Critical Radius of Insulation of Hollow Sphere Solution

STEP 0: Pre-Calculation Summary
Formula Used
Critical Radius of Insulation = 2*Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient
Rc = 2*Kinsulation/houtside
This formula uses 3 Variables
Variables Used
Critical Radius of Insulation - (Measured in Meter) - Critical Radius of Insulation is the radius of insulation at which there is maximum heat transfer and increase or decrease in its value will lead to an overall decrease in heat transfer.
Thermal Conductivity of Insulation - (Measured in Watt per Meter per K) - Thermal Conductivity of Insulation is defined as the ability of insulating material to transmit heat.
External Convection Heat Transfer Coefficient - (Measured in Watt per Square Meter per Kelvin) - External Convection Heat Transfer Coefficient is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat in case of convective heat transfer.
STEP 1: Convert Input(s) to Base Unit
Thermal Conductivity of Insulation: 21 Watt per Meter per K --> 21 Watt per Meter per K No Conversion Required
External Convection Heat Transfer Coefficient: 9.8 Watt per Square Meter per Kelvin --> 9.8 Watt per Square Meter per Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Rc = 2*Kinsulation/houtside --> 2*21/9.8
Evaluating ... ...
Rc = 4.28571428571429
STEP 3: Convert Result to Output's Unit
4.28571428571429 Meter --> No Conversion Required
FINAL ANSWER
4.28571428571429 4.285714 Meter <-- Critical Radius of Insulation
(Calculation completed in 00.004 seconds)

Credits

Created by Ishan Gupta
Birla Institute of Technology & Science (BITS), Pilani
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3 Critical Thickness of Insulation Calculators

Critical Radius of Insulation of Hollow Sphere
Go Critical Radius of Insulation = 2*Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient
Critical Radius of Insulation of Cylinder
Go Critical Radius of Insulation = Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient
Volumetric Heat Generation in Current Carrying Electrical Conductor
Go Volumetric Heat Generation = (Electric Current Density^2)*Resistivity

20 Heat Transfer from Extended Surfaces (Fins), Critical Thickness of Insulation and Thermal Resistance Calculators

Heat Dissipation from Fin Losing Heat at End Tip
Go Fin Heat Transfer Rate = (sqrt(Perimeter of Fin*Heat Transfer Coefficient*Thermal Conductivity of Fin*Cross Sectional Area))*(Surface Temperature-Surrounding Temperature)*((tanh((sqrt((Perimeter of Fin*Heat Transfer Coefficient)/(Thermal Conductivity of Fin*Cross Sectional Area)))*Length of Fin)+(Heat Transfer Coefficient)/(Thermal Conductivity of Fin*(sqrt(Perimeter of Fin*Heat Transfer Coefficient/Thermal Conductivity of Fin*Cross Sectional Area)))))/(1+tanh((sqrt((Perimeter of Fin*Heat Transfer Coefficient)/(Thermal Conductivity of Fin*Cross Sectional Area)))*Length of Fin*(Heat Transfer Coefficient)/(Thermal Conductivity of Fin*(sqrt((Perimeter of Fin*Heat Transfer Coefficient)/(Thermal Conductivity of Fin*Cross Sectional Area))))))
Heat Dissipation from Fin Insulated at End Tip
Go Fin Heat Transfer Rate = (sqrt((Perimeter of Fin*Heat Transfer Coefficient*Thermal Conductivity of Fin*Cross Sectional Area)))*(Surface Temperature-Surrounding Temperature)*tanh((sqrt((Perimeter of Fin*Heat Transfer Coefficient)/(Thermal Conductivity of Fin*Cross Sectional Area)))*Length of Fin)
Heat Dissipation from Infinitely Long Fin
Go Fin Heat Transfer Rate = ((Perimeter of Fin*Heat Transfer Coefficient*Thermal Conductivity of Fin*Cross Sectional Area)^0.5)*(Surface Temperature-Surrounding Temperature)
Thermal Resistance for Conduction at Tube Wall
Go Thermal Resistance = (ln(Outer Radius of Cylinder/Inner Radius of Cylinder))/(2*pi*Thermal Conductivity*Length of Cylinder)
Heat Transfer in Fins given Fin Efficiency
Go Fin Heat Transfer Rate = Overall Heat Transfer Coefficient*Area*Fin Efficiency*Overall Difference in Temperature
Newton's Law of Cooling
Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)
Biot Number using Characteristic Length
Go Biot Number = (Heat Transfer Coefficient*Characteristic Length)/(Thermal Conductivity of Fin)
Critical Radius of Insulation of Hollow Sphere
Go Critical Radius of Insulation = 2*Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient
Critical Radius of Insulation of Cylinder
Go Critical Radius of Insulation = Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient
Correction Length for Cylindrical Fin with Non-Adiabatic Tip
Go Correction Length for Cylindrical Fin = Length of Fin+(Diameter of Cylindrical Fin/4)
Outside Heat Transfer Coefficient given Thermal Resistance
Go External Convection Heat Transfer Coefficient = 1/(Thermal Resistance*Outside Area)
Thermal Resistance for Convection at Outer Surface
Go Thermal Resistance = 1/(External Convection Heat Transfer Coefficient*Outside Area)
Outside Area given Outer Thermal Resistance
Go Outside Area = 1/(External Convection Heat Transfer Coefficient*Thermal Resistance)
Inner Heat Transfer Coefficient given Inner Thermal Resistance
Go Inside Convection Heat Transfer Coefficient = 1/(Inside Area*Thermal Resistance)
Inside Area given Thermal Resistance for Inner Surface
Go Inside Area = 1/(Inside Convection Heat Transfer Coefficient*Thermal Resistance)
Thermal Resistance for Convection at Inner Surface
Go Thermal Resistance = 1/(Inside Area*Inside Convection Heat Transfer Coefficient)
Correction Length for Thin Rectangular Fin with Non-Adiabatic Tip
Go Correction Length for Thin Rectangular Fin = Length of Fin+(Thickness of Fin/2)
Volumetric Heat Generation in Current Carrying Electrical Conductor
Go Volumetric Heat Generation = (Electric Current Density^2)*Resistivity
Total Thermal Resistance
Go Total Thermal Resistance = 1/(Overall Heat Transfer Coefficient*Area)
Correction Length for Square Fin with Non-Adiabatic Tip
Go Correction Length for Sqaure Fin = Length of Fin+(Width of Fin/4)

Critical Radius of Insulation of Hollow Sphere Formula

Critical Radius of Insulation = 2*Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient
Rc = 2*Kinsulation/houtside

Critical Radius of Insulation of a Sphere

Critical Radius of Insulation of a Sphere is the radius of insulation at which there is maximum heat transfer and increase or decrease in its value will lead to an overall decrease in heat transfer.

How to Calculate Critical Radius of Insulation of Hollow Sphere?

Critical Radius of Insulation of Hollow Sphere calculator uses Critical Radius of Insulation = 2*Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient to calculate the Critical Radius of Insulation, Critical Radius of Insulation of Hollow Sphere is the radius of insulation at which there is maximum heat transfer and an increase or decrease in its value will lead to an overall decrease in heat transfer. Critical Radius of Insulation is denoted by Rc symbol.

How to calculate Critical Radius of Insulation of Hollow Sphere using this online calculator? To use this online calculator for Critical Radius of Insulation of Hollow Sphere, enter Thermal Conductivity of Insulation (Kinsulation) & External Convection Heat Transfer Coefficient (houtside) and hit the calculate button. Here is how the Critical Radius of Insulation of Hollow Sphere calculation can be explained with given input values -> 4.285714 = 2*21/9.8.

FAQ

What is Critical Radius of Insulation of Hollow Sphere?
Critical Radius of Insulation of Hollow Sphere is the radius of insulation at which there is maximum heat transfer and an increase or decrease in its value will lead to an overall decrease in heat transfer and is represented as Rc = 2*Kinsulation/houtside or Critical Radius of Insulation = 2*Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient. Thermal Conductivity of Insulation is defined as the ability of insulating material to transmit heat & External Convection Heat Transfer Coefficient is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat in case of convective heat transfer.
How to calculate Critical Radius of Insulation of Hollow Sphere?
Critical Radius of Insulation of Hollow Sphere is the radius of insulation at which there is maximum heat transfer and an increase or decrease in its value will lead to an overall decrease in heat transfer is calculated using Critical Radius of Insulation = 2*Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient. To calculate Critical Radius of Insulation of Hollow Sphere, you need Thermal Conductivity of Insulation (Kinsulation) & External Convection Heat Transfer Coefficient (houtside). With our tool, you need to enter the respective value for Thermal Conductivity of Insulation & External Convection Heat Transfer Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Critical Radius of Insulation?
In this formula, Critical Radius of Insulation uses Thermal Conductivity of Insulation & External Convection Heat Transfer Coefficient. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Critical Radius of Insulation = Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient
  • Critical Radius of Insulation = Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient
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