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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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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

1 D Conduction(Radial conduction in a composite 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

• 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

• 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

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

1D Conduction in Sphere

Inside Solid: