Stationaire warmteoverdracht door conductie I125practicum

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Stationaire warmteoverdrachtdoor
conductieI125-practicum

• Jeroen De Temmerman, Josse de Baerdemaeker
• Acad. Jaar 2003-2004
• Eerste ingenieursjaar Bio-ingenieur

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Chapter 4 - Steady State Heat Conduction
Page 46 Datta, 2002
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Steady State Heat Conduction in a slab

• A heat transfer process is at steady state if the
  temperature does not change with time (no
  storage)
• For no storage and no generation, the governing
  equation becomes
• The simplest boundary conditions are when the two
  surface temperatures are known

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Steady State Heat Conduction in a slab

• The solution shows a linear change in temperature
  at steady state

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Steady-state diffusion in a composite media

• A composite slab can be treated as series or
  parallel combinations of the thermal resistances
  of the individual slabs

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Thermal Resistances and R-Values

• Analagous to electricity if in series, Heat
  Flux Temperature Difference ?Thermal
  Resistances
• Ex Thermal Conduction Resistance R L/kA

The R-Value is the resistance per unit area.
R-Values combine the effect of thickness and
conductivity and therefore are very useful Ex
R-Value L/k for plates Ceilings R-30
(C/(W m²) Walls R-11 (C/(W m²)
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Pas op

• R-waarde (of R-value) is per eenheid oppervlakte
  (ook dikwijls in bouwliteratuur)
• R (thermische weerstand) is voor de totale
  oppervlakte)
• Rtot som van de R's

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Belgische bouw-literatuur

• Courante symbolen en definities
• Het symbool R gebruiken we normaal als thermische
  weerstand over de totale oppervlakte A
• Anders spreken we over R-waarde.

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Een typische muur
Spouw(holte)
Binnenmuur
Pleister
Isolatie
Gevelsteen
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Doorsnede muur
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Stroming in verticale holte
H warm C koud
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Weerstand bij convektie

• Warmte overdracht door convektie
  (hoofdstuk 6)
• Gebruik convektie-coëfficiënt h
• A is de uitwisseloppervlakte ( cylinder-, plaat-,
  bol-oppervlakte enz.)

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Problem 4.8.1

• Datta, 2002 pagina 64
• Weerstanden in series
• convektie weerstand R1/hA
• conductie weerstand RL/kA

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Steady State Heat Conduction in a Cylinder
For Steady State with no heat generation,
G.E.
B.C.s
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Steady State Heat Conduction in a Cylinder
Substituting
When is small, a Taylor series
expansion shows that,
And therefore in this case the thermal resistance
becomes the same as a slab
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Why is the temperature not linear for steady
state in a cylinder?
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Warmteverlies in een arm
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Steady State Heat Conduction with Generation

• The G.E. simplifies to
• The B.C.s are given as
• The G.E. is integrated twice and the B.C.s are
  applied in order to get the temperature profile
  in a slab with heat generation

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Steady State Heat Conduction with Generation

• Steady state temperature profile in a slab with
  constant internal heat generation.

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Heating of a compost pile
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Heat generation and insulation
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Schematic
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Thermoregulation

• Thermoregulation maintains the core body
  temperature of humans and animals
• It is an active process
• The thermo-regulatory process can be behavioral
  or autonomic
• There are limits to thermoregulation

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Fins Steady State heat transfer from extended
surfaces
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Equations for fins (equivalent to Datta, 2002
373 App. G5)Steady State heat transfer from
extended surfaces
Dividing by kA?x and taking limits as ?x ?0, the
Governing Equation becomes,
Boundary conditions,
Therefore, the new GE becomes
With new boundary conditions
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Fins solutions Steady State heat transfer from
extended surfaces (very long finDatta, 2002
pag 58)
The solution to this GE is given by
Where
Solving with the boundary conditions,an
exponential drop in temperature is seen
Therefore Heat Loss with a fin Heat
Loss without a fin
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Vinnen pseudo-1 D
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Koel vin met eindige lengte L

• Vin-weerstand (geleiding convektie)
• LC is de gecorrigeerde lengte LCL AC/P
• N is het aantal vinnen op de plaat
• Tussen de vinnen RB en vinnen Rf in parallel

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Koelvinnen
roestvrij staal ( "stainless steel" )
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Example Fins - Pinna of Elephant

• Heat transfer from an elephant pinna. Here the
  pinna acts like a fin for heat transfer
  purposes. Shown is the right pinna at two
  different ambient temperatures of 18C
  (left) and 32.1C (right). The change in pattern
  indicates that a change in blood flow
  occurs at higher temperatures.
  (Phillips and Heath, 1992)
• A 4000 kg elephant need to release 4.65 kW.