Understanding Convection in Heat Transfer

Welcome to this heat transfer video lecture. In this lecture we're going to introduce convection. We're going to start off by talking about this concept of boundary layers. So I want to start off with a thought experiment. Imagine that you are standing all alone in the middle of a perfectly flat field. There are no obstacles or anything. And then suddenly you encounter some hurricane force winds. And let's just assume that for the sake of this hypothetical example that these winds are strong enough to pick you up and actually hurl you and could really hurt you. So assuming that you have to act within seconds and you have really no time to run and search for cover, what's your first instinct? For me, my first instinct would be to lay down. So one of the reasons that I would be inclined to do that would be to reduce the exposed area of my body for the wind to hit. So if you're able to minimize your profile, you're a little bit more aerodynamic. But another reason is actually that the wind speed would actually be lower. closer to the ground. So for those two reasons, you might be able to minimize the damage that the wind could do to you if you're able to get down close to the ground. So this is certainly confirmed by looking at wind speed profiles. You notice that very near the ground the wind speed is very near zero, and then it increases the further up you go up into the air. This is one of the reasons that they make windmills be very tall, so that they're exposed to this much higher wind velocity so you can extract more energy. Whereas one that is closer to the ground won't be able to turn as fast and won't be able to generate as much power. So, why are we talking about this? We know that this is a course on heat transfer. However, we're getting into convection, and if you recall, convection is heat transfer from a surface to a fluid. So, the characteristics of that fluid actually have a lot to do with how well energy can be transferred, thermal energy can be transferred. So, How the fluid is flowing is going to have a big impact on heat transfer. So we're going to need to cross over into some fluid mechanics knowledge in order to understand convection a little bit better. So let's start off. We'll just go into some basic theory about convection. Let's assume that we have some solid surface with an edge. We're going to call this the leading edge. And let's suppose that we take some kind of fan or there's some kind of wind and it is coming in with this nice uniform velocity profile. As it encounters that leading edge, the fluid that is closest, so we think of this fluid in terms of layers, if it's nice laminar flow, we can think of it that way. So the fluid that is at the very bottom layer is actually going to have some viscous... effects as it encounters that leading edge. We're going to see a very low or even close to zero velocity on that bottom layer. However, because it has just encountered that leading edge, we would expect these other layers to still be flowing along almost as before. As you move further and further down this flat plate, this bottom layer here is going to start to have viscous forces with the next layer. It's going to start to grab onto it, if you will, and slow it down. So if we looked at this velocity profile a little bit later, we might see that our bottom layer has started to grab onto that next layer and slow it down. And as we keep going, you see that gradually those viscous forces start to propagate their way up this velocity profile. And it keeps penetrating higher and higher to the point that... we start to see this much more of a profile developing. So this creates what's called a boundary layer. So that's just if you notice if we were to sort of map or plot these different velocity profiles we might get something that looks a little bit more give me a second to grab a different color. So if we were to plot this velocity profile as a function of y where y is the distance up and we're looking at our u sub x for our x velocity, we start to see these this kind of gradually morphing what's called a velocity profile, but if we were to plot the length of our velocity, this u sub x, we would see that it gets higher and higher. There's a thicker and thicker what's called a boundary layer until we get up here to the top. This is called the free stream velocity. and it's going to be flowing at a speed of u infinity. So very far away from the plate we get this u infinity, which we are going to label the free stream velocity, which is also known as the bulk fluid velocity. But basically the further away you get from the top edge of the flat plate, the closer you get to this initial velocity that you encountered before you hit the leading edge. So if we were to... plot the thickness. So we're going to introduce a new parameter here called delta. So delta is the velocity boundary layer thickness. So this velocity boundary layer thickness is defined as the point at which our velocity, this u, in terms of y, or how far up you are from the plate, relative to the free stream velocity, equals 0.99. So basically, how far away from the plate do we need to get before our velocity is equal to 0.99 of the free stream velocity? And as you can see, as our velocity profile starts to take shape, this boundary layer gets thicker and thicker. as those viscous forces start to propagate their way up into up above the plate. So this is called the velocity boundary layer, and it's defined as the point at which our velocity in the x direction as a function of y reaches 99% of the free stream velocity. Okay, so how does that come into play with heat transfer? Now, so let's think of the same kind of scenario, but now let's assume that the... plate is heated. So let's get our plate here. Let's try to do a better job of making that flat. So here's our same plate with the