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Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series 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} + \frac{\ln (\frac{r 4}{r 3})}{2 \cdot π \cdot k 3 \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?r₄ - Radius of 4th Cylinder?k₃ - Thermal Conductivity 3?π - Archimedes' constant?

Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series Example

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Here is how the Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series equation looks like with Values.

Here is how the Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series equation looks like with Units.

Here is how the Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series equation looks like.

0.5947 = \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} + \frac{\ln (\frac{14}{8})}{2 \cdot 3.1416 \cdot 4 \cdot 0.4}

0.5947K/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} + \frac{\ln (\frac{14m}{8m})}{2 \cdot 3.1416 \cdot 4W/(m*K) \cdot 0.4m}

0.5947 = \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} + \frac{\ln (\frac{14}{8})}{2 \cdot 3.1416 \cdot 4 \cdot 0.4}

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

Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series Solution

Follow our step by step solution on how to calculate Total Thermal Resistance of 3 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} + \frac{\ln (\frac{r 4}{r 3})}{2 \cdot π \cdot k 3 \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} + \frac{\ln (\frac{14m}{8m})}{2 \cdot π \cdot 4W/(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} + \frac{\ln (\frac{14m}{8m})}{2 \cdot 3.1416 \cdot 4W/(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} + \frac{\ln (\frac{14}{8})}{2 \cdot 3.1416 \cdot 4 \cdot 0.4}

Next Step Evaluate

∴

R th = 0.594661648318262K/W

LAST Step Rounding Answer

∴

R th = 0.5947K/W

Total Thermal Resistance of 3 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.

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.

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.

Thermal Conductivity 1

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

Symbol: k₁

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