1. 1-D conduction through cylinders
Lecture on
1-D conduction through cylinders
22 Feb 2013

2. Topics Covered Composite Cylinders
Log Mean Area for hollow cylinder – plane wall
Critical thickness of insulation
HT through Sphere
22 Feb 2013

3. 1 D Conduction(Radial conduction in a composite cylinder)h1
T∞,1 k1 r1 r2 k2
T∞,2 r3 h2
22 Feb 2013

4. 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
22 Feb 2013

5. Logarithmic Mean area for hollow cylinder
22 Feb 2013

6. 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
22 Feb 2013

7. 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
22 Feb 2013

8. Critical Insulation Thickness
Insulation Thickness : r o-r i
Objective : decrease q , increases
Vary r0 ; as r0 increases ,first term increases, second term decreases.
22 Feb 2013

9. CRITICAL RADIUS OF INSULATION
CYLINDER
Thermal conductivity
External convection heat transfer coefficient
show
22 Feb 2013

10. Critical Insulation Thickness
Set
Condition for minimum resistance and consequently max HT
Radius at which resistance to HT is minimum is called critical radius
22 Feb 2013

11. CHOSING INSULATION THICKNESS
max
Before insulation check for critical radius
22 Feb 2013

12. Critical Insulation Thickness (contd…)
Minimum q at r0 =(k/h)=r c r (critical radius)
good for steam pipes etc.
good for electrical cables
R c r=k/h r0
R t o t
22 Feb 2013

13. 1D Conduction in Sphere r2 r1 k T∞,2 Ts,2 Ts,1 T∞,1 Inside Solid:
22 Feb 2013