1-D conduction through cylinders

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Lecture on
1-D conduction through cylinders
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Topics Covered

• Composite Cylinders
• Log Mean Area for hollow cylinder plane wall
• Critical thickness of insulation
• HT through Sphere

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1 D Conduction(Radial conduction in a composite
cylinder)
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Logarithmic Mean area for hollow cylinder

• Convenient to have an expression for heat flow
  through hollow cylinder of the same form as that
  of for a plane wall.
• Then cylinder thickness will be equal to wall
  thickness,
• Area will be equal to Am

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Logarithmic Mean area for hollow cylinder
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Critical Insulation Thickness

• Insulation A material which retard flow of heat
  either from surrounding to system or vice versa,
  with reasonable effectiveness is called
  insulation.
• Applications
• Boilers, steam pipe
• Insulating brick
• Preservation of food and commodities
• Refrigeration Air conditioning
• Condensers
• Common Belief addition of insulation material on
  surface always leads to lower Heat loss
• there are instances when addition of insulation
  material does not reduce Heat loss

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Critical Insulation Thickness

• For cylindrical pipes, HT increasing first, then
  decreasing.
• addition increases conduction resistance,
• but decreases convection resistance due to
  surface area exposed to environment.
• Total thermal resistance decrease resulting in
  increase in heat loss.
• From outer surface of insulation heat is
  dissipated to environment by convection.
• As the thickness goes on increasing, area of
  outer surface increases, which is responsible for
  more heat loss thru convection

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Critical Insulation Thickness
Insulation Thickness r o-r i
Objective decrease q ,
increases
Vary r0 as r0 increases ,first term
increases, second term decreases.
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CRITICAL RADIUS OF INSULATION
CYLINDER
Thermal conductivity External convection heat
transfer coefficient
show
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Critical Insulation Thickness

• Condition for minimum resistance and consequently
  max HT
• Radius at which resistance to HT is minimum is
  called critical radius

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CHOSING INSULATION THICKNESS
max
Before insulation check for critical radius
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Critical Insulation Thickness (contd)
Minimum q at r0 (k/h)r c r (critical radius)
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1D Conduction in Sphere
Inside Solid