Governing Equation Dirichlet Boundary Conditions Solution Heat Flux Heat Flow temperature is not a function of k Notes A is the crosssectional area of the wall perpendicular ID: 283928
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Slide1
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
kSlide2
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 uniformSlide3
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 uniformSlide4
Thermal ResistanceSlide5
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 approximationsSlide6
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:Slide7
fig_02_04Slide8
fig_02_05Slide9
Fins: The Fin Equation
SolutionsSlide10
Fins: Fin Performance Parameters
Fin Efficiencythe ratio of
actual amount of heat removed by a fin to the ideal amount
of heat removed if the fin was an isothermal body at the base temperature
that is, the ratio the actual heat transfer from the fin to ideal heat transfer from the fin if the fin had no conduction resistanceFin Effectiveness
ratio of the fin heat transfer rate to the heat transfer rate that would exist without the fin
Fin Resistancedefined using the temperature difference between the base and fluid as the driving potentialSlide11
Fins: EfficiencySlide12
Fins: EfficiencySlide13
Fins: Arrays
Arraystotal surface area
total heat rate
overall surface efficiency
overall surface resistanceSlide14
Fins: Thermal Circuit
Equivalent Thermal Circuit
Effect of Surface Contact ResistanceSlide15
Fins: Overview
Finsextended surfaces that enhance fluid heat transfer to/from a surface in large part by increasing the
effective surface area of the bodycombine
conduction through the fin and
convection to/from the finthe conduction is assumed to be one-dimensional
Applicationsfins are often used to enhance convection when h
is small (a gas as the working fluid)fins can also be used to increase the surface area for radiationradiators (cars), heat sinks (PCs), heat exchangers (power plants), nature (stegosaurus)
Straight fins of
(a)
uniform and
(b)
non-uniform cross sections; (c)
annularfin, and (
d) pin fin of non-uniform cross section.Slide16
Fins: The Fin Equation
Solutions