Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series Calculator

✖Radius of 2nd Cylinder is the distance from the center of the concentric circles to any point on the Second concentric circle or radius of the third circle.ⓘ Radius of 2nd Cylinder [r₂]			+10% -10%
✖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%
✖Thermal Conductivity 1 is the thermal conductivity of the first body.ⓘ Thermal Conductivity 1 [k₁]			+10% -10%
✖Length of Cylinder is the vertical height of the Cylinder.ⓘ Length of Cylinder [l_cyl]			+10% -10%
✖Radius of 3rd Cylinder is the distance from the center of the concentric circles to any point on the third concentric circle or radius of the third circle.ⓘ Radius of 3rd Cylinder [r₃]			+10% -10%
✖Thermal Conductivity 2 is the thermal conductivity of the second body.ⓘ Thermal Conductivity 2 [k₂]			+10% -10%
✖Radius of 4th Cylinder is the distance from the center of the concentric circles to any point on the fourth concentric circle or radius of the third circle.ⓘ Radius of 4th Cylinder [r₄]			+10% -10%
✖Thermal Conductivity 3 is the thermal conductivity of the third body.ⓘ Thermal Conductivity 3 [k₃]			+10% -10%

✖Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow.ⓘ Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series [R_th]

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Formula

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Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series

Formula

R th = \frac{\ln (\frac{r 2}{r 1})}{2 \cdot π \cdot k 1 \cdot l cyl} + \frac{\ln (\frac{r 3}{r 2})}{2 \cdot π \cdot k 2 \cdot l cyl} + \frac{\ln (\frac{r 4}{r 3})}{2 \cdot π \cdot k 3 \cdot l cyl}

Example

0.594662 K/W = \frac{\ln (\frac{12 m}{0.8 m})}{2 \cdot π \cdot 1.6 W/(m*K) \cdot 0.4 m} + \frac{\ln (\frac{8 m}{12 m})}{2 \cdot π \cdot 1.2 W/(m*K) \cdot 0.4 m} + \frac{\ln (\frac{14 m}{8 m})}{2 \cdot π \cdot 4 W/(m*K) \cdot 0.4 m}

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Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
R_th = (ln(r₂/r₁))/(2*pi*k₁*l_cyl)+(ln(r₃/r₂))/(2*pi*k₂*l_cyl)+(ln(r₄/r₃))/(2*pi*k₃*l_cyl)
This formula uses 1 Constants, 1 Functions, 9 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 of 2nd Cylinder - (Measured in Meter) - Radius of 2nd Cylinder is the distance from the center of the concentric circles to any point on the Second concentric circle or radius of the third circle.
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.
Thermal Conductivity 1 - (Measured in Watt per Meter per K) - Thermal Conductivity 1 is the thermal conductivity of the first body.
Length of Cylinder - (Measured in Meter) - Length of Cylinder is the vertical height of the Cylinder.
Radius of 3rd Cylinder - (Measured in Meter) - Radius of 3rd Cylinder is the distance from the center of the concentric circles to any point on the third concentric circle or radius of the third circle.
Thermal Conductivity 2 - (Measured in Watt per Meter per K) - Thermal Conductivity 2 is the thermal conductivity of the second body.
Radius of 4th Cylinder - (Measured in Meter) - Radius of 4th Cylinder is the distance from the center of the concentric circles to any point on the fourth concentric circle or radius of the third circle.
Thermal Conductivity 3 - (Measured in Watt per Meter per K) - Thermal Conductivity 3 is the thermal conductivity of the third body.

STEP 1: Convert Input(s) to Base Unit

Radius of 2nd Cylinder: 12 Meter --> 12 Meter No Conversion Required
Radius of 1st Cylinder: 0.8 Meter --> 0.8 Meter No Conversion Required
Thermal Conductivity 1: 1.6 Watt per Meter per K --> 1.6 Watt per Meter per K No Conversion Required
Length of Cylinder: 0.4 Meter --> 0.4 Meter No Conversion Required
Radius of 3rd Cylinder: 8 Meter --> 8 Meter No Conversion Required
Thermal Conductivity 2: 1.2 Watt per Meter per K --> 1.2 Watt per Meter per K No Conversion Required
Radius of 4th Cylinder: 14 Meter --> 14 Meter No Conversion Required
Thermal Conductivity 3: 4 Watt per Meter per K --> 4 Watt per Meter per K No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_th = (ln(r₂/r₁))/(2*pi*k₁*l_cyl)+(ln(r₃/r₂))/(2*pi*k₂*l_cyl)+(ln(r₄/r₃))/(2*pi*k₃*l_cyl) --> (ln(12/0.8))/(2*pi*1.6*0.4)+(ln(8/12))/(2*pi*1.2*0.4)+(ln(14/8))/(2*pi*4*0.4)

