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

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

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

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

Logarithmic Mean area for hollow cylinder 22 Feb 2013

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

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

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

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

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

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

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

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