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1-D conduction through cylinders

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1-D conduction through cylinders - PowerPoint PPT Presentation


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Lecture on. 1-D conduction through cylinders. Topics Covered. Composite Cylinders Log Mean Area for hollow cylinder – plane wall Critical thickness of insulation HT through Sphere. h 1. r 1. T ∞,1. r 2. h 2. T ∞,2. k 1. r 3. k 2. T ∞,1. T ∞,2.

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Presentation Transcript
slide1

Lecture on

1-D conduction through cylinders

topics covered
Topics Covered
  • Composite Cylinders
  • Log Mean Area for hollow cylinder – plane wall
  • Critical thickness of insulation
  • HT through Sphere
logarithmic mean area for hollow cylinder
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
slide6

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
slide7

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
slide8

T∞

r0

ri

h

Ti

Critical Insulation Thickness

Insulation Thickness : r o-r i

Objective :decrease q , increases

Vary r0 ; as r0 increases ,first term increases, second term decreases.

critical radius of insulation
CRITICAL RADIUS OF INSULATION

CYLINDER

Thermal conductivity

External convection heat transfer coefficient

show

slide10

Set

Critical Insulation Thickness

  • Condition for minimum resistance and consequently max HT
  • Radius at which resistance to HT is minimum is called critical radius
chosing insulation thickness
CHOSING INSULATION THICKNESS

max

Before insulation check for critical radius

slide12

R t o t

good for electrical cables

good for steam pipes etc.

R c r=k/h

r0

Critical Insulation Thickness (contd…)

Minimum q at r0 =(k/h)=r c r (critical radius)

1d conduction in sphere

r2

r1

k

T∞,2

Ts,2

Ts,1

T∞,1

1D Conduction in Sphere

Inside Solid: