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Biot Number given Characteristic Dimension and Fourier Number Formula

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GoBiot Number using Fourier Number Formula

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

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

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

Biot Number given Characteristic Dimension and Fourier Number Example

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

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

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

110.0234 = \frac{10 \cdot 1937}{15 \cdot 1.5 \cdot 6.9 \cdot 1.134}

110.0234 = \frac{10W/m²*K \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.9m \cdot 1.134}

110.0234 = \frac{10 \cdot 1937}{15 \cdot 1.5 \cdot 6.9 \cdot 1.134}

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Biot Number given Characteristic Dimension and Fourier Number Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Bi = \frac{10W/m²*K \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.9m \cdot 1.134}

Next Step Prepare to Evaluate

∴

Bi = \frac{10 \cdot 1937}{15 \cdot 1.5 \cdot 6.9 \cdot 1.134}

Next Step Evaluate

∴

Bi = 110.023373576782

LAST Step Rounding Answer

∴

Bi = 110.0234

Biot Number given Characteristic Dimension and Fourier Number Formula Elements

Variables

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

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

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

Other Formulas to find Biot Number

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 ∞})

Other formulas in Unsteady State Heat Conduction category

Go Fourier Number using Biot Number

F o = (- \frac{1}{Bi}) \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)

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

Biot Number given Characteristic Dimension and Fourier Number evaluator uses Biot Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Fourier Number) to evaluate the Biot Number, The Biot Number given Characteristic Dimension and Fourier 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. Biot Number is denoted by Bi symbol.

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

FAQs on Biot Number given Characteristic Dimension and Fourier Number

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

The formula of Biot Number given Characteristic Dimension and Fourier Number is expressed as Biot Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Fourier Number). Here is an example- 110.0234 = (10*1937)/(15*1.5*6.9*1.134).

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

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

What are the other ways to Calculate Biot Number?

Here are the different ways to Calculate Biot Number-

Biot Number=(Heat Transfer Coefficient*Thickness of Wall)/Thermal Conductivity
Biot Number=(-1/Fourier Number)*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))
Biot Number=(Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Fourier Number)

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: Unit

Biot Number given Characteristic Dimension and Fourier Number Formula

​GoBiot Number using Heat Transfer Coefficient Formula

​GoBiot Number using Fourier Number Formula

Biot Number given Characteristic Dimension and Fourier Number Example

Biot Number given Characteristic Dimension and Fourier Number Solution

Biot Number given Characteristic Dimension and Fourier Number Formula Elements

Other Formulas to find Biot Number

Other formulas in Unsteady State Heat Conduction category

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

FAQs on Biot Number given Characteristic Dimension and Fourier Number

Variable Name

GoBiot Number using Heat Transfer Coefficient Formula

GoBiot Number using Fourier Number Formula