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Thermal Resistance of Spherical Composite Wall of 2 Layers in Series with Convection Formula

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Thermal resistance of sphere 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{1}{4 \cdot π} \cdot (\frac{1}{h i \cdot {r 1}^{2}} + \frac{1}{k 1} \cdot (\frac{1}{r 1} - \frac{1}{r 2}) + \frac{1}{k 2} \cdot (\frac{1}{r 2} - \frac{1}{r 3}) + \frac{1}{h o \cdot {r 3}^{2}})

R_th - Thermal Resistance of Sphere?h_i - Inner Convection Heat Transfer Coefficient?r₁ - Radius of 1st Concentric Sphere?k₁ - Thermal Conductivity of 1st Body?r₂ - Radius of 2nd Concentric Sphere?k₂ - Thermal Conductivity of 2nd Body?r₃ - Radius of 3rd Concentric Sphere?h_o - External Convection Heat Transfer Coefficient?π - Archimedes' constant?

Thermal Resistance of Spherical Composite Wall of 2 Layers in Series with Convection Example

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Here is how the Thermal Resistance of Spherical Composite Wall of 2 Layers in Series with Convection equation looks like with Values.

Here is how the Thermal Resistance of Spherical Composite Wall of 2 Layers in Series with Convection equation looks like with Units.

Here is how the Thermal Resistance of Spherical Composite Wall of 2 Layers in Series with Convection equation looks like.

7.3198 = \frac{1}{4 \cdot 3.1416} \cdot (\frac{1}{0.001 \cdot 5^{2}} + \frac{1}{0.001} \cdot (\frac{1}{5} - \frac{1}{6}) + \frac{1}{0.002} \cdot (\frac{1}{6} - \frac{1}{7}) + \frac{1}{0.0025 \cdot 7^{2}})

7.3198K/W = \frac{1}{4 \cdot 3.1416} \cdot (\frac{1}{0.001W/m²*K \cdot {5m}^{2}} + \frac{1}{0.001W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m}) + \frac{1}{0.002W/(m*K)} \cdot (\frac{1}{6m} - \frac{1}{7m}) + \frac{1}{0.0025W/m²*K \cdot {7m}^{2}})

7.3198 = \frac{1}{4 \cdot 3.1416} \cdot (\frac{1}{0.001 \cdot 5^{2}} + \frac{1}{0.001} \cdot (\frac{1}{5} - \frac{1}{6}) + \frac{1}{0.002} \cdot (\frac{1}{6} - \frac{1}{7}) + \frac{1}{0.0025 \cdot 7^{2}})

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Thermal Resistance of Spherical Composite Wall of 2 Layers in Series with Convection Solution

Follow our step by step solution on how to calculate Thermal Resistance of Spherical Composite Wall of 2 Layers in Series with Convection?

FIRST Step Consider the formula

R th = \frac{1}{4 \cdot π} \cdot (\frac{1}{h i \cdot {r 1}^{2}} + \frac{1}{k 1} \cdot (\frac{1}{r 1} - \frac{1}{r 2}) + \frac{1}{k 2} \cdot (\frac{1}{r 2} - \frac{1}{r 3}) + \frac{1}{h o \cdot {r 3}^{2}})

Next Step Substitute values of Variables

∴

R th = \frac{1}{4 \cdot π} \cdot (\frac{1}{0.001W/m²*K \cdot {5m}^{2}} + \frac{1}{0.001W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m}) + \frac{1}{0.002W/(m*K)} \cdot (\frac{1}{6m} - \frac{1}{7m}) + \frac{1}{0.0025W/m²*K \cdot {7m}^{2}})

Next Step Substitute values of Constants

∴

R th = \frac{1}{4 \cdot 3.1416} \cdot (\frac{1}{0.001W/m²*K \cdot {5m}^{2}} + \frac{1}{0.001W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m}) + \frac{1}{0.002W/(m*K)} \cdot (\frac{1}{6m} - \frac{1}{7m}) + \frac{1}{0.0025W/m²*K \cdot {7m}^{2}})

Next Step Prepare to Evaluate

∴

R th = \frac{1}{4 \cdot 3.1416} \cdot (\frac{1}{0.001 \cdot 5^{2}} + \frac{1}{0.001} \cdot (\frac{1}{5} - \frac{1}{6}) + \frac{1}{0.002} \cdot (\frac{1}{6} - \frac{1}{7}) + \frac{1}{0.0025 \cdot 7^{2}})

Next Step Evaluate

∴

R th = 7.3197727941082K/W

LAST Step Rounding Answer

∴

R th = 7.3198K/W

Thermal Resistance of Spherical Composite Wall of 2 Layers in Series with Convection Formula Elements

Variables

Constants

Thermal Resistance of Sphere

Thermal resistance of sphere 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 of Sphere

Inner Convection Heat Transfer Coefficient

Inner Convection Heat Transfer Coefficient is the coefficient of convection heat transfer at the inside surface of the body or object or wall, etc.

Symbol: h_i

Measurement: Heat Transfer CoefficientUnit: W/m²*K