Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Rth = 1/(2*pi*r1*lcyl*hi)+(ln(r2/r1))/(2*pi*k*lcyl)+1/(2*pi*r2*lcyl*ho)
This formula uses 1 Constants, 1 Functions, 7 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
Variables Used
Thermal Resistance - (Measured in Kelvin per Watt) - Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow.
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.
Length of Cylinder - (Measured in Meter) - Length of Cylinder is the vertical height of the Cylinder.
Inside Convection Heat Transfer Coefficient - (Measured in Watt per Square Meter per Kelvin) - Inside Convection Heat Transfer Coefficient is the coefficient of convection heat transfer at the inside surface of the body or object or wall, etc.
Radius 2 - (Measured in Meter) - Radius 2 is the radius of the second concentric circle or circle.
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.
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
Radius 1: 0.8 Meter --> 0.8 Meter No Conversion Required
Length of Cylinder: 0.4 Meter --> 0.4 Meter No Conversion Required
Inside Convection Heat Transfer Coefficient: 1.35 Watt per Square Meter per Kelvin --> 1.35 Watt per Square Meter per Kelvin No Conversion Required
Radius 2: 12 Meter --> 12 Meter No Conversion Required
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 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
Rth = 1/(2*pi*r1*lcyl*hi)+(ln(r2/r1))/(2*pi*k*lcyl)+1/(2*pi*r2*lcyl*ho) --> 1/(2*pi*0.8*0.4*1.35)+(ln(12/0.8))/(2*pi*10.18*0.4)+1/(2*pi*12*0.4*9.8)
Evaluating ... ...
Rth = 0.477642305519784
STEP 3: Convert Result to Output's Unit
0.477642305519784 Kelvin per Watt --> No Conversion Required
FINAL ANSWER
0.477642305519784 0.477642 Kelvin per Watt <-- Thermal Resistance
(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)

Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides Formula

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)
Rth = 1/(2*pi*r1*lcyl*hi)+(ln(r2/r1))/(2*pi*k*lcyl)+1/(2*pi*r2*lcyl*ho)

What is thermal resistance?

Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the reciprocal of thermal conductance

How to Calculate Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides?

Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides calculator uses 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) to calculate the Thermal Resistance, The Total Thermal Resistance of Cylindrical wall with Convection on both Sides formula is defined as the sum of thermal resistance due to convection on the inside and outside the cylindrical surface and the thermal resistance due to conduction. Thermal Resistance is denoted by Rth symbol.

How to calculate Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides using this online calculator? To use this online calculator for Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides, enter Radius 1 (r1), Length of Cylinder (lcyl), Inside Convection Heat Transfer Coefficient (hi), Radius 2 (r2), Thermal Conductivity (k) & External Convection Heat Transfer Coefficient (ho) and hit the calculate button. Here is how the Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides calculation can be explained with given input values -> 0.477642 = 1/(2*pi*0.8*0.4*1.35)+(ln(12/0.8))/(2*pi*10.18*0.4)+1/(2*pi*12*0.4*9.8).

FAQ

What is Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides?
The Total Thermal Resistance of Cylindrical wall with Convection on both Sides formula is defined as the sum of thermal resistance due to convection on the inside and outside the cylindrical surface and the thermal resistance due to conduction and is represented as Rth = 1/(2*pi*r1*lcyl*hi)+(ln(r2/r1))/(2*pi*k*lcyl)+1/(2*pi*r2*lcyl*ho) or 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). 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, Length of Cylinder is the vertical height of the Cylinder, Inside Convection Heat Transfer Coefficient is the coefficient of convection heat transfer at the inside surface of the body or object or wall, etc, Radius 2 is the radius of the second concentric circle or circle, 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 & 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 Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides?
The Total Thermal Resistance of Cylindrical wall with Convection on both Sides formula is defined as the sum of thermal resistance due to convection on the inside and outside the cylindrical surface and the thermal resistance due to conduction is calculated using 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). To calculate Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides, you need Radius 1 (r1), Length of Cylinder (lcyl), Inside Convection Heat Transfer Coefficient (hi), Radius 2 (r2), Thermal Conductivity (k) & External Convection Heat Transfer Coefficient (ho). With our tool, you need to enter the respective value for Radius 1, Length of Cylinder, Inside Convection Heat Transfer Coefficient, Radius 2, Thermal Conductivity & 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 Thermal Resistance?
In this formula, Thermal Resistance uses Radius 1, Length of Cylinder, Inside Convection Heat Transfer Coefficient, Radius 2, Thermal Conductivity & External Convection Heat Transfer Coefficient. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • 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)
  • Thermal Resistance = ln(Outer Radius/Inner Radius)/(2*pi*Thermal Conductivity*Length of Cylinder)
  • Thermal Resistance = 1/(Convection heat transfer*2*pi*Cylinder Radius*Length of Cylinder)
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