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Heat Flow Rate through Spherical Wall 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{r 2 - r 1}{4 \cdot π \cdot k \cdot r 1 \cdot r 2}}

Q - Heat Flow Rate?T_i - Inner Surface Temperature?T_o - Outer Surface Temperature?r₂ - Radius of 2nd Concentric Sphere?r₁ - Radius of 1st Concentric Sphere?k - Thermal Conductivity?π - Archimedes' constant?

Heat Flow Rate through Spherical Wall Example

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Here is how the Heat Flow Rate through Spherical Wall equation looks like with Values.

Here is how the Heat Flow Rate through Spherical Wall equation looks like with Units.

Here is how the Heat Flow Rate through Spherical Wall equation looks like.

3769.9112 = \frac{305 - 300}{\frac{6 - 5}{4 \cdot 3.1416 \cdot 2 \cdot 5 \cdot 6}}

3769.9112W = \frac{305K - 300K}{\frac{6m - 5m}{4 \cdot 3.1416 \cdot 2W/(m*K) \cdot 5m \cdot 6m}}

3769.9112 = \frac{305 - 300}{\frac{6 - 5}{4 \cdot 3.1416 \cdot 2 \cdot 5 \cdot 6}}

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Heat Flow Rate through Spherical Wall Solution

Follow our step by step solution on how to calculate Heat Flow Rate through Spherical Wall?

FIRST Step Consider the formula

Q = \frac{T i - T o}{\frac{r 2 - r 1}{4 \cdot π \cdot k \cdot r 1 \cdot r 2}}

Next Step Substitute values of Variables

∴

Q = \frac{305K - 300K}{\frac{6m - 5m}{4 \cdot π \cdot 2W/(m*K) \cdot 5m \cdot 6m}}

Next Step Substitute values of Constants

∴

Q = \frac{305K - 300K}{\frac{6m - 5m}{4 \cdot 3.1416 \cdot 2W/(m*K) \cdot 5m \cdot 6m}}

Next Step Prepare to Evaluate

∴

Q = \frac{305 - 300}{\frac{6 - 5}{4 \cdot 3.1416 \cdot 2 \cdot 5 \cdot 6}}

Next Step Evaluate

∴

Q = 3769.91118430775W

LAST Step Rounding Answer

∴

Q = 3769.9112W

Heat Flow Rate through Spherical Wall Formula Elements

Variables

Constants

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 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

Note: Value should be greater than 0.

Formulas to find Radius of 2nd Concentric Sphere

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

Note: Value should be greater than 0.

Formulas to find Radius of 1st Concentric Sphere

Thermal Conductivity

Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.

Symbol: k

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

Note: Value should be greater than 0.

Formulas to find Thermal Conductivity

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Conduction in Sphere category

Go Convection Resistance for Spherical Layer

r th = \frac{1}{4 \cdot π \cdot r^{2} \cdot h}

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

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}

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

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}

Go Total Thermal Resistance of Spherical Wall of 2 Layers without Convection

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}

How to Evaluate Heat Flow Rate through Spherical Wall?

Heat Flow Rate through Spherical Wall evaluator uses Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)) to evaluate the Heat Flow Rate, The Heat Flow Rate through Spherical Wall formula is the rate of heat flow through a spherical wall when inner and outer surface temperatures, radii, and thermal conductivity of the material of the wall are known. Heat Flow Rate is denoted by Q symbol.

How to evaluate Heat Flow Rate through Spherical Wall using this online evaluator? To use this online evaluator for Heat Flow Rate through Spherical Wall, enter Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Radius of 2nd Concentric Sphere (r₂), Radius of 1st Concentric Sphere (r₁) & Thermal Conductivity (k) and hit the calculate button.

FAQs on Heat Flow Rate through Spherical Wall

What is the formula to find Heat Flow Rate through Spherical Wall?

The formula of Heat Flow Rate through Spherical Wall is expressed as Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)). Here is an example- 3769.911 = (305-300)/((6-5)/(4*pi*2*5*6)).

How to calculate Heat Flow Rate through Spherical Wall?

With Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Radius of 2nd Concentric Sphere (r₂), Radius of 1st Concentric Sphere (r₁) & Thermal Conductivity (k) we can find Heat Flow Rate through Spherical Wall using the formula - Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)). This formula also uses Archimedes' constant .

Can the Heat Flow Rate through Spherical Wall be negative?

Yes, the Heat Flow Rate through Spherical Wall, measured in Power can be negative.

Which unit is used to measure Heat Flow Rate through Spherical Wall?

Heat Flow Rate through Spherical Wall is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Heat Flow Rate through Spherical Wall can be measured.

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Heat Flow Rate through Spherical Wall Formula

Heat Flow Rate through Spherical Wall Example

Heat Flow Rate through Spherical Wall Solution

Heat Flow Rate through Spherical Wall Formula Elements

Other formulas in Conduction in Sphere category

How to Evaluate Heat Flow Rate through Spherical Wall?

FAQs on Heat Flow Rate through Spherical Wall

Variable Name