leading edge, and now let's assume that we apply some heat source here so that this becomes hot. So this is at a temperature of T sub s. So now let's think about our our flow coming in. and let's assume that it's coming in at a cooler temperature of T infinity. So what happens as we, as this flow impacts our plate, we have that velocity boundary layer forming, and that certainly affects things. But what also happens is that you get heat transfer occurring. So now we have this driving force for heat transfer, we have this hot plate that's transferring energy up into the colder fluid. So what will happen here is initially if we looked at temperature profile. I'm going to go ahead and erase these streamlines, but if we looked at a temperature profile, we were looking at temperature, sorry, we're going to do this the other way. We're going to look at temperature as a function of y, where y is basically the height above the surface of the plate. Initially we would see that our temperature profile is totally flat. It's all just going to be at the free stream temperature or the bulk. fluid temperature. But gradually that first bottom layer is going to get a little bit hotter and that heat is going to start propagating upward and gradually over time you'll start to see these more and more pronounced heat profiles or temperature profiles in the y direction. So what happens is we also get something called a thermal boundary layer that forms. So if we were to take that same kind of picture, so now we're looking at y in the y direction and temperature in the x direction, we start to see that we get this temperature profile that forms. So we define another variable. This is known as the thermal boundary layer thickness. So this delta sub t stands for the thermal boundary layer thickness. And similar to the velocity boundary layer thickness, the thermal boundary layer thickness is a measure of how long it takes to get, relatively speaking, how high up you have to go to get to 99% of your bulk fluid temperature. So if we were to plot that point, you can see that this thermal boundary layer starts to grow, and you actually get this temperature profile that gets more and more pronounced the further down the length of that flat plate you get. So if we were to measure the flow of heat, remember this is about heat transfer, so far we've talked about convection in these kind of terms. We have Q equals H, let's do this in flux form, our flux equals H times delta T, and the delta T that we're talking about is the delta T from the surface all the way out to the bulk fluid, and we don't really even think about what's happening in between. Well, now that we're getting into convection, we're going to have to start thinking more about... what's happening in terms of that fluid flow and these velocity and thermal boundary layers. So if we were to plot that same flux and think about this more in terms of conduction, so if this fluid is flowing along really nice and smooth, we would almost experience more of a conduction phenomenon happening where the driving force would be a delta T or a temperature gradient in the y direction and we would characterize that using Fourier's law by the fluid conductivity. So if we're thinking about conduction happening in this fluid, and let's approximate this, or let's at least think about this fluid being fairly stationary for now, if we could put this in purely in terms of Fourier's law right at that initial layer, remember that initial layer has a this no slip condition, so we expect it to be basically going zero right there at the interface. So if we could take our temperature gradient, we could apply Fourier's law using the thermal conductivity of the fluid to calculate q. q double prime the flux. If we thought about this in terms of Newton's law of cooling, we'd be thinking about the flux but going from here to here. So if we were able to equate those two things and say that the flux that is getting through that first layer is going to be the same as the flux that's getting all the way through the boundary layer and into the bulk, then we could actually define a convective heat transfer coefficient this way by just equating those two heat flows. So what this tells us is that our convection coefficient is partially at least a function of the thermal conductivity of the fluid itself, but it's also going to be something that's a characteristic of the flow. So convection, if we think of it that way, is really a combination of conduction and something called advection. So advection is the transfer of heat by the flow of a fluid. So if you remember this relationship from perhaps other courses where we have q is equal to m dot cp times delta t. So this m dot or this flow of fluid can actually transfer heat. If you have the fluid itself physically moving from one point to another, it's going to carry some of that built-in thermal energy with it. So we're going to use this plot later on and we'll explain more about what's going on here. But if you think about once you start to get turbulent flow, you start to get eddies and back propagation. So when that happens, you have fluid moving around freely and mixing. That's actually really effective for transferring heat. So while we will have some heat being transferred by conduction where it's just a molecular motion of a stationary fluid, well, our fluid isn't always stationary. And you can see it's moving here in the laminar region and it's moving here in the turbulent region. So the combination of those two is really what makes up convection. So we've talked a lot about conduction, and really convection has conduction sort of built into it, but because of this other piece, this advection piece, convection actually gets quite a bit more complicated than conduction, so we're going to have different ways of dealing with that over the next few video lectures.

Welcome to this heat transfer video lecture. In this lecture we're going to introduce convection. We're going to start off by talking about this concept of boundary layers.

So I want to start off with a thought experiment. Imagine that you are standing all alone in the middle of a perfectly flat field. There are no obstacles or anything. And then suddenly you encounter some hurricane force winds. And let's just assume that for the sake of this hypothetical example that these winds are strong enough to pick you up and actually hurl you and could really hurt you.

So assuming that you have to act within seconds and you have really no time to run and search for cover, what's your first instinct? For me, my first instinct would be to lay down. So one of the reasons that I would be inclined to do that would be to reduce the exposed area of my body for the wind to hit.

So if you're able to minimize your profile, you're a little bit more aerodynamic. But another reason is actually that the wind speed would actually be lower. closer to the ground.

So for those two reasons, you might be able to minimize the damage that the wind could do to you if you're able to get down close to the ground. So this is certainly confirmed by looking at wind speed profiles. You notice that very near the ground the wind speed is very near zero, and then it increases the further up you go up into the air.

This is one of the reasons that they make windmills be very tall, so that they're exposed to this much higher wind velocity so you can extract more energy. Whereas one that is closer to the ground won't be able to turn as fast and won't be able to generate as much power. So, why are we talking about this?

We know that this is a course on heat transfer. However, we're getting into convection, and if you recall, convection is heat transfer from a surface to a fluid. So, the characteristics of that fluid actually have a lot to do with how well energy can be transferred, thermal energy can be transferred.

So, How the fluid is flowing is going to have a big impact on heat transfer. So we're going to need to cross over into some fluid mechanics knowledge in order to understand convection a little bit better. So let's start off.

We'll just go into some basic theory about convection. Let's assume that we have some solid surface with an edge. We're going to call this the leading edge.

And let's suppose that we take some kind of fan or there's some kind of wind and it is coming in with this nice uniform velocity profile. As it encounters that leading edge, the fluid that is closest, so we think of this fluid in terms of layers, if it's nice laminar flow, we can think of it that way. So the fluid that is at the very bottom layer is actually going to have some viscous...

effects as it encounters that leading edge. We're going to see a very low or even close to zero velocity on that bottom layer. However, because it has just encountered that leading edge, we would expect these other layers to still be flowing along almost as before.

As you move further and further down this flat plate, this bottom layer here is going to start to have viscous forces with the next layer. It's going to start to grab onto it, if you will, and slow it down. So if we looked at this velocity profile a little bit later, we might see that our bottom layer has started to grab onto that next layer and slow it down.

And as we keep going, you see that gradually those viscous forces start to propagate their way up this velocity profile. And it keeps penetrating higher and higher to the point that... we start to see this much more of a profile developing.

So this creates what's called a boundary layer. So that's just if you notice if we were to sort of map or plot these different velocity profiles we might get something that looks a little bit more give me a second to grab a different color. So if we were to plot this velocity profile as a function of y where y is the distance up and we're looking at our u sub x for our x velocity, we start to see these this kind of gradually morphing what's called a velocity profile, but if we were to plot the length of our velocity, this u sub x, we would see that it gets higher and higher. There's a thicker and thicker what's called a boundary layer until we get up here to the top.

This is called the free stream velocity. and it's going to be flowing at a speed of u infinity. So very far away from the plate we get this u infinity, which we are going to label the free stream velocity, which is also known as the bulk fluid velocity.

But basically the further away you get from the top edge of the flat plate, the closer you get to this initial velocity that you encountered before you hit the leading edge. So if we were to... plot the thickness.

So we're going to introduce a new parameter here called delta. So delta is the velocity boundary layer thickness. So this velocity boundary layer thickness is defined as the point at which our velocity, this u, in terms of y, or how far up you are from the plate, relative to the free stream velocity, equals 0.99. So basically, how far away from the plate do we need to get before our velocity is equal to 0.99 of the free stream velocity? And as you can see, as our velocity profile starts to take shape, this boundary layer gets thicker and thicker.

as those viscous forces start to propagate their way up into up above the plate. So this is called the velocity boundary layer, and it's defined as the point at which our velocity in the x direction as a function of y reaches 99% of the free stream velocity. Okay, so how does that come into play with heat transfer?

Now, so let's think of the same kind of scenario, but now let's assume that the... plate is heated. So let's get our plate here. Let's try to do a better job of making that flat.

