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Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series Formula

GoTotal Thermal Resistance of 3 Cylindrical Resistances Connected in Series Formula

GoThermal Resistance for Radial Heat Conduction in Cylinders Formula

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Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Check FAQs

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}

R_th - Thermal Resistance?r₂ - Radius of 2nd Cylinder?r₁ - Radius of 1st Cylinder?k₁ - Thermal Conductivity 1?l_cyl - Length of Cylinder?r₃ - Radius of 3rd Cylinder?k₂ - Thermal Conductivity 2?π - Archimedes' constant?

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series Example

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Here is how the Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series equation looks like.

0.539 = \frac{\ln (\frac{12}{0.8})}{2 \cdot 3.1416 \cdot 1.6 \cdot 0.4} + \frac{\ln (\frac{8}{12})}{2 \cdot 3.1416 \cdot 1.2 \cdot 0.4}

0.539K/W = \frac{\ln (\frac{12m}{0.8m})}{2 \cdot 3.1416 \cdot 1.6W/(m*K) \cdot 0.4m} + \frac{\ln (\frac{8m}{12m})}{2 \cdot 3.1416 \cdot 1.2W/(m*K) \cdot 0.4m}

0.539 = \frac{\ln (\frac{12}{0.8})}{2 \cdot 3.1416 \cdot 1.6 \cdot 0.4} + \frac{\ln (\frac{8}{12})}{2 \cdot 3.1416 \cdot 1.2 \cdot 0.4}

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Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series Solution

Follow our step by step solution on how to calculate Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series?

FIRST Step Consider the 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}

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

R th = \frac{\ln (\frac{12m}{0.8m})}{2 \cdot 3.1416 \cdot 1.6W/(m*K) \cdot 0.4m} + \frac{\ln (\frac{8m}{12m})}{2 \cdot 3.1416 \cdot 1.2W/(m*K) \cdot 0.4m}

Next Step Prepare to Evaluate

∴

R th = \frac{\ln (\frac{12}{0.8})}{2 \cdot 3.1416 \cdot 1.6 \cdot 0.4} + \frac{\ln (\frac{8}{12})}{2 \cdot 3.1416 \cdot 1.2 \cdot 0.4}

Next Step Evaluate

∴

R th = 0.538995636516894K/W

LAST Step Rounding Answer

∴

R th = 0.539K/W

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series Formula Elements

Variables

Constants

Functions

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.

Symbol: R_th

Measurement: Thermal ResistanceUnit: K/W

Note: Value can be positive or negative.

Formulas to find Thermal Resistance

Radius of 2nd 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.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius of 2nd Cylinder

Radius of 1st Cylinder

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.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius of 1st Cylinder

Thermal Conductivity 1

Thermal Conductivity 1 is the thermal conductivity of the first body.

Symbol: k₁

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value should be greater than 0.

Formulas to find Thermal Conductivity 1

Length of Cylinder

Length of Cylinder is the vertical height of the Cylinder.

Symbol: l_cyl

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Cylinder

Radius of 3rd 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.

Symbol: r₃

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of 3rd Cylinder

Thermal Conductivity 2

Thermal Conductivity 2 is the thermal conductivity of the second body.

Symbol: k₂

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value should be greater than 0.

Formulas to find Thermal Conductivity 2

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Thermal Resistance

Go Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series

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}

Go Thermal Resistance for Radial Heat Conduction in Cylinders

R th = \frac{\ln (\frac{r o}{r i})}{2 \cdot π \cdot k \cdot l cyl}

Other formulas in Conduction in Cylinder category

Go Inner Surface Temperature of Cylindrical Wall in Conduction

T i = T o + \frac{Q \cdot \ln (\frac{r 2}{r 1})}{2 \cdot π \cdot k \cdot l cyl}

Go Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate

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

How to Evaluate Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series?

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series evaluator 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) to evaluate the Thermal Resistance, Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series is defined as the equivalent thermal resistance offered by 2 cylindrical resistances when connected in series. Thermal Resistance is denoted by R_th symbol.

How to evaluate Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series using this online evaluator? To use this online evaluator for Total Thermal Resistance of 2 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) and hit the calculate button.

FAQs on Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series

What is the formula to find Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series?

The formula of Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series is expressed as 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). Here is an example- 0.538996 = (ln(12/0.8))/(2*pi*1.6*0.4)+(ln(8/12))/(2*pi*1.2*0.4).

How to calculate Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series?

With 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) we can find Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series using the formula - 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). This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

What are the other ways to Calculate Thermal Resistance?

Here are the different ways to Calculate Thermal Resistance-

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)
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)

Can the Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series be negative?

Yes, the Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series, measured in Thermal Resistance can be negative.

Which unit is used to measure Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series?

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series is usually measured using the Kelvin per Watt[K/W] for Thermal Resistance. Degree Fahrenheit hour per Btu (IT)[K/W], Degree Fahrenheit Hour per Btu (th)[K/W], Kelvin per Milliwatt[K/W] are the few other units in which Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series can be measured.

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Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series Formula

​GoTotal Thermal Resistance of 3 Cylindrical Resistances Connected in Series Formula

​GoThermal Resistance for Radial Heat Conduction in Cylinders Formula

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series Example

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series Solution

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series Formula Elements

Other Formulas to find Thermal Resistance

Other formulas in Conduction in Cylinder category

How to Evaluate Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series?

FAQs on Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series

Variable Name

GoTotal Thermal Resistance of 3 Cylindrical Resistances Connected in Series Formula

GoThermal Resistance for Radial Heat Conduction in Cylinders Formula