Thickness of Cylindrical Wall to Maintain given Temperature Difference Calculator

✖Radius of 1st Cylinder is the distance from the center of the concentric circles to any point on the first/smallest concentric circle for the first cylinder in the series.ⓘ Radius of 1st Cylinder [r₁]			+10% -10%
✖Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.ⓘ Inner Surface Temperature [T_i]			+10% -10%
✖Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).ⓘ Outer Surface Temperature [T_o]			+10% -10%
✖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.ⓘ Thermal Conductivity [k]			+10% -10%
✖Length of Cylinder is the vertical height of the Cylinder.ⓘ Length of Cylinder [l_cyl]			+10% -10%
✖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.ⓘ Heat Flow Rate [Q]			+10% -10%

✖Thickness is the distance through an object.ⓘ Thickness of Cylindrical Wall to Maintain given Temperature Difference [t]

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Formula

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Thickness of Cylindrical Wall to Maintain given Temperature Difference

Formula

t = r 1 \cdot (e^{\frac{(T i - T o) \cdot 2 \cdot π \cdot k \cdot l cyl}{Q}} - 1)

Example

787657 m = 0.8 m \cdot (e^{\frac{(305 K - 300 K) \cdot 2 \cdot π \cdot 10.18 W/(m*K) \cdot 0.4 m}{9.27 W}} - 1)

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Thickness of Cylindrical Wall to Maintain given Temperature Difference Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thickness = Radius of 1st Cylinder*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1)
t = r₁*(e^(((T_i-T_o)*2*pi*k*l_cyl)/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 of 1st Cylinder - (Measured in Meter) - Radius of 1st Cylinder is the distance from the center of the concentric circles to any point on the first/smallest concentric circle for the first cylinder in the series.
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 of 1st Cylinder: 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: 9.27 Watt --> 9.27 Watt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t = r₁*(e^(((T_i-T_o)*2*pi*k*l_cyl)/Q)-1) --> 0.8*(e^(((305-300)*2*pi*10.18*0.4)/9.27)-1)

Evaluating ... ...

t = 787656.991978615

STEP 3: Convert Result to Output's Unit

787656.991978615 Meter --> No Conversion Required

FINAL ANSWER

787656.991978615 ≈ 787657 Meter <-- Thickness

(Calculation completed in 00.004 seconds)

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Created by Sai Venkata Phanindra Chary Arendra

Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNRVJIET), Hyderabad

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< Conduction in Cylinder Calculators

Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series

Go Thermal Resistance = (ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius of 3rd Cylinder/Radius of 2nd Cylinder))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius of 4th Cylinder/Radius of 3rd Cylinder))/(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 of 1st Cylinder*Length of Cylinder*Inside Convection Heat Transfer Coefficient)+(ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Thermal Conductivity*Length of Cylinder)+1/(2*pi*Radius of 2nd Cylinder*Length of Cylinder*External Convection Heat Transfer Coefficient)

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series

Thermal Resistance for Radial Heat Conduction in Cylinders

Go Thermal Resistance = ln(Outer Radius/Inner Radius)/(2*pi*Thermal Conductivity*Length of Cylinder)

Thickness of Cylindrical Wall to Maintain given Temperature Difference Formula

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 of 1st Cylinder*(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 of 1st Cylinder (r₁), Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Thermal Conductivity (k), Length of Cylinder (l_cyl) & 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 -> 787657 = 0.8*(e^(((305-300)*2*pi*10.18*0.4)/9.27)-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^(((T_i-T_o)*2*pi*k*l_cyl)/Q)-1) or Thickness = Radius of 1st Cylinder*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1). Radius of 1st Cylinder is the distance from the center of the concentric circles to any point on the first/smallest concentric circle for the first cylinder in the series, 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 of 1st Cylinder*(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 of 1st Cylinder (r₁), Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Thermal Conductivity (k), Length of Cylinder (l_cyl) & Heat Flow Rate (Q). With our tool, you need to enter the respective value for Radius of 1st Cylinder, 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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