3.3

## University of Liverpool

Skip to 0 minutes and 3 secondsHere's the first law of thermodynamics expressed for a thermodynamic system. I hope you're already familiar with the equations for kinetic energy and potential energy. Last week, we talked about internal energy and work. This week, I'm going to focus on mass flow and heat transfer. We'll come to mass flow later. So let's look at heat transfer first. I'd like to use this radiator to talk about the different types of heat transfer that can occur. So the first type is conduction. And in my example, that's occurring through the wall of the radiator from the inside to the outside. The second type is forced convection.

Skip to 0 minutes and 49 secondsHot water from the boiler downstairs is being forced by a pump up into the radiator, causing heat transfer from the boiler to the radiator.

Skip to 1 minute and 1 secondThe third type of heat transfer that's occurring is natural convection. And that's heat transfer carried by the rising currents of warm air that is a consequence of the buoyancy of the warm air next to the radiator rising up towards the ceiling and pulling in cold air underneath. So that's a natural convection current. And the fourth type is radiation. That's electromagnetic waves, infrared light if you'd like, travelling straight out of the radiator at the speed of light. And so if you hold your hand away from the radiator, you can actually feel the heat radiating off the hot radiator. So I'd like now to talk in a little bit more detail about each of those four types of heat transfer.

Skip to 1 minute and 42 secondsSo let's start with the conduction that's occurring through the wall gradient from the inside to the outside. And conduction occurs at a molecular level. The internal energy of the material is equal to the kinetic energy of the atoms in the molecules. And conduction is the flow of kinetic energy from one molecule to the next by direct contact. So the kinetic energy of the water inside the radiator is transferred through the metal of the radiator out to the outside surface.

Skip to 2 minutes and 14 secondsIt's described by Fourier's law, which assumes that the heat transfer is occurring at a steady state, and the rate of heat transfer per unit area is equal to the thermal conductivity - and we normally give that the symbol, k - multiplied by the temperature gradient through the wall.

Skip to 2 minutes and 34 secondsSo now let's talk about the next type of heat transfer I refered to, which is convection. And this is heat transfer as a result of fluid flow carrying energy along. And it can be described by Newton's law of cooling, where the rate of heat transfer per unit area is equal to the heat transfer coefficient - and we normally give that the symbol, h, multiplied by the temperature difference between the surface and the fluid flow next to it. The heat transfer coefficient h is dependent on the fluid velocity, as well as on the physical properties of the flow. And so it's different to the thermal conductivity, k that we talked about a moment ago.

Skip to 3 minutes and 15 secondsWe have two types of convection that can occur natural convection - so that's the flow as a consequence of the hot air rising with buoyancy above the radiator, and the cold air coming in underneath. And the velocities are low in those cases. And that leads to a low heat transfer coefficient. And so every-day applications besides space heating is the heat dissipation from the back of a fridge and the cooling of most electronic components.

Skip to 3 minutes and 45 secondsIn forced convection - so in the case of the radiator - that's the type where the pump downstairs is pushing the hot water from the boiler up into the radiator - we have to do some work to produce the flow. And the heat transfer occurs as a consequence of the movement of turbulent eddies in the flow. And so the main barrier to heat transfer is the boundary layer. That's a thin layer of slow or stationary fluid next to the wall of the pipe or the duct. The heat transfer across the boundary layer is just by conduction. And so the boundary layer thickness is the dominant factor in controlling forced convection. And then the final type of heat transfer is radiation.

Skip to 4 minutes and 25 secondsAnd that's the energy emitted by matters as electromagnetic waves or photons coming off the hot surface. And that happens due to changes in the electronic configuration of the atoms and the molecules. They behave like light. It's a form of electromagnetic radiation. And it's the most effective form of heat transfer in a vacuum. The maximum rate at which radiation can occur is related to the absolute temperature of the surface. And it's equal to that temperature to the power 4 multiplied by Stefan-Boltzmann's constant. We normally give it the symbol sigma. The Stefan-Boltzmann's constant is quite small. It's 5.67 times 10 to the minus 8 watts per square metre Kelvin to the 4.

Skip to 5 minutes and 10 secondsA body that emits at this level is known as a black body. But most real surfaces, emit at a much lower rate. And so then the heat transfer rate per unit area is the emissivity, given the little symbol, e, times the Stefan-Boltzmann constant times the temperature to the power of 4. And the deviation from our black body is given by the value of emissivity which ranges from about 0 - so for this radiator, a nice white, shiny radiator, it's 0.05 up to a rough black surface where we might have an emissivity of about 0.97.

# Heat transfer

Eann uses a radiator in his bathroom to explain different types of heat transfer including free and forced convection, conduction and radiation. He introduces the expressions that describe the rates of heat transfer in these processes.

The downloads at the bottom of the page are the overview of the first law of thermodynamics that Eann uses at the start of the video and a summary of the heat transfer laws that Eann describes in the video.