Thickness of Cylindrical Wall to Maintain given Temperature Difference Solution

STEP 0: Pre-Calculation Summary
Formula Used
Thickness = Radius 1*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1)
t = r1*(e^(((Ti-To)*2*pi*k*lcyl)/Q)-1)
This formula uses 2 Constants, 7 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Variables Used
Thickness - (Measured in Meter) - Thickness is the distance through an object.
Radius 1 - (Measured in Meter) - Radius 1 is the distance from the center of the concentric circles to any point on the first/smallest concentric circle or the radius of the first circle.
Inner Surface Temperature - (Measured in Kelvin) - Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.
Outer Surface Temperature - (Measured in Kelvin) - Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Length of Cylinder - (Measured in Meter) - Length of Cylinder is the vertical height of the Cylinder.
Heat Flow Rate - (Measured in Watt) - Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium.
STEP 1: Convert Input(s) to Base Unit
Radius 1: 0.8 Meter --> 0.8 Meter No Conversion Required
Inner Surface Temperature: 305 Kelvin --> 305 Kelvin No Conversion Required
Outer Surface Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Length of Cylinder: 0.4 Meter --> 0.4 Meter No Conversion Required
Heat Flow Rate: 125 Watt --> 125 Watt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
t = r1*(e^(((Ti-To)*2*pi*k*lcyl)/Q)-1) --> 0.8*(e^(((305-300)*2*pi*10.18*0.4)/125)-1)
Evaluating ... ...
t = 1.42612336536852
STEP 3: Convert Result to Output's Unit
1.42612336536852 Meter --> No Conversion Required
FINAL ANSWER
1.42612336536852 โ‰ˆ 1.426123 Meter <-- Thickness
(Calculation completed in 00.004 seconds)

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14 Conduction in Cylinder Calculators

Heat Flow Rate through Cylindrical Composite Wall of 3 Layers
Go Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius 4/Radius 3))/(2*pi*Thermal Conductivity 3*Length of Cylinder))
Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series
Go Thermal Resistance = (ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius 4/Radius 3))/(2*pi*Thermal Conductivity 3*Length of Cylinder)
Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides
Go Thermal Resistance = 1/(2*pi*Radius 1*Length of Cylinder*Inside Convection Heat Transfer Coefficient)+(ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder)+1/(2*pi*Radius 2*Length of Cylinder*External Convection Heat Transfer Coefficient)
Heat Flow Rate through Cylindrical Composite Wall of 2 Layers
Go Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder))
Outer Surface Temperature of Cylindrical Composite Wall of 2 Layers
Go Outer Surface Temperature = Inner Surface Temperature-Heat Flow Rate*((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder))
Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series
Go Thermal Resistance = (ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)
Heat Flow Rate through Cylindrical Wall
Go Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder))
Thermal Conductivity of Cylindrical Wall given Temperature Difference
Go Thermal Conductivity = (Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Length of Cylinder*(Inner Surface Temperature-Outer Surface Temperature))
Length of Cylindrical Wall for given Heat Flow Rate
Go Length of Cylinder = (Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*(Inner Surface Temperature-Outer Surface Temperature))
Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate
Go Outer Surface Temperature = Inner Surface Temperature-(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder)
Inner Surface Temperature of Cylindrical Wall in Conduction
Go Inner Surface Temperature = Outer Surface Temperature+(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder)
Thickness of Cylindrical Wall to Maintain given Temperature Difference
Go Thickness = Radius 1*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1)
Thermal Resistance for Radial Heat Conduction in Cylinders
Go Thermal Resistance = ln(Outer Radius/Inner Radius)/(2*pi*Thermal Conductivity*Length of Cylinder)
Convection Resistance for Cylindrical Layer
Go Thermal Resistance = 1/(Convection heat transfer*2*pi*Cylinder Radius*Length of Cylinder)

Thickness of Cylindrical Wall to Maintain given Temperature Difference Formula

Thickness = Radius 1*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1)
t = r1*(e^(((Ti-To)*2*pi*k*lcyl)/Q)-1)

What is steady state conduction?

Steady-state conduction is the form of conduction that happens when the temperature difference(s) driving the conduction are constant, so that (after an equilibration time), the spatial distribution of temperatures (temperature field) in the conducting object does not change any further.

How to Calculate Thickness of Cylindrical Wall to Maintain given Temperature Difference?

Thickness of Cylindrical Wall to Maintain given Temperature Difference calculator uses Thickness = Radius 1*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1) to calculate the Thickness, The Thickness of cylindrical wall to maintain given temperature difference formula is defined as the thickness of the cylindrical wall required to maintain a given temperature difference across the cylindrical wall when heat flow rate, inner radius, and thermal conductivity are known. Thickness is denoted by t symbol.

How to calculate Thickness of Cylindrical Wall to Maintain given Temperature Difference using this online calculator? To use this online calculator for Thickness of Cylindrical Wall to Maintain given Temperature Difference, enter Radius 1 (r1), Inner Surface Temperature (Ti), Outer Surface Temperature (To), Thermal Conductivity (k), Length of Cylinder (lcyl) & Heat Flow Rate (Q) and hit the calculate button. Here is how the Thickness of Cylindrical Wall to Maintain given Temperature Difference calculation can be explained with given input values -> 1.426123 = 0.8*(e^(((305-300)*2*pi*10.18*0.4)/125)-1).

FAQ

What is Thickness of Cylindrical Wall to Maintain given Temperature Difference?
The Thickness of cylindrical wall to maintain given temperature difference formula is defined as the thickness of the cylindrical wall required to maintain a given temperature difference across the cylindrical wall when heat flow rate, inner radius, and thermal conductivity are known and is represented as t = r1*(e^(((Ti-To)*2*pi*k*lcyl)/Q)-1) or Thickness = Radius 1*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1). Radius 1 is the distance from the center of the concentric circles to any point on the first/smallest concentric circle or the radius of the first circle, Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc, Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc), Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance, Length of Cylinder is the vertical height of the Cylinder & Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium.
How to calculate Thickness of Cylindrical Wall to Maintain given Temperature Difference?
The Thickness of cylindrical wall to maintain given temperature difference formula is defined as the thickness of the cylindrical wall required to maintain a given temperature difference across the cylindrical wall when heat flow rate, inner radius, and thermal conductivity are known is calculated using Thickness = Radius 1*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1). To calculate Thickness of Cylindrical Wall to Maintain given Temperature Difference, you need Radius 1 (r1), Inner Surface Temperature (Ti), Outer Surface Temperature (To), Thermal Conductivity (k), Length of Cylinder (lcyl) & Heat Flow Rate (Q). With our tool, you need to enter the respective value for Radius 1, Inner Surface Temperature, Outer Surface Temperature, Thermal Conductivity, Length of Cylinder & Heat Flow Rate and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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