1. Heat Transfer Rates Conduction: Fourier’s Law
heat flux
[W/m2]
thermal conductivity
[W/m-K]
temperature gradient
[K/m]
Convection: Newton’s Law of Cooling
fluid temperature
[K]
heat flux
[W/m2]
heat transfer coefficient
[W/m2-K]
surface temperature
[K]
Radiation: Stefan-Boltzmann Law (modified)
surface temperature
[K]
emissive power
[W/m2]
surface emissivity
[ ]
Stefan-Boltzmann constant
[5.67×10-8 W/m2-K4]

2. Transient Conduction: Lumped Capacitance
General Transient Problem: Special Case  negligible radiation, heat flux & heat generation
Define: thermal time constant
We can plot the normalized solution to the general problem
Notes:
The change in thermal energy storage due to the transient process is:

3. 1-D Steady Conduction: Plane Wall
Governing Equation:
Dirichlet Boundary Conditions:
Solution:
temperature is not a function of k
Heat Flux:
heat flux/flow are a function of k
Heat Flow:
Notes:
A is the cross-sectional area of the wall perpendicular to the heat flow
both heat flux and heat flow are uniform  independent of position (x)
temperature distribution is governed by boundary conditions and length of domain  independent of thermal conductivity (k)

4. 1-D Steady Conduction: Cylinder Wall
Governing Equation:
Dirichlet Boundary Conditions:
Solution:
Heat Flux:
Heat Flow:
heat flow per unit length
heat flux is non-uniform
heat flow is uniform
Notes:
heat flux is not uniform  function of position (r)
both heat flow and heat flow per unit length are uniform  independent of position (r)

5. 1-D Steady Conduction: Spherical Shell
Governing Equation:
Dirichlet Boundary Conditions:
Solution:
Heat Flux:
Heat Flow:
heat flux is non-uniform
heat flow is uniform
Notes:
heat flux is not uniform  function of position (r)
heat flow is uniform  independent of position (r)

6. Thermal Resistance

7. Thermal Circuits: Composite Plane Wall
Circuits based on assumption of
isothermal surfaces normal to x direction or
adiabatic surfaces parallel to x direction
Actual solution for the heat rate q is bracketed by these two approximations

8. Thermal Circuits: Contact Resistance
In the real world, two surfaces in contact do not transfer heat perfectly
Contact Resistance: values depend on materials (A and B), surface roughness, interstitial conditions, and contact pressure  typically calculated or looked up
Equivalent total thermal resistance: