1-D conduction through cylinders

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# 1-D conduction through cylinders - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about '1-D conduction through cylinders' - noble-osborne

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Presentation Transcript

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
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

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.
• 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
CHOSING INSULATION THICKNESS

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

1D Conduction in Sphere

Inside Solid: