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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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1-D conduction through cylinders

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1 d conduction through cylinders

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


1 d conduction radial conduction in a composite cylinder

h1

r1

T∞,1

r2

h2

T∞,2

k1

r3

k2

T∞,1

T∞,2

1 D Conduction(Radial conduction in a composite cylinder)


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


Logarithmic mean area for hollow cylinder1

Logarithmic Mean area for hollow cylinder


1 d conduction through cylinders

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


1 d conduction through cylinders

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


1 d conduction through cylinders

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


1 d conduction through cylinders

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


1 d conduction through cylinders

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:


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