“Before we talk about thermal resistance, let’s talk about a type “Good morning class, today we of resistance we all know of, will be learning about thermal electrical resistance. Voltage (V) resistance” drives charge through a wire, and current (I) is the transfer rate.”

“Ohm’s law states that 푉 = 퐼푅 “From electrical resistance we can which can be rearranged to show 푉 generalize resistance to be the that 푅 = . This demonstrates that 퐼 ratio of the driving force over the electrical resistance is the ratio of transfer rate. This will give us the electric potential over the charge basis for our thermal resistance transfer rate.” equation.”

“Let’s look at a single slab wall of “Thus, our equation for thermal a material with constant resistance is the ratio of properties. According to Fourier’s temperature gradient over the heat 휕푇 Law, 푞′′ = −푘 . Which can transfer rate since a temperature 푐표푛푑 휕푥 difference cause heat to be ′′ 훥푇 be simplified to 푞푐표푛푑 = −푘 . transferred.” 훥푥

“ Now that we have a relationship “And since we know that between resistance and heat rate, ′′ 푞푐표푛푑 = 퐴푞푐표푛푑 . We know that we can combine the equations to 훥푇 show that conductive thermal the heat rate is 푞푐표푛푑 = −푘퐴 .” 훥푥 훥푥 resistance for is 푅푐표푛푑 = . 푘퐴

“Materials with a low thermal “As you can see from the conductivity (k) are known as conductive thermal resistance insulators, and materials with a equation, the resistance depends high thermal conductivity (k) are on the material as materials vary known as conductors. Insulators in thermal conductivity (k).” have high resistance, while conductors have low resistance.”

“Similar to how we derived conductive thermal resistance we “We can then derive the derive convective thermal convective resistance relationship 1 resistance. We know that to be 푅 = .” 푐표푛푣 ℎ퐴 ′′ 푞푐표푛푣 = ℎ(푇푠 − 푇∞) and thus 푞푐표푛푣 = ℎ퐴(푇푠 − 푇∞).”

“In an electric circuit, the “Here we have a system that resistance of resistors in series can consists of two conductive

be combined to a total resistance. materials, and one convective fluid

In heat transfer we can do the between them. We will use the

same thing, to get the overall thermal circuit on the left to

resistance of the system.” represent the system.”

“Let’s assume the system is steady-state, has no generation, has “We can then set up a thin-shell constant properties, and heat is balance and solve to show that our flowing in only one direction. This heat flux is constant!” reduces our energy balance to

퐼푛 − 푂푢푡 = 0. ” “We can then find the total “With our flux constant, we can resistance of our system in terms apply the right constitutive of our constant properties and set equation to each section of our it equal to the ratio of the system and see show how to temperature difference across the determine the heat flux.” system to the heat transfer rate through the system.”

“By rearranging our total “We can then use the same idea to

resistance equation, we can show minimize our system and find the

that the temperature difference temperature difference across only across the entire system is equal to 2 components. This can be even the product of the the heat transfer further simplified to only one

and the total resistance.” component.”

“Anyways, thermal resistance has a major application in the real world. Systems with high resistances are used to keep heat from travelling into or out of the surroundings.”

“Airplanes have double-pane “On the other hand, the walls of windows while walls in homes heat exchangers are made from often have a layer of insulation. In materials with low resistance. This both cases, the boundaries consist is because heat exchangers need to of a component with high thermal promote the exchange of heat. resistance, to keep the heat from Thus, for maximum heat transfer, the inside from escaping.” walls have low resistances.”