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Heat Flow Rate through Cylindrical Composite Wall of 3 Layers Formula

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GoHeat Flow Rate through Cylindrical Composite Wall of 2 Layers Formula

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Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium. Check FAQs

Q = \frac{T i - T o}{\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}}

Q - Heat Flow Rate?T_i - Inner Surface Temperature?T_o - Outer Surface Temperature?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?

Heat Flow Rate through Cylindrical Composite Wall of 3 Layers Example

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Here is how the Heat Flow Rate through Cylindrical Composite Wall of 3 Layers equation looks like with Values.

Here is how the Heat Flow Rate through Cylindrical Composite Wall of 3 Layers equation looks like with Units.

Here is how the Heat Flow Rate through Cylindrical Composite Wall of 3 Layers equation looks like.

8.4081 = \frac{305 - 300}{\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}}

8.4081W = \frac{305K - 300K}{\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}}

8.4081 = \frac{305 - 300}{\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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Heat Flow Rate through Cylindrical Composite Wall of 3 Layers Solution

Follow our step by step solution on how to calculate Heat Flow Rate through Cylindrical Composite Wall of 3 Layers?

FIRST Step Consider the formula

Q = \frac{T i - T o}{\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

∴

Q = \frac{305K - 300K}{\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

∴

Q = \frac{305K - 300K}{\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

∴

Q = \frac{305 - 300}{\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

∴

Q = 8.4081427045788W

LAST Step Rounding Answer

∴

Q = 8.4081W

Heat Flow Rate through Cylindrical Composite Wall of 3 Layers Formula Elements

Variables

Constants

Functions

Heat Flow Rate

Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. 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

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

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.

Formulas to find Radius of 2nd Cylinder

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.

Formulas to find Radius of 1st Cylinder

Thermal Conductivity 1

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

Symbol: k₁

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