AME 60634 Int. Heat Trans. D. B. Go 1 Heat Transfer Rates heat
flux [W/m 2 ] thermal conductivity [W/m-K] temperature gradient
[K/m] heat flux [W/m 2 ] heat transfer coefficient [W/m 2 -K]
surface temperature [K] fluid temperature [K] emissive power [W/m 2
] surface emissivity [ ] Stefan-Boltzmann constant [5.6710 -8 W/m 2
-K 4 ] surface temperature [K] Conduction: Fouriers Law Convection:
Newtons Law of Cooling Radiation: Stefan-Boltzmann Law
(modified)
Slide 2
AME 60634 Int. Heat Trans. D. B. Go 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:
Slide 3
AME 60634 Int. Heat Trans. D. B. Go 3 1-D Steady Conduction:
Plane Wall Governing Equation: Dirichlet Boundary Conditions:
Solution: Heat Flux: Heat Flow: temperature is not a function of k
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 ) heat flux/flow are a function of k
Slide 4
AME 60634 Int. Heat Trans. D. B. Go 4 1-D Steady Conduction:
Cylinder Wall Governing Equation: Dirichlet Boundary Conditions:
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 ) Solution: Heat Flux: Heat Flow: heat flow per unit
length heat flux is non-uniform heat flow is uniform
Slide 5
AME 60634 Int. Heat Trans. D. B. Go 5 1-D Steady Conduction:
Spherical Shell Governing Equation: Dirichlet Boundary Conditions:
Solution: Heat Flux: Heat Flow: Notes: heat flux is not uniform
function of position ( r ) heat flow is uniform independent of
position ( r ) heat flux is non-uniform heat flow is uniform
Slide 6
AME 60634 Int. Heat Trans. D. B. Go 6 Thermal Resistance
Slide 7
AME 60634 Int. Heat Trans. D. B. Go 7 Thermal Circuits:
Composite Plane Wall Circuits based on assumption of (a)isothermal
surfaces normal to x direction or (b)adiabatic surfaces parallel to
x direction Actual solution for the heat rate q is bracketed by
these two approximations
Slide 8
AME 60634 Int. Heat Trans. D. B. Go 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: