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Fourier Number given Characteristic Dimension and Biot Number Formula

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Fourier Number is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter. Check FAQs

F o = \frac{h \cdot 𝜏}{ρ B \cdot c \cdot s \cdot Bi}

F_o - Fourier Number?h - Heat Transfer Coefficient?𝜏 - Time Constant?ρ_B - Density of Body?c - Specific Heat Capacity?s - Characteristic Dimension?Bi - Biot Number?

Fourier Number given Characteristic Dimension and Biot Number Example

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Here is how the Fourier Number given Characteristic Dimension and Biot Number equation looks like with Values.

Here is how the Fourier Number given Characteristic Dimension and Biot Number equation looks like with Units.

Here is how the Fourier Number given Characteristic Dimension and Biot Number equation looks like.

4.5955 = \frac{10 \cdot 1937}{15 \cdot 1.5 \cdot 6.9 \cdot 27.15}

4.5955 = \frac{10W/m²*K \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.9m \cdot 27.15}

4.5955 = \frac{10 \cdot 1937}{15 \cdot 1.5 \cdot 6.9 \cdot 27.15}

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Fourier Number given Characteristic Dimension and Biot Number Solution

Follow our step by step solution on how to calculate Fourier Number given Characteristic Dimension and Biot Number?

FIRST Step Consider the formula

F o = \frac{h \cdot 𝜏}{ρ B \cdot c \cdot s \cdot Bi}

Next Step Substitute values of Variables

∴

F o = \frac{10W/m²*K \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.9m \cdot 27.15}

Next Step Prepare to Evaluate

∴

F o = \frac{10 \cdot 1937}{15 \cdot 1.5 \cdot 6.9 \cdot 27.15}

Next Step Evaluate

∴

F o = 4.59545140464349

LAST Step Rounding Answer

∴

F o = 4.5955

Fourier Number given Characteristic Dimension and Biot Number Formula Elements

Variables

Fourier Number

Fourier Number is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter.

Symbol: F_o

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Fourier Number

Heat Transfer Coefficient

The Heat Transfer Coefficient is the heat transferred per unit area per kelvin. Thus area is included in the equation as it represents the area over which the transfer of heat takes place.

Symbol: h

Measurement: Heat Transfer CoefficientUnit: W/m²*K

Note: Value can be positive or negative.

Formulas to find Heat Transfer Coefficient

Time Constant

Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature.

Symbol: 𝜏

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time Constant

Density of Body

Density of Body is the physical quantity that expresses the relationship between its mass and its volume.

Symbol: ρ_B

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Body

Specific Heat Capacity

Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

Symbol: c

Measurement: Specific Heat CapacityUnit: J/(kg*K)

Note: Value should be greater than 0.

Formulas to find Specific Heat Capacity

Characteristic Dimension

Characteristic Dimension is the ratio of volume and the area.

Symbol: s

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Characteristic Dimension

Biot Number

Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.

Symbol: Bi

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Biot Number

Other Formulas to find Fourier Number

Go Fourier Number using Biot Number

F o = (- \frac{1}{Bi}) \cdot \ln (\frac{T - T ∞}{T 0 - T ∞})

Go Fourier Number

F o = \frac{α \cdot 𝜏 c}{s^{2}}

Other formulas in Unsteady State Heat Conduction category

Go Biot Number using Heat Transfer Coefficient

Bi = \frac{h \cdot 𝓁}{k}

Go Biot Number using Fourier Number

Bi = (- \frac{1}{F o}) \cdot \ln (\frac{T - T ∞}{T 0 - T ∞})

How to Evaluate Fourier Number given Characteristic Dimension and Biot Number?

Fourier Number given Characteristic Dimension and Biot Number evaluator uses Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number) to evaluate the Fourier Number, The Fourier Number given Characteristic Dimension and Biot Number formula is defined as the function of heat transfer coefficient, time constant, density of body, specific heat capacity, characteristic dimension and fourier number. The exponential part of Lumped Heat capacity equation can also be expressed as the the product of Biot number and fourier number. Fourier Number is denoted by F_o symbol.

How to evaluate Fourier Number given Characteristic Dimension and Biot Number using this online evaluator? To use this online evaluator for Fourier Number given Characteristic Dimension and Biot Number, enter Heat Transfer Coefficient (h), Time Constant (𝜏), Density of Body (ρ_B), Specific Heat Capacity (c), Characteristic Dimension (s) & Biot Number (Bi) and hit the calculate button.

FAQs on Fourier Number given Characteristic Dimension and Biot Number

What is the formula to find Fourier Number given Characteristic Dimension and Biot Number?

The formula of Fourier Number given Characteristic Dimension and Biot Number is expressed as Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number). Here is an example- 4.595451 = (10*1937)/(15*1.5*6.9*27.15).

How to calculate Fourier Number given Characteristic Dimension and Biot Number?

With Heat Transfer Coefficient (h), Time Constant (𝜏), Density of Body (ρ_B), Specific Heat Capacity (c), Characteristic Dimension (s) & Biot Number (Bi) we can find Fourier Number given Characteristic Dimension and Biot Number using the formula - Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number).

What are the other ways to Calculate Fourier Number?

Here are the different ways to Calculate Fourier Number-

Fourier Number=(-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))
Fourier Number=(Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2)
Fourier Number=((Thermal Conductivity*Characteristic Time)/(Density of Body*Specific Heat Capacity*(Characteristic Dimension^2)))

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Fourier Number given Characteristic Dimension and Biot Number Formula

​GoFourier Number using Biot Number Formula

​GoFourier Number Formula

Fourier Number given Characteristic Dimension and Biot Number Example

Fourier Number given Characteristic Dimension and Biot Number Solution

Fourier Number given Characteristic Dimension and Biot Number Formula Elements

Other Formulas to find Fourier Number

Other formulas in Unsteady State Heat Conduction category

How to Evaluate Fourier Number given Characteristic Dimension and Biot Number?

FAQs on Fourier Number given Characteristic Dimension and Biot Number

Variable Name

GoFourier Number using Biot Number Formula

GoFourier Number Formula