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Total Thermal Resistance of Spherical wall of 3 Layers without Convection Formula

GoTotal Thermal Resistance of Spherical Wall with Convection on Both Side Formula

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Sphere 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 tr = \frac{r 2 - r 1}{4 \cdot π \cdot k 1 \cdot r 1 \cdot r 2} + \frac{r 3 - r 2}{4 \cdot π \cdot k 2 \cdot r 2 \cdot r 3} + \frac{r 4 - r 3}{4 \cdot π \cdot k 3 \cdot r 3 \cdot r 4}

R_tr - Sphere Thermal Resistance?r₂ - Radius of 2nd Concentric Sphere?r₁ - Radius of 1st Concentric Sphere?k₁ - Thermal Conductivity of 1st Body?r₃ - Radius of 3rd Concentric Sphere?k₂ - Thermal Conductivity of 2nd Body?r₄ - Radius of 4th Concentric Sphere?k₃ - Thermal Conductivity of 3rd Body?π - Archimedes' constant?

Total Thermal Resistance of Spherical wall of 3 Layers without Convection Example

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Here is how the Total Thermal Resistance of Spherical wall of 3 Layers without Convection equation looks like with Values.

Here is how the Total Thermal Resistance of Spherical wall of 3 Layers without Convection equation looks like with Units.

Here is how the Total Thermal Resistance of Spherical wall of 3 Layers without Convection equation looks like.

3.9552 = \frac{6 - 5}{4 \cdot 3.1416 \cdot 0.001 \cdot 5 \cdot 6} + \frac{7 - 6}{4 \cdot 3.1416 \cdot 0.002 \cdot 6 \cdot 7} + \frac{8 - 7}{4 \cdot 3.1416 \cdot 0.004 \cdot 7 \cdot 8}

3.9552K/W = \frac{6m - 5m}{4 \cdot 3.1416 \cdot 0.001W/(m*K) \cdot 5m \cdot 6m} + \frac{7m - 6m}{4 \cdot 3.1416 \cdot 0.002W/(m*K) \cdot 6m \cdot 7m} + \frac{8m - 7m}{4 \cdot 3.1416 \cdot 0.004W/(m*K) \cdot 7m \cdot 8m}

3.9552 = \frac{6 - 5}{4 \cdot 3.1416 \cdot 0.001 \cdot 5 \cdot 6} + \frac{7 - 6}{4 \cdot 3.1416 \cdot 0.002 \cdot 6 \cdot 7} + \frac{8 - 7}{4 \cdot 3.1416 \cdot 0.004 \cdot 7 \cdot 8}

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Total Thermal Resistance of Spherical wall of 3 Layers without Convection Solution

Follow our step by step solution on how to calculate Total Thermal Resistance of Spherical wall of 3 Layers without Convection?

FIRST Step Consider the formula

R tr = \frac{r 2 - r 1}{4 \cdot π \cdot k 1 \cdot r 1 \cdot r 2} + \frac{r 3 - r 2}{4 \cdot π \cdot k 2 \cdot r 2 \cdot r 3} + \frac{r 4 - r 3}{4 \cdot π \cdot k 3 \cdot r 3 \cdot r 4}

Next Step Substitute values of Variables

∴

R tr = \frac{6m - 5m}{4 \cdot π \cdot 0.001W/(m*K) \cdot 5m \cdot 6m} + \frac{7m - 6m}{4 \cdot π \cdot 0.002W/(m*K) \cdot 6m \cdot 7m} + \frac{8m - 7m}{4 \cdot π \cdot 0.004W/(m*K) \cdot 7m \cdot 8m}

Next Step Substitute values of Constants

∴

R tr = \frac{6m - 5m}{4 \cdot 3.1416 \cdot 0.001W/(m*K) \cdot 5m \cdot 6m} + \frac{7m - 6m}{4 \cdot 3.1416 \cdot 0.002W/(m*K) \cdot 6m \cdot 7m} + \frac{8m - 7m}{4 \cdot 3.1416 \cdot 0.004W/(m*K) \cdot 7m \cdot 8m}

Next Step Prepare to Evaluate

∴

R tr = \frac{6 - 5}{4 \cdot 3.1416 \cdot 0.001 \cdot 5 \cdot 6} + \frac{7 - 6}{4 \cdot 3.1416 \cdot 0.002 \cdot 6 \cdot 7} + \frac{8 - 7}{4 \cdot 3.1416 \cdot 0.004 \cdot 7 \cdot 8}

Next Step Evaluate

∴

R tr = 3.95518980600395K/W

LAST Step Rounding Answer

∴

R tr = 3.9552K/W

Total Thermal Resistance of Spherical wall of 3 Layers without Convection Formula Elements

Variables

Constants

Sphere Thermal Resistance

Sphere 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_tr

Measurement: Thermal ResistanceUnit: K/W

Note: Value can be positive or negative.

Formulas to find Sphere Thermal Resistance

Radius of 2nd Concentric Sphere

Radius of 2nd Concentric Sphere is the distance from the center of the concentric spheres to any point on the second concentric sphere or radius of the second sphere.

Symbol: r₂

Measurement: LengthUnit: m