So here's our same plate with the leading edge, and now let's assume that we apply some heat source here so that this becomes hot. So this is at a temperature of T sub s. So now let's think about our our flow coming in. and let's assume that it's coming in at a cooler temperature of T infinity. So what happens as we, as this flow impacts our plate, we have that velocity boundary layer forming, and that certainly affects things.

But what also happens is that you get heat transfer occurring. So now we have this driving force for heat transfer, we have this hot plate that's transferring energy up into the colder fluid. So what will happen here is initially if we looked at temperature profile.

I'm going to go ahead and erase these streamlines, but if we looked at a temperature profile, we were looking at temperature, sorry, we're going to do this the other way. We're going to look at temperature as a function of y, where y is basically the height above the surface of the plate. Initially we would see that our temperature profile is totally flat.

It's all just going to be at the free stream temperature or the bulk. fluid temperature. But gradually that first bottom layer is going to get a little bit hotter and that heat is going to start propagating upward and gradually over time you'll start to see these more and more pronounced heat profiles or temperature profiles in the y direction. So what happens is we also get something called a thermal boundary layer that forms. So if we were to take that same kind of picture, so now we're looking at y in the y direction and temperature in the x direction, we start to see that we get this temperature profile that forms.

So we define another variable. This is known as the thermal boundary layer thickness. So this delta sub t stands for the thermal boundary layer thickness.

And similar to the velocity boundary layer thickness, the thermal boundary layer thickness is a measure of how long it takes to get, relatively speaking, how high up you have to go to get to 99% of your bulk fluid temperature. So if we were to plot that point, you can see that this thermal boundary layer starts to grow, and you actually get this temperature profile that gets more and more pronounced the further down the length of that flat plate you get. So if we were to measure the flow of heat, remember this is about heat transfer, so far we've talked about convection in these kind of terms.

We have Q equals H, let's do this in flux form, our flux equals H times delta T, and the delta T that we're talking about is the delta T from the surface all the way out to the bulk fluid, and we don't really even think about what's happening in between. Well, now that we're getting into convection, we're going to have to start thinking more about... what's happening in terms of that fluid flow and these velocity and thermal boundary layers. So if we were to plot that same flux and think about this more in terms of conduction, so if this fluid is flowing along really nice and smooth, we would almost experience more of a conduction phenomenon happening where the driving force would be a delta T or a temperature gradient in the y direction and we would characterize that using Fourier's law by the fluid conductivity. So if we're thinking about conduction happening in this fluid, and let's approximate this, or let's at least think about this fluid being fairly stationary for now, if we could put this in purely in terms of Fourier's law right at that initial layer, remember that initial layer has a this no slip condition, so we expect it to be basically going zero right there at the interface.

So if we could take our temperature gradient, we could apply Fourier's law using the thermal conductivity of the fluid to calculate q. q double prime the flux. If we thought about this in terms of Newton's law of cooling, we'd be thinking about the flux but going from here to here. So if we were able to equate those two things and say that the flux that is getting through that first layer is going to be the same as the flux that's getting all the way through the boundary layer and into the bulk, then we could actually define a convective heat transfer coefficient this way by just equating those two heat flows.

So what this tells us is that our convection coefficient is partially at least a function of the thermal conductivity of the fluid itself, but it's also going to be something that's a characteristic of the flow. So convection, if we think of it that way, is really a combination of conduction and something called advection. So advection is the transfer of heat by the flow of a fluid. So if you remember this relationship from perhaps other courses where we have q is equal to m dot cp times delta t.

So this m dot or this flow of fluid can actually transfer heat. If you have the fluid itself physically moving from one point to another, it's going to carry some of that built-in thermal energy with it. So we're going to use this plot later on and we'll explain more about what's going on here. But if you think about once you start to get turbulent flow, you start to get eddies and back propagation.

So when that happens, you have fluid moving around freely and mixing. That's actually really effective for transferring heat. So while we will have some heat being transferred by conduction where it's just a molecular motion of a stationary fluid, well, our fluid isn't always stationary.

And you can see it's moving here in the laminar region and it's moving here in the turbulent region. So the combination of those two is really what makes up convection. So we've talked a lot about conduction, and really convection has conduction sort of built into it, but because of this other piece, this advection piece, convection actually gets quite a bit more complicated than conduction, so we're going to have different ways of dealing with that over the next few video lectures.

Transcript for:Understanding Convection in Heat Transfer

Transcript for:
Understanding Convection in Heat Transfer