Evaluating ... ...

R_th = 0.594661648318262

STEP 3: Convert Result to Output's Unit

0.594661648318262 Kelvin per Watt --> No Conversion Required

FINAL ANSWER

0.594661648318262 ≈ 0.594662 Kelvin per Watt <-- Thermal Resistance

(Calculation completed in 00.020 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Mechanical » Conduction in Cylinder » Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series

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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)

Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series Formula

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 3 Cylindrical Resistances Connected in Series?

Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series calculator uses 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) to calculate the Thermal Resistance, The total thermal resistance of 3 cylindrical resistances connected in series formula is defined as the equivalent resistance offered by the three cylindrical resistances when connected in series. Thermal Resistance is denoted by R_th symbol.

How to calculate Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series using this online calculator? To use this online calculator for Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series, enter Radius of 2nd Cylinder (r₂), Radius of 1st Cylinder (r₁), Thermal Conductivity 1 (k₁), Length of Cylinder (l_cyl), Radius of 3rd Cylinder (r₃), Thermal Conductivity 2 (k₂), Radius of 4th Cylinder (r₄) & Thermal Conductivity 3 (k₃) and hit the calculate button. Here is how the Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series calculation can be explained with given input values -> 0.594662 = (ln(12/0.8))/(2*pi*1.6*0.4)+(ln(8/12))/(2*pi*1.2*0.4)+(ln(14/8))/(2*pi*4*0.4).

FAQ

What is Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series?

The total thermal resistance of 3 cylindrical resistances connected in series formula is defined as the equivalent resistance offered by the three cylindrical resistances when connected in series and is represented as R_th = (ln(r₂/r₁))/(2*pi*k₁*l_cyl)+(ln(r₃/r₂))/(2*pi*k₂*l_cyl)+(ln(r₄/r₃))/(2*pi*k₃*l_cyl) or 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). Radius of 2nd Cylinder is the distance from the center of the concentric circles to any point on the Second concentric circle or radius of the third circle, 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, Thermal Conductivity 1 is the thermal conductivity of the first body, Length of Cylinder is the vertical height of the Cylinder, Radius of 3rd Cylinder is the distance from the center of the concentric circles to any point on the third concentric circle or radius of the third circle, Thermal Conductivity 2 is the thermal conductivity of the second body, Radius of 4th Cylinder is the distance from the center of the concentric circles to any point on the fourth concentric circle or radius of the third circle & Thermal Conductivity 3 is the thermal conductivity of the third body.

How to calculate Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series?

The total thermal resistance of 3 cylindrical resistances connected in series formula is defined as the equivalent resistance offered by the three cylindrical resistances when connected in series is calculated using 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). To calculate Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series, you need Radius of 2nd Cylinder (r₂), Radius of 1st Cylinder (r₁), Thermal Conductivity 1 (k₁), Length of Cylinder (l_cyl), Radius of 3rd Cylinder (r₃), Thermal Conductivity 2 (k₂), Radius of 4th Cylinder (r₄) & Thermal Conductivity 3 (k₃). With our tool, you need to enter the respective value for Radius of 2nd Cylinder, Radius of 1st Cylinder, Thermal Conductivity 1, Length of Cylinder, Radius of 3rd Cylinder, Thermal Conductivity 2, Radius of 4th Cylinder & Thermal Conductivity 3 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 of 2nd Cylinder, Radius of 1st Cylinder, Thermal Conductivity 1, Length of Cylinder, Radius of 3rd Cylinder, Thermal Conductivity 2, Radius of 4th Cylinder & Thermal Conductivity 3. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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