
sun, well, it can work either way. You don't
know that, you don't know this top surface.
Call this temperature here t 1. Call this
temperature here t 2. Oh, I know t 2 is minus
10, given to me. I don't know t 1. Maybe it's
less than 32 or greater than 32. I'm going
to say that it's less than 32 for right now,
just right now. So, what comes into here now
is convection. What goes out of here is radiation,
okay, and so this is q radiation. Okay. And,
you're supposed to find the temperature of
the top skin of the truck, t 1. Find t 1.
And then find the heat load q.
The heat load is how much heat gets into the
truck interior because then you have to size
your air conditioner for the truck. The heat
load, then, tells you how much heat goes through
here, gets into the inside of the truck body
because your refrigeration unit has to take
that heat out. Okay. Go back to chapter 1,
energy balance. e dot in minus e dot out.
If I want, I can maybe do it for the whole
thing, e dot [inaudible] equal e dot storage,
and maybe I'll do it for the whole top of
the truck. Not a good idea because I know
what's coming in and going out the top. I
know those cues. At the bottom, I don't know
what those cues are. Is that convection radiation,
or what's happening down here? I have no idea,
so I'd soon convince myself that I don't think
it's a good idea to draw a control volume
around the whole top of the truck because
I don't know what's going on in here. I don't
know the interior temperature of the air in
there. It's not minus 10. So, you're left
with conclusion. If I want to find t 1, I
think what I'm going to do is I'm going to
draw my control volume on the top surface
of the truck, a surface control volume. Chapter
1. Okay, get rid of those two terms. Chapter
1, a surface control volume looks like that.
It's a top surface control volume. Okay. Let's
see. The top surface, what comes in? Let's
see. Irradiation g and the convection. How
much of g is absorbed by the top surface?
Alpha g. Absorbed radiation. He gave me alpha.
I know alpha. He gave it to me. What else
comes in? Convection, okay. h times the area.
I'm going to do this on a per square meter
basis, so h times t infinity minus t 1.
What goes out? Radiation. Plus, epsilon. He
gave me epsilon in the problem. I know epsilon.
Sigma t 1 to the 4th. I don't think it's going
to be much of a problem, but I'll leave it
in there. It is leaving a top surface. What
else? Oh, there's conduction from the top
surface down that way. Conduction. Okay. This
is a minus sign because it's going out. Now,
we have conduction. Conduction chapter 3.
This is a three layer in series combination.
Aluminum, insulation, aluminum. High temperature,
t 1. Cold temperature, t 2. Divided by our
total. l insulation over k insulation. This
is on a per square meter, per square meter
basis. Plus 2 times l aluminum divided by
ka, but a is 1 aluminum. So, there's our total.
And, that's equal to 0. Solve for, I know
everything. Solve for t 1. But, you better
make sure to make to make a crazy mistake
on an exam. You do not want to leave that
guy at 32 degrees because this guy has to
be absolute. So, everything in that equation
with a capital T better be an absolute except,
yep. I don't know this guy. I don't know this
guy. I don't know this guy. Oh, I forgot.
I don't know h-bar either. Oh, okay. That's
why you're in chapter 7. Okay. So, let's read
the problem. Oh, thank you very much. He says,
"Turbulent flow may be assumed over the entire
length." All right. I got it now. Chapter
7, turbulent flow over the whole length. Assume
turbulent flow.
All right. Get the equation. Nusselt d equal
for turbulent flow. Calculate h-bar from that
equation. When you get h-bar, put it in there.
Done.
Okay. So, that's how you know. Every problem
I'm choosing here is a good review for the
final because where did we start out? Here
it is, chapter 1. What's this guy right here?
Series resistances, chapter 3. What's this
h over here? Chapter 7. One problem, chapter
1, chapter 3, chapter 7. This guy's chapter
1 here, you know. This guy's chapter 1. This
is mentioned in chapter 1. I know I saw it.
But, this guy's chapter 3, series resistances.
If you don't know which one, if t 1 is hotter
or colder than t infinity, if you don't know
it, because you don't know it to start with.
Change the sign over here for convection.
Change the sign. Solve it again. One solution
will probably give you reasonable numbers.
One'll give you kind of nonsensical numbers.
So, you'll know when you solve it which one's
the right way. So, take your normal feeling
first. I think, I think that may get hot form
that g up here, so I'm just saying, I think
that that's going to be hotter than 32, so
I'd put it like. I flip flopped it, didn't
I? The other way. t infinity [inaudible] than
t 1. Yeah. Colder not hotter. Oh, and then
part b. You want the heat load? There it is
right there. This is how much gets down to
the inside from here. That gets down to the
inside. That's what you've got to take out
by an air condition on the front of the truck
trailer. All right. So, that's that guy. Any
questions on that one? Okay. Let's see if
we have time for one more. Yeah, we do. All
right. Let's look at 7, 24. All right. 7,
24 is steel plates. We know it's AISI whatever
it is, 10, 1010, yeah. All right. So, we have
these steel plates. They look like this.
And, and the air flowing over them like this.
So, if you want to look at the plate on the
side, it looks like this. This is l. This
is w.
Okay. Picking one plate. Air's on both sides,
so there's a boundary layer on the top and
the bottom. And, here's the approaching t
infinity.
Let's see what we're supposed to find here,
now. Part a. We know its air. We know its
temperature. We know its velocity. We can
find the Reynolds number. So, we find the
Reynolds number.
Based on l, on the dimension l, it's going
to turn out to be laminar. q from one side,
0.664 Reynolds l to the 1/2 Prandtl to the
1/3. Okay. Yeah, I think that's all in there
now. What's the rate of heat transfer from
the plate if the initial plate temperature's
300? It's really hot. The air blowing over
it is really cool, 20 degrees C. Yeah.
Oh. One side. q both sides equal 2 times q
one side. So, laminar, laminar. Now, what'd
you say? I'm sorry.
The, that equation, that's for the Nusselt
number, right?
Oh, yeah, yeah, yeah, yeah. Thank you. Thank
you. It is. So, let's put Nusselt up there.
Thanks.
And, so this is 2 times h-bar times the area
is w times l t infinity minus t surface. Right?
Thanks. Okay. Now, second part. What's the
corresponding rate of change of the plate
temperature? Okay. Corresponding rate of change
of the plate temperature. Okay. Here we go
again. Problem 7, 20. Chapter 1. Surface control
volume. Chapter 1. I'm going to take the whole
plate as my control volume. So, energy balance.
On whole plate.
All right. e dot in minus e dot out plus e
dot [inaudible] equal e dot storage. Okay.
Look at my plate. The plate comes in hot.
It's being cooled by air blowing over it.
Okay. Any energy come in? No, 0. Energy goes
out? Oh, yeah. Oh, yeah. By convection. Generation?
No. Storage? Of course. Okay. Minus e dot
out. I know the area, so it's h-bar. There's
two sides, again, so 2 h-bar times the area
w times l. It's right there. t infinity minus
ts. [inaudible] right there. Storage mc sub
p dt d time.
That's what I'm supposed to find. How's the
temperature vary with time? Okay. What is
the mass, the density times the volume? Do
I know the density? Yeah, I know the density.
It's in the back of the book for steel. Okay.
Got it. So, solve that guy for dt d time.
Okay. Chapter 1 again. Realize what e dot
storage is. mc sub p dt d time. And then,
get h-bar from up here chapter 7. So, chapter
1, chapter 7, and what's e dot storage from
chapter 1, too. Okay. I think it's a good
stopping point, so we'll stop for today. We'll.
