What is critical insulation thickness for pipes?
We know that by adding more insulation to a wall always decreases heat transfer. The thicker the insulation, the lower the heat transfer rate. This is expected, since the heat transfer area A is constant, and adding insulation always increases the thermal resistance of the wall without affecting the convection resistance.
Adding insulation to a cylindrical piece or a spherical shell, however, is a different ma즈er. The additional insulation increases the conduction resistance of the insulation layer but decreases the convection resistance of the surface because of the increase in the outer surface area for convection. The heat transfer from the pipe may increase or decrease, depending on which effect dominates.
Consider a cylindrical pipe of outer radius r1 whose outer surface temperature T1 is maintained constant. The pipe is now insulated with a material whose thermal conductivity s k and outer radius is r2 .
Heat is lost from the pipe to the surrounding medium at temperature T∞ with a convection heat transfer coefficient h. The rate of heat transfer from the insulated pipe to the surrounding air
can be expressed as The value of r2 at which heat transfer rate reaches maximum is determined from the requirement that (zero slope). Performing the differentiation and solving for r2 yields the critical radius of insulation for a cylindrical body to be rcr,cylinder = k/h
Note that the critical radius of insulation depends on the thermal conductivity of the insulation k and the external convection heat transfer coefficient h.The rate of heat transfer from the cylinder increases with the addition of insulation for r2< rcr, reaches a maximum when r2= rcr, and starts to decrease for r2> rcr. Thus, insulating the pipe may actually increase the rate of heat transfer from the pipe
instead of decreasing it when r2< rcr.
Coutesy:IITB Source
(h즈 //www.cdeep.iitb.ac.in/nptel/Mechanical/Heat%20and%20Mass%20Transfer/Conduction/Module%202/main/2.6.4.html)
We know that by adding more insulation to a wall always decreases heat transfer. The thicker the insulation, the lower the heat transfer rate. This is expected, since the heat transfer area A is constant, and adding insulation always increases the thermal resistance of the wall without affecting the convection resistance.
Adding insulation to a cylindrical piece or a spherical shell, however, is a different ma즈er. The additional insulation increases the conduction resistance of the insulation layer but decreases the convection resistance of the surface because of the increase in the outer surface area for convection. The heat transfer from the pipe may increase or decrease, depending on which effect dominates.
Consider a cylindrical pipe of outer radius r1 whose outer surface temperature T1 is maintained constant. The pipe is now insulated with a material whose thermal conductivity s k and outer radius is r2 .
Heat is lost from the pipe to the surrounding medium at temperature T∞ with a convection heat transfer coefficient h. The rate of heat transfer from the insulated pipe to the surrounding air
can be expressed as The value of r2 at which heat transfer rate reaches maximum is determined from the requirement that (zero slope). Performing the differentiation and solving for r2 yields the critical radius of insulation for a cylindrical body to be rcr,cylinder = k/h
Note that the critical radius of insulation depends on the thermal conductivity of the insulation k and the external convection heat transfer coefficient h.The rate of heat transfer from the cylinder increases with the addition of insulation for r2< rcr, reaches a maximum when r2= rcr, and starts to decrease for r2> rcr. Thus, insulating the pipe may actually increase the rate of heat transfer from the pipe
instead of decreasing it when r2< rcr.
Coutesy:IITB Source
(h즈 //www.cdeep.iitb.ac.in/nptel/Mechanical/Heat%20and%20Mass%20Transfer/Conduction/Module%202/main/2.6.4.html)
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