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QIQI WANG: Welcome to 16.90.

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00:00:32,650 --> 00:00:35,180
I'm Professor Qiqi Wang and
this is Professor Wilcox.

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00:00:38,990 --> 00:00:44,600
So we are going to be together
teaching 16.90 this year.

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So 16.90 is Introduction
to Computation Methods

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00:00:47,730 --> 00:00:49,930
for Engineering
Aerospace Engineering.

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00:00:52,500 --> 00:00:54,590
So what I'm going to
do today is [INAUDIBLE]

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But before that let's go over
about what this class is about.

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00:01:08,600 --> 00:01:09,100
[INAUDIBLE]

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00:01:12,060 --> 00:01:12,990
OK.

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00:01:12,990 --> 00:01:16,060
So I'm first going to
go over the syllabus.

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00:01:16,060 --> 00:01:18,502
And then professor
Willcox is going

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00:01:18,502 --> 00:01:21,720
to show you something
new this semester that

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is very exciting for you
to-- actual a great way

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00:01:23,720 --> 00:01:26,830
to guide yourself to learn
the material yourself.

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00:01:26,830 --> 00:01:29,042
Because this lecture
is really-- this class

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00:01:29,042 --> 00:01:33,532
is really taking advantage
of the [INAUDIBLE]

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00:01:33,532 --> 00:01:36,176
classroom structure, we really
want you to learn the material

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00:01:36,176 --> 00:01:38,180
before you come to class.

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00:01:38,180 --> 00:01:40,700
And in class we are
going to be assuming

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00:01:40,700 --> 00:01:42,660
you have read the
material and we

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00:01:42,660 --> 00:01:46,750
are going to be solving
problems together.

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00:01:46,750 --> 00:01:51,080
So this is really
not a new style.

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00:01:51,080 --> 00:01:54,900
This style has been practiced
in this department for a while.

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00:01:54,900 --> 00:01:55,650
So lecture one.

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We are now using computers
to do a lot of things.

33
00:02:01,090 --> 00:02:03,730
Every one of you
are using computers

34
00:02:03,730 --> 00:02:05,230
checking email [INAUDIBLE].

35
00:02:09,220 --> 00:02:12,410
The reason we have computers
is because of things we

36
00:02:12,410 --> 00:02:15,150
are going to be talking
about in this class.

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00:02:15,150 --> 00:02:17,790
So the first real
computer is designed

38
00:02:17,790 --> 00:02:25,260
not for checking emails but
for computational simulation

39
00:02:25,260 --> 00:02:28,440
to help engineers solve
problems in ballistics.

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00:02:28,440 --> 00:02:32,050
And these are really
aero problems.

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00:02:32,050 --> 00:02:35,310
So we are going to see
something very similar

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00:02:35,310 --> 00:02:39,755
to the world's first computer
applications in this subject.

43
00:02:43,520 --> 00:02:44,020
OK.

44
00:02:44,020 --> 00:02:48,710
So let's fast forward in
time and come to today.

45
00:02:48,710 --> 00:02:51,480
Today's computer
simulations are--

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00:02:51,480 --> 00:02:54,770
haven't become less important
but increasingly important

47
00:02:54,770 --> 00:02:56,940
for studying, interpreting,
and predicting

48
00:02:56,940 --> 00:02:59,320
many different processes.

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00:02:59,320 --> 00:03:01,530
And we are in
aerospace engineering

50
00:03:01,530 --> 00:03:04,228
so I'm just going to be talking
about aerospace examples.

51
00:03:04,228 --> 00:03:07,100
But outside aerospace
you can find

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00:03:07,100 --> 00:03:11,820
even a lot of broad application
for computational simulation.

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00:03:11,820 --> 00:03:17,590
So this is a class even though
you not end up doing aerospace,

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00:03:17,590 --> 00:03:21,380
it is going to be
also [INAUDIBLE]

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00:03:21,380 --> 00:03:24,300
--related to either
science or engineering.

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00:03:24,300 --> 00:03:26,450
This is going to be useful.

57
00:03:26,450 --> 00:03:33,250
So two examples are simulation
of spacecraft reentry.

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00:03:33,250 --> 00:03:37,660
And this is a real thing.
[INAUDIBLE] Another example

59
00:03:37,660 --> 00:03:44,462
is designing [INAUDIBLE]
this is the simulation.

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00:03:44,462 --> 00:03:47,494
And we're going to be
talking about how to perform

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00:03:47,494 --> 00:03:48,535
this kind of simulations.

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00:03:48,535 --> 00:03:51,270
And these are
[? PD's ?] because you

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00:03:51,270 --> 00:03:55,440
have multiple spacial dimensions
where you have x, y, and z.

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00:03:55,440 --> 00:03:58,420
And if you are unsteady you
also have a fourth dimension

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00:03:58,420 --> 00:04:02,380
which is time.

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00:04:02,380 --> 00:04:06,430
So, to solve problems using
numerical methods some problems

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00:04:06,430 --> 00:04:08,060
like that.

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00:04:08,060 --> 00:04:10,990
It really involves two steps.

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00:04:10,990 --> 00:04:13,620
So this subject we are
going to be spending

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a lot of money talking about
how to solve differential

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equations.

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00:04:17,956 --> 00:04:21,120
But let's not forget
the first step.

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00:04:21,120 --> 00:04:25,355
That is how you would actually
get this differential equation.

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00:04:25,355 --> 00:04:28,530
OK, so the first really
is to reduce a real system

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or process or [INAUDIBLE]
into a mathematical model.

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00:04:33,310 --> 00:04:35,310
And in a lot of
times you are going

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to find out the
mathematical model is going

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00:04:37,590 --> 00:04:39,790
to be a differential equation.

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So to figure out what
kind of mathematical model

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00:04:44,240 --> 00:04:48,816
is suitable for the system or
process you are studying you

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00:04:48,816 --> 00:04:53,424
have to first know what are
the quantities of interest.

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00:04:53,424 --> 00:04:56,844
[INAUDIBLE] What do
you want to know?

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00:04:56,844 --> 00:04:58,140
OK.

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00:04:58,140 --> 00:05:01,690
And what are the key
processes involved?

85
00:05:01,690 --> 00:05:05,920
What approximations
can we reasonably make

86
00:05:05,920 --> 00:05:11,720
that is going to lead
you to [INAUDIBLE]

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00:05:11,720 --> 00:05:14,336
And the model we
are going to derive

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00:05:14,336 --> 00:05:15,710
[INAUDIBLE] from
the differential

89
00:05:15,710 --> 00:05:20,620
equation-- [INAUDIBLE] it
can be linear or non-linear.

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00:05:20,620 --> 00:05:23,170
Or you could look at the
[? method outcomes, ?]

91
00:05:23,170 --> 00:05:26,360
distinguished between linear
and non-linear equations--

92
00:05:26,360 --> 00:05:31,580
[INAUDIBLE] It can be
deterministic or probabilistic.

93
00:05:31,580 --> 00:05:34,700
At the end of this
chapter we are going

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00:05:34,700 --> 00:05:37,810
to be looking at [INAUDIBLE].

95
00:05:37,810 --> 00:05:43,660
It can be static or dynamic,
involve time or [INAUDIBLE].

96
00:05:43,660 --> 00:05:46,410
It can be discrete or
continuous, either based

97
00:05:46,410 --> 00:05:49,020
on [INAUDIBLE]
principle [INAUDIBLE]

98
00:05:49,020 --> 00:05:56,280
of math, --of momentum,
[INAUDIBLE] --or empirical.

99
00:06:01,414 --> 00:06:03,580
And once you have that you
design a computation code

100
00:06:03,580 --> 00:06:05,980
and solve the
mathematical model.

101
00:06:05,980 --> 00:06:08,650
So let's take a
look at an example

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00:06:08,650 --> 00:06:10,690
of a computational model.

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00:06:10,690 --> 00:06:13,200
The model is a thermal problem.

104
00:06:13,200 --> 00:06:17,232
So this is really-- this
guy is a [INAUDIBLE]

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00:06:17,232 --> 00:06:18,190
thermodynamics problem.

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00:06:20,980 --> 00:06:23,460
Problems like this
[INAUDIBLE] where

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00:06:23,460 --> 00:06:26,490
you have something spinning up.

108
00:06:26,490 --> 00:06:30,180
Different parts are going to
heat up at different rates

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00:06:30,180 --> 00:06:31,680
and expand at different rates.

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00:06:31,680 --> 00:06:33,960
You want during
the entire process

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00:06:33,960 --> 00:06:36,220
of different parts expanding
at different rates,

112
00:06:36,220 --> 00:06:38,761
nothing is going to
heat another part.

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00:06:38,761 --> 00:06:39,260
Right?

114
00:06:39,260 --> 00:06:42,010
You know on the spinning--
spinning [INAUDIBLE]

115
00:06:42,010 --> 00:06:45,590
or turbines which
actually expands--

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00:06:45,590 --> 00:06:48,960
heats up faster than the
outside of the turbine engine

117
00:06:48,960 --> 00:06:51,070
to actually keep
the outside safe.

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00:06:51,070 --> 00:06:52,830
So you need to
really predict well

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00:06:52,830 --> 00:06:58,740
how fast different parts
heat up during the process.

120
00:06:58,740 --> 00:07:01,170
So our model problem is this.

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00:07:01,170 --> 00:07:03,390
This is aluminum.

122
00:07:03,390 --> 00:07:10,130
It's a 3.89 cm cube,
initially at room temperature.

123
00:07:10,130 --> 00:07:13,940
It is going to be heated
up by this [INAUDIBLE].

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00:07:13,940 --> 00:07:17,400
starting at time equals t0.

125
00:07:17,400 --> 00:07:22,030
We're going to be turning off
our air at time equals t1.

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00:07:22,030 --> 00:07:25,370
So here comes the
quality [INAUDIBLE]

127
00:07:25,370 --> 00:07:27,156
the measured temperature.

128
00:07:27,156 --> 00:07:31,790
So you see here it's a
thermocouple basically stuck

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00:07:31,790 --> 00:07:43,560
inside [INAUDIBLE] how
this thing heats up.

130
00:07:43,560 --> 00:07:46,110
No, what I want
you to do is form

131
00:07:46,110 --> 00:07:48,708
a team of either two or three.

132
00:07:52,596 --> 00:07:58,280
[INAUDIBLE] And
answer this question.

133
00:08:00,840 --> 00:08:04,020
I've already given you what
is the quantity of interest,

134
00:08:04,020 --> 00:08:06,820
the temperature in the
middle of the cube.

135
00:08:06,820 --> 00:08:09,980
Now the question is what are
the important [INAUDIBLE],

136
00:08:09,980 --> 00:08:14,400
and how to model the
[INAUDIBLE] mathematically.

137
00:08:14,400 --> 00:08:15,120
OK.

138
00:08:15,120 --> 00:08:18,286
And last, I'm actually
going to show you

139
00:08:18,286 --> 00:08:20,522
because this is
what you are going

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00:08:20,522 --> 00:08:21,730
to be learning in this class.

141
00:08:21,730 --> 00:08:23,340
How to use the
mathematical model

142
00:08:23,340 --> 00:08:25,970
to make the prediction
which means how to solve

143
00:08:25,970 --> 00:08:28,680
this equation [INAUDIBLE].

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00:08:28,680 --> 00:08:33,390
So, when we're here and start
with these two questions,

145
00:08:33,390 --> 00:08:37,034
at the same time
as you form a team

146
00:08:37,034 --> 00:08:39,234
I'm going to start [INAUDIBLE].

147
00:08:39,234 --> 00:08:40,858
The last time we
actually had more time

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00:08:40,858 --> 00:08:44,430
for you to solve
these so this time

149
00:08:44,430 --> 00:08:46,540
we are running out of time.

150
00:08:46,540 --> 00:08:52,010
I know a lot of you haven't
gotten to the bottom yet.

151
00:08:52,010 --> 00:08:55,220
A lot of you I think
given more time is

152
00:08:55,220 --> 00:08:58,140
going to derive the equation,
especially some of you

153
00:08:58,140 --> 00:09:01,760
are looking up online and taking
a lot of time to calculate.

154
00:09:01,760 --> 00:09:09,110
So here I think I'm just going
to wrap up by telling you

155
00:09:09,110 --> 00:09:11,170
how I would model.

156
00:09:11,170 --> 00:09:15,200
There is no single
way of modeling this.

157
00:09:15,200 --> 00:09:31,330
But, my way is just a-- OK.

158
00:09:31,330 --> 00:09:32,240
All right.

159
00:09:32,240 --> 00:09:36,660
So, what is the
physical process that

160
00:09:36,660 --> 00:09:38,720
determines the quantity
of interest which

161
00:09:38,720 --> 00:09:42,037
is the temperature of the cube?

162
00:09:42,037 --> 00:09:43,620
I'm saying the
temperature of the cube

163
00:09:43,620 --> 00:09:48,550
because aluminum is very
good conductor of heat.

164
00:09:48,550 --> 00:09:52,160
So If there is uneven
heat in the temperature

165
00:09:52,160 --> 00:09:56,310
distribution inside the cube, it
is going to even out very fast.

166
00:09:56,310 --> 00:09:59,506
Especially for a cube
of this small size.

167
00:09:59,506 --> 00:10:01,240
All right?

168
00:10:01,240 --> 00:10:04,080
So one can assume
that the temperature

169
00:10:04,080 --> 00:10:06,395
distribution inside
the aluminum is

170
00:10:06,395 --> 00:10:09,410
basically uniform throughout.

171
00:10:09,410 --> 00:10:11,240
When you look at
the time history

172
00:10:11,240 --> 00:10:17,050
it heats up slowly over
the course of many minutes.

173
00:10:17,050 --> 00:10:20,780
The temperature-- the
conduction inside the aluminum

174
00:10:20,780 --> 00:10:22,680
is actually much
faster than that.

175
00:10:22,680 --> 00:10:33,790
So we can say that the
temperature-- [INAUDIBLE]

176
00:10:33,790 --> 00:10:36,200
OK the temperature
of the aluminum

177
00:10:36,200 --> 00:10:38,540
is only a function of time.

178
00:10:41,120 --> 00:10:48,440
So this is the
temperature of the cube.

179
00:10:48,440 --> 00:10:48,974
OK.

180
00:10:48,974 --> 00:10:50,640
Now we have the
temperature of the cube.

181
00:10:50,640 --> 00:10:54,250
So what governs the
temperature of the cube?

182
00:10:54,250 --> 00:10:57,986
What makes the temperature
of the cube change?

183
00:10:57,986 --> 00:10:59,550
Heat convection.

184
00:10:59,550 --> 00:11:00,400
OK.

185
00:11:00,400 --> 00:11:03,988
So we have heat convection.

186
00:11:07,060 --> 00:11:07,880
OK?

187
00:11:07,880 --> 00:11:09,850
We have heat
convection that makes

188
00:11:09,850 --> 00:11:14,290
the delta of the internal
energy of the cube.

189
00:11:14,290 --> 00:11:15,510
Right?

190
00:11:15,510 --> 00:11:16,460
Equal to what?

191
00:11:16,460 --> 00:11:21,500
So let's say that
been two time points

192
00:11:21,500 --> 00:11:25,002
the change of the
energy of the cube

193
00:11:25,002 --> 00:11:29,560
is equal to what-- what has
contributed to the energy

194
00:11:29,560 --> 00:11:30,990
change?

195
00:11:30,990 --> 00:11:34,500
Yes, what I'm looking for
is the change in the energy

196
00:11:34,500 --> 00:11:41,560
is really equal to the heat that
goes into the cube plus what's

197
00:11:41,560 --> 00:11:42,630
done to the cube.

198
00:11:42,630 --> 00:11:43,560
Right?

199
00:11:43,560 --> 00:11:46,510
And nobody did any
work to the cube.

200
00:11:46,510 --> 00:11:47,010
Right?

201
00:11:47,010 --> 00:11:49,800
I didn't, I don't
know if you did.

202
00:11:49,800 --> 00:11:54,466
So it is only equal to the
heat convection into the cube.

203
00:11:54,466 --> 00:11:56,330
All right?

204
00:11:56,330 --> 00:12:00,305
So this is how you start
putting the physical process

205
00:12:00,305 --> 00:12:03,040
into equations.

206
00:12:03,040 --> 00:12:06,390
Now let's look at
how do we relate

207
00:12:06,390 --> 00:12:11,450
both sides of the equation to
the temperature of the cube.

208
00:12:11,450 --> 00:12:12,150
OK?

209
00:12:12,150 --> 00:12:16,240
How do you relate the delta
in the internal energy

210
00:12:16,240 --> 00:12:18,600
to the temperature of the cube?

211
00:12:18,600 --> 00:12:20,610
So the change in
the energy relates

212
00:12:20,610 --> 00:12:22,000
to the change in temperature.

213
00:12:22,000 --> 00:12:22,240
Right?

214
00:12:22,240 --> 00:12:24,240
How does it relate to the
change in temperature?

215
00:12:26,630 --> 00:12:27,870
Delta t times what?

216
00:12:30,591 --> 00:12:31,090
C?

217
00:12:34,803 --> 00:12:35,302
Cp?

218
00:12:38,120 --> 00:12:42,280
Times the mass.

219
00:12:42,280 --> 00:12:43,070
Right?

220
00:12:43,070 --> 00:12:47,030
OK and the mass we-- although we
don't know exactly what it is,

221
00:12:47,030 --> 00:12:51,070
we can look up for the
density of the aluminum

222
00:12:51,070 --> 00:12:57,850
and the size of the cube.

223
00:12:57,850 --> 00:12:58,610
Right?

224
00:12:58,610 --> 00:13:02,460
So this is going to give
us the changing energy.

225
00:13:02,460 --> 00:13:08,420
And what is the-- what
determines how much heat

226
00:13:08,420 --> 00:13:09,956
has convected it into the cube?

227
00:13:09,956 --> 00:13:10,456
[INAUDIBLE]

228
00:13:15,380 --> 00:13:15,880
OK.

229
00:13:15,880 --> 00:13:19,260
So I think I should
write it like this.

230
00:13:19,260 --> 00:13:20,990
What determines Q?

231
00:13:20,990 --> 00:13:25,400
What determines the heat
that goes through the surface

232
00:13:25,400 --> 00:13:27,780
of the cube into the cube?

233
00:13:27,780 --> 00:13:33,680
So that is Q from
the gun minus Q--

234
00:13:33,680 --> 00:13:36,250
so this is gun to cube right?

235
00:13:36,250 --> 00:13:40,060
So this is cube to air.

236
00:13:40,060 --> 00:13:43,850
So this is gun to cube
minus cube to air.

237
00:13:43,850 --> 00:13:48,600
Now how do you model--
how does the rate of heat

238
00:13:48,600 --> 00:13:50,130
transfer from the
gun to the cube

239
00:13:50,130 --> 00:13:54,060
depends on the temperature.

240
00:13:54,060 --> 00:13:57,900
And how does the rate
of-- how does the heat

241
00:13:57,900 --> 00:14:01,420
convect from the
cube to the air?

242
00:14:01,420 --> 00:14:01,920
[INAUDIBLE]

243
00:14:16,300 --> 00:14:18,540
Yeah, they linearly
depend on the difference

244
00:14:18,540 --> 00:14:19,840
in the temperature.

245
00:14:19,840 --> 00:14:23,880
So if you look back on
unit five notes-- OK.

246
00:14:23,880 --> 00:14:27,310
So this is-- these are
heat convection right?

247
00:14:27,310 --> 00:14:28,870
Heat convection.

248
00:14:28,870 --> 00:14:32,220
And the way you blow air
from the gun to the cube

249
00:14:32,220 --> 00:14:34,930
is forced convection.

250
00:14:34,930 --> 00:14:35,660
OK.

251
00:14:35,660 --> 00:14:39,470
So this is C-- the rate
of the forced convection,

252
00:14:39,470 --> 00:14:42,210
it is proportional
to the temperature

253
00:14:42,210 --> 00:14:46,310
of the hot air minus the
temperature of the cube

254
00:14:46,310 --> 00:14:48,150
times the coefficient.

255
00:14:48,150 --> 00:14:53,610
And the coefficient is the
forced convection coefficient

256
00:14:53,610 --> 00:14:58,237
in the air times the
area of the convection.

257
00:14:58,237 --> 00:14:59,403
And for example, [INAUDIBLE]

258
00:15:10,170 --> 00:15:14,720
So maybe we can just say
2 times the square is

259
00:15:14,720 --> 00:15:17,090
the temperature of the heat.

260
00:15:17,090 --> 00:15:25,810
And maybe the cube to air is
C free convection times now

261
00:15:25,810 --> 00:15:29,612
four [INAUDIBLE] now
is T minus T air.

262
00:15:33,050 --> 00:15:35,590
All right?

263
00:15:35,590 --> 00:15:42,190
And this is the rate
of heat conversion.

264
00:15:42,190 --> 00:15:47,280
Now we time the delta of time.

265
00:15:47,280 --> 00:15:52,355
We are going to get the amount
of heat that went into the cube

266
00:15:52,355 --> 00:15:56,170
during a small time unit.

267
00:15:56,170 --> 00:16:00,410
Now this is going to give
us a differential equation.

268
00:16:00,410 --> 00:16:03,520
Because if we let the
delta T, the amount

269
00:16:03,520 --> 00:16:06,590
of time we are looking
at goes to zero,

270
00:16:06,590 --> 00:16:11,340
we are going to get to the
equation of Cp times rho d

271
00:16:11,340 --> 00:16:15,870
cubed dT/dt.

272
00:16:15,870 --> 00:16:20,740
So this is the rate of
change in the temperature

273
00:16:20,740 --> 00:16:29,185
equal to C force times 2 d
squared T H minus T minus C

274
00:16:29,185 --> 00:16:35,871
free, 4 d squared T minus T air.

275
00:16:35,871 --> 00:16:36,370
right

276
00:16:36,370 --> 00:16:38,310
So this is the differential
equation we get.

277
00:16:41,750 --> 00:16:45,630
Now what changes when we
turn off the heat gun?

278
00:16:45,630 --> 00:16:49,850
C force is gone and the C
free becomes [INAUDIBLE].

279
00:16:49,850 --> 00:16:50,550
Right.

280
00:16:50,550 --> 00:16:51,980
So that's the difference.

281
00:16:51,980 --> 00:16:57,990
And let's go to Matlab,
and I wrote a code

282
00:16:57,990 --> 00:17:03,220
for simulating this.

283
00:17:03,220 --> 00:17:04,819
So here is the parameters.

284
00:17:04,819 --> 00:17:06,530
Ambient temperature
we said today

285
00:17:06,530 --> 00:17:11,480
is a little bit
colder than I thought.

286
00:17:11,480 --> 00:17:15,560
And the hot air temperature,
if we look at this,

287
00:17:15,560 --> 00:17:17,530
I think is like
106 or something.

288
00:17:17,530 --> 00:17:22,730
Let's put 106.

289
00:17:22,730 --> 00:17:28,860
And the start time in seconds
I actually don't know, so let's

290
00:17:28,860 --> 00:17:30,580
just put 0 here.

291
00:17:30,580 --> 00:17:33,630
And the T stopped in seconds.

292
00:17:33,630 --> 00:17:36,470
What time is it like 11 minutes?

293
00:17:36,470 --> 00:17:40,490
What is 11 minutes in-- so
this is 11 minutes right?

294
00:17:40,490 --> 00:17:42,312
OK.

295
00:17:42,312 --> 00:17:46,600
tend I think I'll just do this.

296
00:17:46,600 --> 00:17:47,210
OK.

297
00:17:47,210 --> 00:17:50,610
So these are what
I looked up online.

298
00:17:50,610 --> 00:17:54,970
Some of the values for
the free air convection

299
00:17:54,970 --> 00:17:56,922
and the forced air convection.

300
00:17:56,922 --> 00:17:58,380
And the [INAUDIBLE]
of the aluminum

301
00:17:58,380 --> 00:18:02,040
cube the density of aluminum,
and the specific heat

302
00:18:02,040 --> 00:18:04,160
capacitance.

303
00:18:04,160 --> 00:18:04,780
All right.

304
00:18:04,780 --> 00:18:09,420
And these you don't need to look
at them because they are never

305
00:18:09,420 --> 00:18:13,360
used in the code because
radiation exactly

306
00:18:13,360 --> 00:18:14,440
is not important.

307
00:18:14,440 --> 00:18:18,330
So heating and we are
using [INAUDIBLE] so solve

308
00:18:18,330 --> 00:18:19,790
the equation.

309
00:18:19,790 --> 00:18:24,320
I'm basically saying
that the heating rate is

310
00:18:24,320 --> 00:18:28,280
proportional to two sides, and
the cooling rate et. cetera,

311
00:18:28,280 --> 00:18:30,230
and we are also
doing the cooling.

312
00:18:30,230 --> 00:18:33,880
So let's do the simulation.

313
00:18:33,880 --> 00:18:41,110
We are getting a plot like this.

314
00:18:41,110 --> 00:18:56,670
And let's compare our
temperatur.txt-- [INAUDIBLE]

315
00:19:08,354 --> 00:19:10,360
Oh, OK.

316
00:19:10,360 --> 00:19:13,890
I need to get rid of this.

317
00:19:13,890 --> 00:19:16,090
Let me push the stop.

318
00:19:20,500 --> 00:19:23,440
Not responding.

319
00:19:23,440 --> 00:19:24,260
Error writing.

320
00:19:24,260 --> 00:19:24,760
[INAUDIBLE]

321
00:19:39,491 --> 00:19:39,990
OK.

322
00:19:45,100 --> 00:19:46,030
Now we are plotting.

323
00:19:49,520 --> 00:19:52,844
So look at the difference
between the simulation

324
00:19:52,844 --> 00:19:53,635
and the experiment.

325
00:19:57,370 --> 00:19:58,570
It's huge.

326
00:19:58,570 --> 00:20:00,120
Right?

327
00:20:00,120 --> 00:20:03,660
So what is causing
this Difference

328
00:20:03,660 --> 00:20:06,520
It is because now
here what I said

329
00:20:06,520 --> 00:20:10,220
is the force convection
coefficient is

330
00:20:10,220 --> 00:20:14,100
10 watt per meter
square plus K. Right?

331
00:20:14,100 --> 00:20:21,220
Now let's go to the internet
and search for force convection

332
00:20:21,220 --> 00:20:24,080
coefficient of air.

333
00:20:27,150 --> 00:20:28,040
Engineering toolbox.

334
00:20:34,000 --> 00:20:35,360
Is it this one?

335
00:20:39,080 --> 00:20:40,940
Yes.

336
00:20:40,940 --> 00:20:47,510
Forced convection of air goes
all the way from 10 to 200.

337
00:20:47,510 --> 00:20:48,160
OK.

338
00:20:48,160 --> 00:20:51,790
And here I am actually
putting the lower bound.

339
00:20:51,790 --> 00:20:59,260
If I put something like 200
and do the simulation again,

340
00:20:59,260 --> 00:21:08,290
and do the experiment
again, this is what I got.

341
00:21:08,290 --> 00:21:08,790
OK.

342
00:21:08,790 --> 00:21:16,340
I've got a much better match and
I also have my free convection

343
00:21:16,340 --> 00:21:17,450
to be 5.

344
00:21:17,450 --> 00:21:21,160
If you look over the
internet free convection

345
00:21:21,160 --> 00:21:23,880
goes from 5 to 25.

346
00:21:23,880 --> 00:21:24,420
OK.

347
00:21:24,420 --> 00:21:31,170
And also if I go to
25 I think I am also

348
00:21:31,170 --> 00:21:34,540
going to be getting
a much better match.

349
00:21:34,540 --> 00:21:35,040
OK.

350
00:21:35,040 --> 00:21:38,520
So the rate of decaying
is much better now.

351
00:21:38,520 --> 00:21:41,382
And another thing I
assume there are only

352
00:21:41,382 --> 00:21:46,360
two sides of the cube are
being heated. [INAUDIBLE]

353
00:21:46,360 --> 00:21:50,234
But actually if you switch
over to the next problem

354
00:21:50,234 --> 00:21:54,360
you will see more than two
sides are being heated.

355
00:21:54,360 --> 00:21:56,470
So that is actually
another motivation

356
00:21:56,470 --> 00:21:59,390
for why we need to look
at not only one simulation

357
00:21:59,390 --> 00:22:01,222
but several simulations.

358
00:22:01,222 --> 00:22:04,416
And that is leading
into the fourth part

359
00:22:04,416 --> 00:22:08,396
of this subject,
probabilistic simulations.

360
00:22:08,396 --> 00:22:11,690
Because when you look at a
lot of physical phenomena

361
00:22:11,690 --> 00:22:15,030
there is a lot of
uncertainty in it

362
00:22:15,030 --> 00:22:19,470
when you look at the
range of coefficients

363
00:22:19,470 --> 00:22:23,880
you can possibly get
in modeling physics.

364
00:22:23,880 --> 00:22:27,030
And convection is
a primary example

365
00:22:27,030 --> 00:22:29,960
if this because there
are so much uncertainty

366
00:22:29,960 --> 00:22:33,480
in what rate you can get.

367
00:22:33,480 --> 00:22:33,980
All right.

368
00:22:33,980 --> 00:22:36,411
So this is our first lecture.

369
00:22:36,411 --> 00:22:38,516
I will see you next Monday.

370
00:22:38,516 --> 00:22:42,100
But remember, one thing
is you need to read and do

371
00:22:42,100 --> 00:22:44,830
the homework, do the
embedded questions

372
00:22:44,830 --> 00:22:48,410
before you come to
class next Monday.