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]

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:

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)

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)

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)

Thermal Resistance

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

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: