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1-D conduction through cylinders

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Lecture on

1-D conduction through cylinders

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

h1

r1

T∞,1

r2

h2

T∞,2

k1

r3

k2

T∞,1

T∞,2

- 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

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

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

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.

CYLINDER

Thermal conductivity

External convection heat transfer coefficient

show

Set

Critical Insulation Thickness

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

max

Before insulation check for critical radius

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)

r2

r1

k

T∞,2

Ts,2

Ts,1

T∞,1

Inside Solid: