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0:15
>> We're going to talk about today Chapter 1, starting off and heat transfer. What is heat transfer? Heat transfer is the exchange of thermal energy due to a difference in temperature. So there has to be a difference in temperature in order for there to be heat transfer.
0:43
There is a difference. You can heat a turkey in your oven and looking there when the oven is on and you'll see it glowing red on the coils or your toaster look in there, you'll see electrical wires glowing red, wires are hot, the toaster is cool, the bread is cool. There's heat transfer occurring because there's a difference in temperature.
1:16
Look at your microwave, turn it on, you'll say, "The side walls are glowing red." Well, if they are, get out of the kitchen room fast. That's bad news. Nothing is blowing red but there's transfer of energy taking place. What kind of energy? Microwave energy. So there's thermal energy and there's microwave energy. We're talking in this class about thermal energy, that's the difference. Go back to thermal. You've heard thermal, it's a prerequisite. This is the first law for a closed system,
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equation Q equal Delta U plus W. In thermal, let's say it's a piston cylinder, you're taught how to find Delta U, give me some pressures and temperatures of air in the piston cylinder, and I'll tell you Delta U. I can find it on the table. W was called the work done during the process. In the chapter on work, they always give you a few equations on how to calculate work. The first question they ask you is, is the process constant pressure? Is it a polytropic process?
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Is there spring work being done? Is there electrical work being done? They give you equations for that. Now, comes Q heat transfer. Try to find one equation for Q in that thermal text. There isn't any. Here's what they'll say, "The heat loss through the insulated turbine is so many BTU per hour." They give you Q and thermal, or they'll say, "If this much work is done and the process goes through this temperature and pressure, how much heat transfer occurred?. But they'll never tell you how
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to calculate heat transfer. That's why we have this class, this class is meant to fill in all those blanks. How do we find that Q? So in heat transfer, we pretty much lump in the first course heat transfer into one of three modes or three ways that heat can be transferred. Number 1, it can be transferred by conduction. Number 2, by a process called convection, and number 3 by what we call radiation heat transfer. Chapter 1 briefly goes into these three modes of heat transfer.
4:02
But then we get into depth in conduction in chapters 2, 3, 4 and 5. We get into depth in convection in chapters 6, 7, 8 and 9, and we cover radiation in chapters 12 and 13 in more depth but chapter 1 is an introduction to those three modes of heat transfer. So we'll start with conduction heat transfer HT. Transfer of thermal energy from more energetic to less energetic particles due to their interaction. If I heat a steel plate on one side with a welding torch or
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you can put a Bunsen burner under it, heat one side of that steel plate, the molecules in there start to vibrate, they get more energy from that heat. They vibrate, they interact with their neighbors exchanging energy and the energy exchange goes the from hot side of the steel plate to the cold side of the steel plate by what? By conduction. So that's what occurs in conduction. Now, we can then look at how we calculate conduction. To do that, we'll write down Fourier's Law, the governing law.
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This is the basic one dimensional format of that law.
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First of all, what is Q? Here's what Q is. Q is called the heat rate. It's in [inaudible] of heat transfer but officially the heat rate. It's in watts. What does the double-prime mean? It means per unit area, Q per unit area means you take Q divided it by the area in square meters and the units then become watts per square meter. Q with no prime is watts. Q double-prime, watts per square meter. The heat transfer in this case is in the x-direction, so it's a one-dimensional heat transfer case.
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Its officially in Chapter 2, three-dimensional and we'll do that later on but for right now in Chapter 1 is one-dimensional. So the heat transfer is in one-dimensional x.
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So for instance, if this inside the wall, I'm making something up, is at 100 degrees Fahrenheit and the whole sides on the wall is 30 degrees Fahrenheit. Here's going to be some heat transfer through those concrete wall from the inside here to the whole side here. Which direction is it in? Hot to cold, this way, that's my x-direction. Heat transfer occurs to what direction? X-direction, this way. So that's what this means. Now, that K is a property of the material, in that case, concrete wall.
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K will be the K of that wall at what temperature? The average temperature 100 plus 30 divided by 2. So K is a property called thermal conductivity,
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it's in watts per meter K. Our textbook is all in SI for better or worse, for you is for better until you graduate and the you say, "Oh my gosh, I got to convert these guys into whatever English engineering and you're back to SI." So the good news is everything is in SI in the textbook, homework examples etc, which makes life turns easier.
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What do you find K back at the book? Give me fluid or give me a substance. Aluminum. Give me a temperature, 500 degrees C. Go to the back of the book, There it is. Right there, material and temperature.
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Now, if we look at this, let's draw a wall here,
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and I'm going to measure this x in this direction and the wall thickness is L. I'm going to assume the temperature on the left hand side, the hot temperature T_1, the temperature on the right hand side is called temperature T_2. Material has thermal conductivity K. This is one-dimensional heat conduction, we'll discuss that in Chapter 2 and 3 but for one-dimensional heat transfer we can get rid of the ordinary differential dT, dx and replace it by T_2 minus T_1 divided by L minus 0.
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That's one-dimensional heat transfer. We can just put it up 1D heat transfer.
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Turns out for that case the temperature profile is linear.
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We'll discuss that also in I think it's Chapter 3, linear. Now, let's replace the dT dx with this then. So we get q
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double prime x equals minus K, T_2 minus T_1 divided by L. K, T_1 minus T_2 divided by L, K Delta T over L.
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>> So in chapter 1, this is the important equation from Fourier's Law for how we find conduction heat transfer through, for instance, a wall. Now, if you don't want the answer in double prime, let's say, I want q in watts for the wall. What do you do to cute q double prime? You multiply q double prime by the area to get q. So q_x
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equal KA Delta T over L.
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Area is the normal area.
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So if the pen is heat flow direction, the appropriate area is the area of my hand. Here's the heat flow, here's the area I put in. If it's this wall and the temperature of this side is a 100 degrees c and the temperature out here is 30 degrees c. Which way is the heat flow from the hot inside, the cold outside? Heat flow goes that way. What area do I use? The height of wall here times the length of the wall, rectangular area, height times length.
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One other thing. This law came from Professor Fourier way, way back.
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But he didn't derive it from something. He did some experimental investigations. He found out that this way the heat float seem to respond to a change in temperature or a change in length or a change in material. So he derived this thing from looking at experimental results.
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But you might say, "I don't understand him.".
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Why would he put a minus sign in front of that? It sounds ridiculous to me. He put there really? Professor Fourier? Well, yes, you have to. He figured out. You have to. Here's a picture. Hot temperature, cold temperature. You know which way heat flows, from hot to cold, q. Which way does it flow positive or negative x? Positive x, positive x. What sign is that q? Positive. What sign is dt/dx? Look at it. Negative. What's k? It's always a positive number. It's a property.
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Does it checkout? Oh, it sure does. Plus on the left or right, minus sign, plus sign, minus sign. Yeah, it checks out. If he don't do that, minus side, it says, you know what the heat flows in the negative x direction. Oh, no, it's not. Heat all goes hot to cold. That's why I put the minus sign there.
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So that pretty much wraps up chapter 1, conduction. Next week, we'll cover chapters 2, 3, 4, and 5 in great depth on conduction. So now we're going to change this to convection.
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So let's get that down.
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By the way, in order for there to be convection, there's a fluid flowing over a surface, convection, a fluid flowing over a surface. That's fluid mechanics. So we go back to fluid mechanics.
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Here's our surface.
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If you recall from fluid mechanics, there was a boundary they would buildup on a surface with a fluid flowing over it and the boundary layer would look like this. This maybe called u infinity and this is be called u as a function of that vertical distance y.
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That's fluid mechanics. Well, how about heat transfer? Let's say the surface is at a warm temperature T_s and the fluid maybe air, is at a temperature T_infinity. So the bounded air builds up for heat transfer called the thermal boundary layer. This is the surface temperature T_s,
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the free stream temperature T_infinity, which is cooler. So now we have a boundary layer that looks like this. That's the temperature or thermal boundary layer. But you can't work the heat transfer problem unless you really understand what's going on from fluid mechanics. That's why fluid mechanics is prerequisite to heat transfer. We have to have a really have a good feeling for fluid mechanics in order to tackle convection heat transfer. So the rate equation
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is Newton's Law of Cooling.
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Q equal hA T_s minus T_infinity. We've defined Ts and we've defined T_infinity. A is the surface area,
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that's the area touching the fluid, the surface area in contact with the fluid.
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I'm going to put here convection heat transfer just so we know, between surface and fluid.
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To have convection, we have a surface and we have a fluid. The fluid is moving over the surface. Surface area A. Take that pen. The pen's hot. The air is this room is cooler. Convection heat transfer. I blow air over. There's the equation. What's the right area Pi D times L. There's L. That area Pi DL. Pi D circumference, L the length. Where does the air touch the fluid or touch the surface. That's what it means. So that's our basic convection equation. Now h, h is
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the convection heat transfer coefficient.
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Depends on fluid properties.
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It depends on geometry. Depends on flow regime.
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Possibly others. First question is what's the temperature and pressure? From that you find the properties. Second question. What's the geometry? Is it a circular tube? Is it a flat plate? Is it a sphere? Second question. Third question, is it laminar flow, turbulent flow, mixed flow, cavitation? Whats the flow regime? Whats going on there? All those things are tied into h. You won't find h in the back of the book in the appendix because it's way too complicated. Way too complicated.
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The main focus of chapter 6, 7, 8 is to find h. That's why you do chapter six, seven, eight. How do I find eight to put in Newton's Law of Cooling to get the heat transfer of q? That's the name of the game.
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H's they can vary. I'll just give some rough numbers. Let's see. This is for gasses.
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H rose with 25.
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Maybe these are just rough numbers, 250.
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By the way h is in watts per meter squared k. If it's liquids,
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h is much, much larger.
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Typical numbers like that up to 20,000 compared to gasses, high number roughly 250.
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>> So if you want good heat transfer, you want to use a liquid. If you want to cool your engine block, you're going to use water. Because water takes lots of heat out not air.
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But on the other side, the radiator you got air. I'm going to pay a penalty because I got a very low h because they got air on the outsider the radiator. Well, that's why we have fins on the radiator. As chapter three, hang on to chapter three we'll talk about that. So that's how we engineer's work. If we say, ''My h is too low, I'll do something about it. I'll put fins on it." If I've got water in here, I'm doing good. Took a lot of heat out with water. Convection heat transfer,
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fluid, and the surface. Is flat plate? Is it a cylinder? Now, that gets us down to the, I'll just put this up here by the way. This q is called heat rate.
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This one is called heat flux.
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You might want to call this heat transfer, that's okay. But the official name is heat rate, that's in watts.
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Now we get to the third one,
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radiation heat transfer.
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It can occur in a vacuum, you don't need air or anything. That's why it's so important for space applications, obviously. Because if you want to cool something up, there you got to dump heat from a power plant or electronics. You got to dump heat and you can't dump it by conduction or convection to displace, no. So you dump it by radiation into black space. So heat transfer from hot a surface to a cold temperature surface and it can occur in a vacuum. The rate equation,
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Stefan-Boltzmann Law,
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q double-prime sigma ts to the fourth.
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That constant sigma is called the Stefan-Boltzmann Constant 5.67 10 to minus 8 watts per square meter K to the fourth.
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So you give me a surface temperature, by the way. I will tell you the heat transfer from that surface. But there's a qualifier, that's maximum energy the surface can emit. This is for an ideal emitter.
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The ideal emitter is called a blackbody.
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So that's the maximum energy the surface can emit, but it's only valid if it's an ideal emitter. Blackbody means like it appears to our eyes to be black, some surfaces black, the phone over there, whatever it might be.
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We can get really close to blackbody, but normally we deal with non-blackbodys. So those are other cases. So for non-blackbodys,
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q double-prime epsilon sigma T surface to the fourth.
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Epsilon accounts for surface not being the ideal emitter. Its value can go from zero to one. If epsilon is one, it behaves like a blackbody.
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You can find values of epsilon in the back of the textbook. So you could find those values for epsilon polished aluminum, corroded steel, whatever it might be it's in the back of the book.
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So that's what we have for that. Now we have when other one, which is the radiation heat transfer
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between a small object and the walls of a large enclosure.
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So here's a small object in very large enclosure. The walls of the enclosure are at temperature called T surroundings. The object is added temperature T sub s. The emissivity is emissivity of the surface epsilon and if that's the case. Then we have this equation for q double prime.
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But that's only valid if small object in a large enclosure. Like put a dime inside of a basketball. That qualifies, dime is a small object, thousand degrees Fahrenheit. In a basketball temperature of 60 degrees Fahrenheit. Find out how much heat transfer occurs between those two. There is the equation you use. We're going to prove that. In chapter 13 that's the proof. Right now we can't prove it. Just except it and use it for homework. We'll prove in chapter 13. So here's the picture,
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epsilon is the objects emissivity, t-s the surface temperature of the object T surroundings temperatures of the wall and the enclosure. So we have a couple equations in convention, conduction, and radiation, which we use in chapter one for the most basic type homework problems. >> [inaudible] >> Now, which one for instance? >> The one. [inaudible] the middle one. >> This one? >> Yeah. >> Now what about it I'm sorry? >> That's just surrounded by [inaudible] >> No, that's strictly
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the surface, taker surface. Don't worry what's surrounded by it, just the surface and you want to know how many watts per square meter leave that surface, I don't care where they go. This one here now here I do care where they Go, it goes to the walls of the room or the furnace, whatever might be. This one is just the Surface itself. Like if I get rid of this, how much energy leaves that surface? There it is right there, epsilon, epsilon T-s, Ts put in here. That's how much energy it is.
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But the problem is, some energy goes on to walls, but some goes back,
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minus sign, see what it means there.
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It's a good stopping point, so I can add people to class after class here, so we'll see you on Friday. If you came in late and didn't get my handouts, come in front and pick up the handouts before you leave.
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