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Fourier Number using Biot Number Formula

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GoFourier Number using Thermal Conductivity 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{1}{Bi}) \cdot \ln (\frac{T - T ∞}{T 0 - T ∞})

F_o - Fourier Number?Bi - Biot Number?T - Temperature at Any Time T?T_∞ - Temperature of Bulk Fluid?T₀ - Initial Temperature of Object?

Fourier Number using Biot Number Example

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Here is how the Fourier Number using Biot Number equation looks like with Values.

Here is how the Fourier Number using Biot Number equation looks like with Units.

Here is how the Fourier Number using Biot Number equation looks like.

0.032 = (- \frac{1}{27.15}) \cdot \ln (\frac{589 - 373}{887.36 - 373})

0.032 = (- \frac{1}{27.15}) \cdot \ln (\frac{589K - 373K}{887.36K - 373K})

0.032 = (- \frac{1}{27.15}) \cdot \ln (\frac{589 - 373}{887.36 - 373})

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Fourier Number using Biot Number Solution

Follow our step by step solution on how to calculate Fourier Number using Biot Number?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F o = (- \frac{1}{27.15}) \cdot \ln (\frac{589K - 373K}{887.36K - 373K})

Next Step Prepare to Evaluate

∴

F o = (- \frac{1}{27.15}) \cdot \ln (\frac{589 - 373}{887.36 - 373})

Next Step Evaluate

∴

F o = 0.0319574586268167

LAST Step Rounding Answer

∴

F o = 0.032

Fourier Number using Biot Number Formula Elements

Variables

Functions

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

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

Temperature at Any Time T

Temperature at Any Time T is defined as the temperature of an object at any given time t measured using thermometer.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature at Any Time T

Temperature of Bulk Fluid

Temperature of Bulk Fluid is defined as the temperature of bulk fluid or fluid at given instant measured using thermometer.

Symbol: T_∞

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature of Bulk Fluid

Initial Temperature of Object

The Initial temperature of Object is defined as the measure of heat under initial state or conditions.

Symbol: T₀

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Initial Temperature of Object

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Fourier Number

Go Fourier Number

F o = \frac{α \cdot 𝜏 c}{s^{2}}

Go Fourier Number using Thermal Conductivity

F o = (\frac{k \cdot 𝜏 c}{ρ B \cdot c \cdot (s^{2})})

Go Fourier Number given Heat Transfer Coefficient and Time Constant

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

Go Fourier Number given Characteristic Dimension and Biot Number

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

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 ∞})

Go Initial Internal Energy Content of Body in Reference to Environment Temperature

Q o = ρ B \cdot c \cdot V \cdot (T i - T amb)

Go Thermal Conductivity given Biot Number

k = \frac{h \cdot 𝓁}{Bi}

How to Evaluate Fourier Number using Biot Number?

Fourier Number using Biot Number evaluator uses Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid)) to evaluate the Fourier Number, The Fourier Number using Biot Number formula is defined as the function of temp at any time t , temp of bulk fluid, initial temp and biot number. Fourier Number is denoted by F_o symbol.

How to evaluate Fourier Number using Biot Number using this online evaluator? To use this online evaluator for Fourier Number using Biot Number, enter Biot Number (Bi), Temperature at Any Time T (T), Temperature of Bulk Fluid (T_∞) & Initial Temperature of Object (T₀) and hit the calculate button.

FAQs on Fourier Number using Biot Number

What is the formula to find Fourier Number using Biot Number?

The formula of Fourier Number using Biot Number is expressed as Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid)). Here is an example- 0.031957 = (-1/(27.15))*ln((589-373)/(887.36-373)).

How to calculate Fourier Number using Biot Number?

With Biot Number (Bi), Temperature at Any Time T (T), Temperature of Bulk Fluid (T_∞) & Initial Temperature of Object (T₀) we can find Fourier Number using Biot Number using the formula - Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid)). This formula also uses Natural Logarithm (ln) function(s).

What are the other ways to Calculate Fourier Number?

Here are the different ways to Calculate Fourier Number-

Fourier Number=(Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2)
Fourier Number=((Thermal Conductivity*Characteristic Time)/(Density of Body*Specific Heat Capacity*(Characteristic Dimension^2)))
Fourier Number=(Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Biot Number)

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Fourier Number using Biot Number Formula

​GoFourier Number Formula

​GoFourier Number using Thermal Conductivity Formula

Fourier Number using Biot Number Example

Fourier Number using Biot Number Solution

Fourier Number using Biot Number Formula Elements

Other Formulas to find Fourier Number

Other formulas in Unsteady State Heat Conduction category

How to Evaluate Fourier Number using Biot Number?

FAQs on Fourier Number using Biot Number

Variable Name

GoFourier Number Formula

GoFourier Number using Thermal Conductivity Formula