Heat Transfer

Heat Transfer is the seventh lecture within the Properties of Matter section of PH1011. It covers the differences between conduction, convection and radiation, calculation of rates of conduction and the derivation of an expression for thermal conductivity in gases.

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Conduction
In conduction, thermal energy is passed by the interactions of molecules. As the heated molecules vibrate, their neighbours are forced to vibrate faster too, passing energy along in a solid setting. In gases, this occurs due to collisions; high energy molecules collide with lower energy molecules and transfer energy.

In consideration of a solid bar of length Δy, cross section A and temperature gradient ΔT, the rate of heat flow dQ/dt = -kAΔT/Δy = -kAdT/dy. k is the thermal conductivity of the material.

Convection
Convection occurs via mass transport; for example air currents. As gases are heated they rise, and the energy of the hot molecules rises with them. This causes the convection cells in the Earth's atmosphere and the sun itself.

Radiation
Radiation is evergy emitted and absorbed electromaganetically. By Stefans' Law, all bodies with an associated temperature emit energy:

P = σεAT4

ε is the material's emissivity and σ is the Stefan-Boltzmann constant (5.67x10-8W/m2K4.

Thermal Conductivity in Gas
In gases, heat flow can be modelled as passing across three plates; as hot air rises and cool air falls, there is a constant flow per second upward and downward. The hot air flows can be given as N/VvyA x Cv(T-dT/dyλ). However, vy can be taken as 1/6[v]; as given Brownian motion only 1/6 of molecules present move upward rather than any other direction. This gives (N/V [v]A/6)Cv(T-dT/dyλ). The two downward flows are (N/V[v]A/6)CvT. The combination of all of these to find total air flow though one plate in one direction is dQ/dt = -(N/V[v]/3)Cv(dT/dy)λ. Substituting in dQ/dt = -k A(dT/dy) gives:

k = (N/V [v] /3)Cvλ

Summary
Conduction passes energy via vibration of molecules. Convection passes energy via movement of particles. All objects radiate energy. In gases heat passes upward and downward at a constant rate, and this rate can be used to find the thermal conductivity of the gas.