Heat transfer via conduction:


Conduction is the movement of energy across a temperature gradient through interactions between higher and lower energy particles. Depending on the phase of the substance, the particle will primarily transfer energy through one of two methods. Gases and liquids will transfer energy through their random interactions, while solids will transfer energy through vibrations of molecules in a lattice and the transfer of free electrons.

Conduction in fluids
Image 1: Method of heat transfer through through a fluid. Higher energy
particles transfer energy though collisions with lower energy electrons.
Image accessed from: https://courses.lumenlearning.com/boundless-physics/chapter/methods-of-heat-transfer/


The rate of conduction through a substance is controlled by:
Q•=kAΔTΔx\overset{•}{Q}=kA\frac{ΔT}{Δx}where Q•\overset{•}{Q} is the rate of heat transfer (SI units in watts), k is the conductivity of the substance, A is the cross-sectional area of the substance normal to the direction of heat transfer, ΔT is the temperature difference across the substance, and Δx is the thickness of the substance. In in differential form, the equation becomes Fourier's law of heat conduction:

Q•=−kAdTdx\overset{•}{Q}=-kA\frac{dT}{dx}

Conduction across a substance
Image 2: visualization of the variables that control the rate of conduction through a substance.
Image accessed from: Çengel, Y. A., Boles, M. A., & Kanoğlu, M. (2020).
Thermodynamics an engineering approach [9th edition]. Singapore: McGraw-Hill.


k is dependent on the material that heat transfer is passing through. Some common k values are:

Thermal conductivites; k values

Image 3: thermal conductivity of materials.
Image accessed from: Çengel, Y. A., Boles, M. A., & Kanoğlu, M. (2020).
Thermodynamics an engineering approach [9th edition]. Singapore: McGraw-Hill.


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