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Heat Transfer between Concentric Spheres Formula

GoNet Energy Leaving given Radiosity and Irradiation Formula

GoHeat Transfer between Small Convex Object in Large Enclosure Formula

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Heat Transfer is the amount of heat that is transferred per unit of time in some material, usually measured in watts (joules per second). Check FAQs

q = \frac{A 1 \cdot [Stefan-BoltZ] \cdot (({T 1}^{4}) - ({T 2}^{4}))}{(\frac{1}{ε 1}) + (((\frac{1}{ε 2}) - 1) \cdot ({(\frac{r 1}{r 2})}^{2}))}

q - Heat Transfer?A₁ - Surface Area of Body 1?T₁ - Temperature of Surface 1?T₂ - Temperature of Surface 2?ε₁ - Emissivity of Body 1?ε₂ - Emissivity of Body 2?r₁ - Radius of Smaller Sphere?r₂ - Radius of Larger Sphere?[Stefan-BoltZ] - Stefan-Boltzmann Constant?

Heat Transfer between Concentric Spheres Example

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Here is how the Heat Transfer between Concentric Spheres equation looks like with Values.

Here is how the Heat Transfer between Concentric Spheres equation looks like with Units.

Here is how the Heat Transfer between Concentric Spheres equation looks like.

731.5713 = \frac{34.74 \cdot 5.7E-8 \cdot ((202^{4}) - (151^{4}))}{(\frac{1}{0.4}) + (((\frac{1}{0.3}) - 1) \cdot ({(\frac{10}{20})}^{2}))}

731.5713W = \frac{34.74m² \cdot 5.7E-8 \cdot (({202K}^{4}) - ({151K}^{4}))}{(\frac{1}{0.4}) + (((\frac{1}{0.3}) - 1) \cdot ({(\frac{10m}{20m})}^{2}))}

731.5713 = \frac{34.74 \cdot 5.7E-8 \cdot ((202^{4}) - (151^{4}))}{(\frac{1}{0.4}) + (((\frac{1}{0.3}) - 1) \cdot ({(\frac{10}{20})}^{2}))}

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Heat Transfer between Concentric Spheres Solution

Follow our step by step solution on how to calculate Heat Transfer between Concentric Spheres?

FIRST Step Consider the formula

q = \frac{A 1 \cdot [Stefan-BoltZ] \cdot (({T 1}^{4}) - ({T 2}^{4}))}{(\frac{1}{ε 1}) + (((\frac{1}{ε 2}) - 1) \cdot ({(\frac{r 1}{r 2})}^{2}))}

Next Step Substitute values of Variables

∴

q = \frac{34.74m² \cdot [Stefan-BoltZ] \cdot (({202K}^{4}) - ({151K}^{4}))}{(\frac{1}{0.4}) + (((\frac{1}{0.3}) - 1) \cdot ({(\frac{10m}{20m})}^{2}))}

Next Step Substitute values of Constants

∴

q = \frac{34.74m² \cdot 5.7E-8 \cdot (({202K}^{4}) - ({151K}^{4}))}{(\frac{1}{0.4}) + (((\frac{1}{0.3}) - 1) \cdot ({(\frac{10m}{20m})}^{2}))}

Next Step Prepare to Evaluate

∴

q = \frac{34.74 \cdot 5.7E-8 \cdot ((202^{4}) - (151^{4}))}{(\frac{1}{0.4}) + (((\frac{1}{0.3}) - 1) \cdot ({(\frac{10}{20})}^{2}))}

Next Step Evaluate

∴

q = 731.571272104003W

LAST Step Rounding Answer

∴

q = 731.5713W

Heat Transfer between Concentric Spheres Formula Elements

Variables

Constants

Heat Transfer

Heat Transfer is the amount of heat that is transferred per unit of time in some material, usually measured in watts (joules per second).

Symbol: q

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Heat Transfer

Surface Area of Body 1

The Surface Area of Body 1 is the area of body 1 through which the radiation takes place.

Symbol: A₁

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Surface Area of Body 1

Temperature of Surface 1

Temperature of Surface 1 is the temperature of the 1st surface.

Symbol: T₁

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature of Surface 1

Temperature of Surface 2

Temperature of Surface 2 is the temperature of the 2nd surface.

Symbol: T₂

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature of Surface 2

Emissivity of Body 1

The Emissivity of Body 1 is the ratio of the energy radiated from a body's surface to that radiated from a perfect emitter.

Symbol: ε₁

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Emissivity of Body 1

Emissivity of Body 2

The Emissivity of Body 2 is the ratio of the energy radiated from a body's surface to that radiated from a perfect emitter.

Symbol: ε₂

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Emissivity of Body 2

Radius of Smaller Sphere

Radius of Smaller Sphere is the distance from center of the Sphere to any point on the Sphere.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Smaller Sphere

Radius of Larger Sphere

Radius of Larger Sphere is the distance from center of the Sphere to any point on the Sphere.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Larger Sphere

Stefan-Boltzmann Constant

Stefan-Boltzmann Constant relates the total energy radiated by a perfect black body to its temperature and is fundamental in understanding blackbody radiation and astrophysics.

Symbol: [Stefan-BoltZ]

Value: 5.670367E-8

Other Formulas to find Heat Transfer

Go Net Energy Leaving given Radiosity and Irradiation

q = A \cdot (J - G)

Go Heat Transfer between Small Convex Object in Large Enclosure

q = A 1 \cdot ε 1 \cdot [Stefan-BoltZ] \cdot (({T 1}^{4}) - ({T 2}^{4}))

Other formulas in Radiation Heat Transfer category

Go Absorptivity given Reflectivity and Transmissivity

α = 1 - ρ - 𝜏

Go Area of Surface 1 given Area 2 and Radiation Shape Factor for Both Surfaces

A 1 = A 2 \cdot (\frac{F 21}{F 12})

How to Evaluate Heat Transfer between Concentric Spheres?

Heat Transfer between Concentric Spheres evaluator uses Heat Transfer = (Surface Area of Body 1*[Stefan-BoltZ]*((Temperature of Surface 1^4)-(Temperature of Surface 2^4)))/((1/Emissivity of Body 1)+(((1/Emissivity of Body 2)-1)*((Radius of Smaller Sphere/Radius of Larger Sphere)^2))) to evaluate the Heat Transfer, The Heat Transfer between Concentric Spheres formula is defined as the function of surface area, emissivity, temperature of Both surface and radius of both the sphere. Heat Transfer is denoted by q symbol.

How to evaluate Heat Transfer between Concentric Spheres using this online evaluator? To use this online evaluator for Heat Transfer between Concentric Spheres, enter Surface Area of Body 1 (A₁), Temperature of Surface 1 (T₁), Temperature of Surface 2 (T₂), Emissivity of Body 1 (ε₁), Emissivity of Body 2 (ε₂), Radius of Smaller Sphere (r₁) & Radius of Larger Sphere (r₂) and hit the calculate button.

FAQs on Heat Transfer between Concentric Spheres

What is the formula to find Heat Transfer between Concentric Spheres?

The formula of Heat Transfer between Concentric Spheres is expressed as Heat Transfer = (Surface Area of Body 1*[Stefan-BoltZ]*((Temperature of Surface 1^4)-(Temperature of Surface 2^4)))/((1/Emissivity of Body 1)+(((1/Emissivity of Body 2)-1)*((Radius of Smaller Sphere/Radius of Larger Sphere)^2))). Here is an example- 731.5713 = (34.74*[Stefan-BoltZ]*((202^4)-(151^4)))/((1/0.4)+(((1/0.3)-1)*((10/20)^2))).

How to calculate Heat Transfer between Concentric Spheres?

With Surface Area of Body 1 (A₁), Temperature of Surface 1 (T₁), Temperature of Surface 2 (T₂), Emissivity of Body 1 (ε₁), Emissivity of Body 2 (ε₂), Radius of Smaller Sphere (r₁) & Radius of Larger Sphere (r₂) we can find Heat Transfer between Concentric Spheres using the formula - Heat Transfer = (Surface Area of Body 1*[Stefan-BoltZ]*((Temperature of Surface 1^4)-(Temperature of Surface 2^4)))/((1/Emissivity of Body 1)+(((1/Emissivity of Body 2)-1)*((Radius of Smaller Sphere/Radius of Larger Sphere)^2))). This formula also uses Stefan-Boltzmann Constant .

What are the other ways to Calculate Heat Transfer?

Here are the different ways to Calculate Heat Transfer-

Heat Transfer=Area*(Radiosity-Irradiation)
Heat Transfer=Surface Area of Body 1*Emissivity of Body 1*[Stefan-BoltZ]*((Temperature of Surface 1^4)-(Temperature of Surface 2^4))
Heat Transfer=(Area*[Stefan-BoltZ]*((Temperature of Surface 1^4)-(Temperature of Surface 2^4)))/((1/Emissivity of Body 1)+(1/Emissivity of Body 2)-1)

Can the Heat Transfer between Concentric Spheres be negative?

Yes, the Heat Transfer between Concentric Spheres, measured in Power can be negative.

Which unit is used to measure Heat Transfer between Concentric Spheres?

Heat Transfer between Concentric Spheres is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Heat Transfer between Concentric Spheres can be measured.

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Heat Transfer between Concentric Spheres Formula

​GoNet Energy Leaving given Radiosity and Irradiation Formula

​GoHeat Transfer between Small Convex Object in Large Enclosure Formula

Heat Transfer between Concentric Spheres Example

Heat Transfer between Concentric Spheres Solution

Heat Transfer between Concentric Spheres Formula Elements

Other Formulas to find Heat Transfer

Other formulas in Radiation Heat Transfer category

How to Evaluate Heat Transfer between Concentric Spheres?

FAQs on Heat Transfer between Concentric Spheres

Variable Name

GoNet Energy Leaving given Radiosity and Irradiation Formula

GoHeat Transfer between Small Convex Object in Large Enclosure Formula