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

GoTotal Thermal Resistance of Spherical wall of 3 Layers without Convection 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{1}{4 \cdot π \cdot {r 1}^{2} \cdot h i} + \frac{r 2 - r 1}{4 \cdot π \cdot k \cdot r 1 \cdot r 2} + \frac{1}{4 \cdot π \cdot {r 2}^{2} \cdot h o}

R_tr - Sphere Thermal Resistance?r₁ - Radius of 1st Concentric Sphere?h_i - Inner Convection Heat Transfer Coefficient?r₂ - Radius of 2nd Concentric Sphere?k - Thermal Conductivity?h_o - External Convection Heat Transfer Coefficient?π - Archimedes' constant?

Total Thermal Resistance of Spherical Wall with Convection on Both Side Example

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Here is how the Total Thermal Resistance of Spherical Wall with Convection on Both Side equation looks like with Values.

Here is how the Total Thermal Resistance of Spherical Wall with Convection on Both Side equation looks like with Units.

Here is how the Total Thermal Resistance of Spherical Wall with Convection on Both Side equation looks like.

3.9571 = \frac{1}{4 \cdot 3.1416 \cdot 5^{2} \cdot 0.001} + \frac{6 - 5}{4 \cdot 3.1416 \cdot 2 \cdot 5 \cdot 6} + \frac{1}{4 \cdot 3.1416 \cdot 6^{2} \cdot 0.0025}

3.9571K/W = \frac{1}{4 \cdot 3.1416 \cdot {5m}^{2} \cdot 0.001W/m²*K} + \frac{6m - 5m}{4 \cdot 3.1416 \cdot 2W/(m*K) \cdot 5m \cdot 6m} + \frac{1}{4 \cdot 3.1416 \cdot {6m}^{2} \cdot 0.0025W/m²*K}

3.9571 = \frac{1}{4 \cdot 3.1416 \cdot 5^{2} \cdot 0.001} + \frac{6 - 5}{4 \cdot 3.1416 \cdot 2 \cdot 5 \cdot 6} + \frac{1}{4 \cdot 3.1416 \cdot 6^{2} \cdot 0.0025}

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Total Thermal Resistance of Spherical Wall with Convection on Both Side Solution

Follow our step by step solution on how to calculate Total Thermal Resistance of Spherical Wall with Convection on Both Side?

FIRST Step Consider the formula

R tr = \frac{1}{4 \cdot π \cdot {r 1}^{2} \cdot h i} + \frac{r 2 - r 1}{4 \cdot π \cdot k \cdot r 1 \cdot r 2} + \frac{1}{4 \cdot π \cdot {r 2}^{2} \cdot h o}

Next Step Substitute values of Variables

∴

R tr = \frac{1}{4 \cdot π \cdot {5m}^{2} \cdot 0.001W/m²*K} + \frac{6m - 5m}{4 \cdot π \cdot 2W/(m*K) \cdot 5m \cdot 6m} + \frac{1}{4 \cdot π \cdot {6m}^{2} \cdot 0.0025W/m²*K}

Next Step Substitute values of Constants

∴

R tr = \frac{1}{4 \cdot 3.1416 \cdot {5m}^{2} \cdot 0.001W/m²*K} + \frac{6m - 5m}{4 \cdot 3.1416 \cdot 2W/(m*K) \cdot 5m \cdot 6m} + \frac{1}{4 \cdot 3.1416 \cdot {6m}^{2} \cdot 0.0025W/m²*K}

Next Step Prepare to Evaluate

∴

R tr = \frac{1}{4 \cdot 3.1416 \cdot 5^{2} \cdot 0.001} + \frac{6 - 5}{4 \cdot 3.1416 \cdot 2 \cdot 5 \cdot 6} + \frac{1}{4 \cdot 3.1416 \cdot 6^{2} \cdot 0.0025}

Next Step Evaluate

∴

R tr = 3.95706902213782K/W

LAST Step Rounding Answer

∴

R tr = 3.9571K/W

Total Thermal Resistance of Spherical Wall with Convection on Both Side 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 1st Concentric Sphere

Radius of 1st Concentric Sphere is the distance from the center of the concentric spheres to any point on the first concentric sphere or radius of the first sphere.

Symbol: r₁

Measurement: LengthUnit: m