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Heat Flow Rate through Spherical Composite Wall of 2 Layers in Series Formula

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Heat Flow Rate of wall of 2 layers is the amount of heat that is transferred per unit of time in material. Heat is the flow of thermal energy driven by thermal non-equilibrium. Check FAQs

Q' = \frac{T i - T o}{\frac{1}{4 \cdot π \cdot k 1} \cdot (\frac{1}{r 1} - \frac{1}{r 2}) + \frac{1}{4 \cdot π \cdot k 2} \cdot (\frac{1}{r 2} - \frac{1}{r 3})}

Q^' - Heat Flow Rate of Wall of 2 Layers?T_i - Inner Surface Temperature?T_o - Outer Surface Temperature?k₁ - Thermal Conductivity of 1st Body?r₁ - Radius of 1st Concentric Sphere?r₂ - Radius of 2nd Concentric Sphere?k₂ - Thermal Conductivity of 2nd Body?r₃ - Radius of 3rd Concentric Sphere?π - Archimedes' constant?

Heat Flow Rate through Spherical Composite Wall of 2 Layers in Series Example

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Here is how the Heat Flow Rate through Spherical Composite Wall of 2 Layers in Series equation looks like with Values.

Here is how the Heat Flow Rate through Spherical Composite Wall of 2 Layers in Series equation looks like with Units.

Here is how the Heat Flow Rate through Spherical Composite Wall of 2 Layers in Series equation looks like.

1.3889 = \frac{305 - 300}{\frac{1}{4 \cdot 3.1416 \cdot 0.001} \cdot (\frac{1}{5} - \frac{1}{6}) + \frac{1}{4 \cdot 3.1416 \cdot 0.002} \cdot (\frac{1}{6} - \frac{1}{7})}

1.3889W = \frac{305K - 300K}{\frac{1}{4 \cdot 3.1416 \cdot 0.001W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m}) + \frac{1}{4 \cdot 3.1416 \cdot 0.002W/(m*K)} \cdot (\frac{1}{6m} - \frac{1}{7m})}

1.3889 = \frac{305 - 300}{\frac{1}{4 \cdot 3.1416 \cdot 0.001} \cdot (\frac{1}{5} - \frac{1}{6}) + \frac{1}{4 \cdot 3.1416 \cdot 0.002} \cdot (\frac{1}{6} - \frac{1}{7})}

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Heat Flow Rate through Spherical Composite Wall of 2 Layers in Series Solution

Follow our step by step solution on how to calculate Heat Flow Rate through Spherical Composite Wall of 2 Layers in Series?

FIRST Step Consider the formula

Q' = \frac{T i - T o}{\frac{1}{4 \cdot π \cdot k 1} \cdot (\frac{1}{r 1} - \frac{1}{r 2}) + \frac{1}{4 \cdot π \cdot k 2} \cdot (\frac{1}{r 2} - \frac{1}{r 3})}

Next Step Substitute values of Variables

∴

Q' = \frac{305K - 300K}{\frac{1}{4 \cdot π \cdot 0.001W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m}) + \frac{1}{4 \cdot π \cdot 0.002W/(m*K)} \cdot (\frac{1}{6m} - \frac{1}{7m})}

Next Step Substitute values of Constants

∴

Q' = \frac{305K - 300K}{\frac{1}{4 \cdot 3.1416 \cdot 0.001W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m}) + \frac{1}{4 \cdot 3.1416 \cdot 0.002W/(m*K)} \cdot (\frac{1}{6m} - \frac{1}{7m})}

Next Step Prepare to Evaluate

∴

Q' = \frac{305 - 300}{\frac{1}{4 \cdot 3.1416 \cdot 0.001} \cdot (\frac{1}{5} - \frac{1}{6}) + \frac{1}{4 \cdot 3.1416 \cdot 0.002} \cdot (\frac{1}{6} - \frac{1}{7})}

Next Step Evaluate

∴

Q' = 1.38891464685022W

LAST Step Rounding Answer

∴

Q' = 1.3889W

Heat Flow Rate through Spherical Composite Wall of 2 Layers in Series Formula Elements

Variables

Constants

Heat Flow Rate of Wall of 2 Layers

Heat Flow Rate of wall of 2 layers is the amount of heat that is transferred per unit of time in material. Heat is the flow of thermal energy driven by thermal non-equilibrium.

Symbol: Q^'

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Heat Flow Rate of Wall of 2 Layers

Inner Surface Temperature

Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.

Symbol: T_i

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Inner Surface Temperature

Outer Surface Temperature

Outer Surface Temperature is the temperature at the outer surface of the wall either plane wall or cylindrical wall or spherical wall, etc.

Symbol: T_o

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Outer Surface Temperature

Thermal Conductivity of 1st Body

Thermal Conductivity of 1st body is expressed as amount of heat flows per unit time through a unit area of first body with temperature gradient of one degree per unit distance.

Symbol: k₁

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